An Introduction to Behavioral Economics

One advantage of this tactic was the great favorable publicity that resulted. The album ‘sold’ more than 1.2 million copies in the first week alone, compared with the 300,000 copies sold in the first week of their previous album in 2003. Another even more important advantage is that the band is able to retain 100% of the revenues, whereas when artists use a recording company they only get to keep a relatively small fraction of the revenues generated.

However, this still raises the issue: why would people pay for music when they can easily get it for free? On average buyers paid £4 ($6) per album in the days following its release. Some online music labels, like Magnatune, have followed a similar strategy, allowing customers to pay what they want for albums, as long as the payment is within a certain price range ($5–18). On average customers have been paying $8.20, far more than the minimum of $5, and even more than the recommended price of $8. This behavior is completely anomalous to standard economic behavior involving purely selfish preferences.

A study by Regner and Barria (2009) analyzed the behavior using a game-theoretic model of social preferences based on sequential reciprocity. The first move is made by the band, or the online label, offering the music on an open contract basis. This generates goodwill, or positive reciprocity, among customers. Thus they respond to this move by offering to pay substantial sums for the music, which also allows them to avoid feelings of guilt that they would incur if they paid only a small amount for something they enjoy. Regner and Barria conclude that a sequential reciprocity equilibrium corresponds to the observed pattern of behavior.

This case demonstrates the power of sequential reciprocity in social interactions, and also the signficance of psychological game theory, which incorporates emotional reactions like anger, fear, pride, shame, gratitude and guilt into game situations.

10.1 The standard model

Nature

As with other aspects of economic behavior discussed in previous chapters, our starting point is the standard model and its shortcomings. In the case of social preferences and fairness the key assumption in the standard model is that economic agents are motivated purely by self-interest. Indeed, the standard model is often referred to as a self-interest model. As we will discuss in the next chapter, this assumption is closely related to the rationality assumption. Advocates of this model tend to agree with an often-quoted statement by Stigler (1981):

... when self-interest and ethical values with wide verbal allegiance are in conflict, much of the time, most of the time in fact, self-interest theory … will win (p. 323).

Behavioral economists in general tend to take issue with this stance, appealing to a large amount of evidence for various kinds of social preference, such as reciprocity. Before we begin to consider the meaning of these terms and any related evidence, however, it is necessary to clarify one fundamental and often overlooked point in the burgeoning literature relating to this alleged conflict. ‘Pure’ self-interest models are in many ways a straw man; they represent a simplified situation that is easy to model and apply, in a similar way to the model of pure competition. It is this simplicity that makes the model attractive, not its realism, since only pathological individuals have no consideration for the effects of their behavior on others. Furthermore, such individuals, while motivated by pure self-interest, are extremely unlikely to achieve their objectives, because they alienate others. All normal individuals, even those we would describe as ‘selfish’, take into account the effects of their behavior on others to some extent, and also take into account the welfare of others. As we shall see, this ‘taking into account’ may not be deliberate, but be a result of emotions such as guilt, anger, envy, pity, outrage or even disgust. Thus a model based on people acting in their self-interest, which many would claim is part of the standard model, is also consistent with people having other-regarding preferences. It is important to understand that there is no fundamental incompatibility here. Likewise, it is also important to understand that all behavioral models are essentially extensions of the self-interest model, not negations of it, in the same way that some intertemporal choice models extend and modify the instantaneous utility function. The analogy is a close one, since the pure self-interest model assumes that people maximize utility functions that only take into account self-regarding preferences and are not affected by the utility of others, whereas behavioral models modify this utility function to take into account other-regarding preferences as well. We shall return to this point a number of times in this chapter, since it is the cause of a number of confusions. In order to prevent some of these confusions we will distinguish between ‘self-interest’ and ‘self-regarding preferences’. ‘Self-interest’ in the broad sense can take other-regarding preferences into account; ‘pure self-interest’ does not.

Anomalies

There is an impressive list of anomalies relating to the ‘pure self-interest’ aspect of the standard model, which arise both from field studies and from experiments. The following examples give some flavor to the kinds of behavior that will be examined in the course of the chapter:

Tipping waiters
Giving to charity
Voting
Completing tax returns honestly
Voluntary unpaid work
Working harder when there are no monetary incentives than when there are monetary incentives
Firms laying off workers in a recession rather than cutting wages
Monopolies not raising prices when there are shortages
Contributing to the provision of public goods
Punishing ‘free riders’, even when there is a cost in doing so
Cooperating in prisoner’s dilemma games
Investing in others, and trusting them to repay
Making generous offers in ultimatum bargaining games
Rejecting ungenerous offers in ultimatum bargaining games

These anomalies relate to aspects of behavior that can be described as either altruistic or spiteful. While altruism can be defined in many ways, as we will see, a basic definition is that it relates to behavior that confers a benefit to others, while involving a cost to the originator of the behavior, with no corresponding material benefit. Tipping waiters at restaurants, where one is unlikely to return, is an example. Spiteful behavior can be viewed as the flip side of altruistic behavior. This is behavior that imposes a cost on others, while also involving a cost to the originator of the behavior, with no corresponding material benefit. An example is punishing those who throw litter out of their car by yelling at them (the cost may be small in terms of effort, but there is a risk of a hostile altercation). It should be noted that spiteful behavior is not necessarily bad for society; in the above example it may help to enforce valued social norms. It is notable that both altruistic behavior and spiteful behavior confer benefits to the originator that are non-material, or psychological. Case 1.3 gave an illustration of this, and also indicated that the ‘warm glow’ people feel in gift-giving is supported by neuroeconomic evidence. We will see in examining social preferences that neuroeconomic studies are also particularly revealing in understanding social behavior. This kind of altruism, sometimes called ‘warm-glow’ altruism, is also referred to as impure altruism, to distinguish it from pure altruism, where a person experiences a psychic benefit from an increase in someone else’s wellbeing even if they are not responsible for causing this increase. Thus, if your car breaks down and I gain satisfaction from giving you a lift, but not if someone else gives you a lift, then this is an example of impure altruism; if I gain satisfaction regardless of who gives you a lift, this is pure altruism. The distinction between these two types of altruism is important, since the evolutionary factors leading to their existence are different in nature. As we will see in more detail later, pure altruism is based on empathy and the mirror neuron system, while impure altruism is related to signaling intentions and reciprocity.

It can also be seen that a number of the anomalies above relate to games, some of which were discussed in the last chapter. As we saw, games in this context refer to situations where there is an interdependency in decision-making. The essence of these interdependent decision-making situations is that when A makes a decision (for example regarding price, entry into a market, whether to take a job), it will consider the reactions of other persons or firms to its different strategies, and how these reactions will affect their own utility or profit. It must also take into account that the other parties, or players, in selecting their reactive strategies, will consider how A will react to their reactions. As we have also seen in games like the ‘beauty contest’, this can continue in a virtually infinite progression. In this situation there is often a considerable amount of uncertainty regarding the results of any decision.

Many elements of real-life strategic situations can be simulated in game experiments, which have the considerable advantage of isolating a particular behavioral factor and simplifying analysis. In this chapter we will discuss games related to social preferences, in particular involving trust, bargaining and punishment. In each case the predictions of standard game theory are examined, and compared with empirical evidence, and we will consider how the standard model can be improved by modification and extension. Now that the basic tools of game-theoretic analysis have been described in the previous chapter, it will be easier to understand both the basic model and appropriate extensions.

In order to appreciate the basis of behavioral game theory, it is important to understand the nature of inferences from empirical studies. If empirical data do not ‘fit’ the predictions of a particular theory involving the use of game-theoretical analysis this does not mean that game theory as a method of analysis is wrong. There are a number of possible conclusions: (1) the utility functions of the players were mis-specified; (2) bounded rationality prevented the players from using the game-theoretical analysis properly; (3) learning factors caused a time lag in terms of reaching an equilibrium situation; or (4) the players misunderstood the nature of the game, or played a different game from that intended by the experimenters.

While game theory is an important element of the standard model, in its standard form (sometimes confusingly called ‘analytical’ game theory), we have seen that it makes a number of important assumptions related to the conclusions above: (1) people have correct mental representations of the relevant game; (2) people have unbounded rationality; (3) equilibria are reached instantly, since there are no time lags due to learning effects or other factors; and (4) people are motivated purely by self-interest. Behavioral game theory (BGT) relaxes all four of these assumptions. The first three assumptions were discussed in the previous chapter, along with the implications of relaxing them; in this chapter we will focus on the last assumption, although the first three are still relevant because there is some interdependency between the assumptions.

10.2 The nature of social preferences

Social preferences and fairness

Fehr and Fischbacher (2005) define social preferences as ‘other-regarding preferences in the sense that individuals who exhibit them behave as if they value the payoff of relevant reference agents positively or negatively’. Several things are noteworthy regarding this definition. First, we shall see that it is not just the payoffs of other people that are important, but also their beliefs and intentions that are relevant. Second, these payoffs, beliefs and intentions can be valued positively or negatively, depending on the reference agent. Our perceptions of other people’s beliefs and intentions determine whether we are well-disposed or ill-disposed toward them. If we feel well-disposed to the other agent we value their payoffs positively, but if we are ill-disposed toward the agent we value their payoffs negatively. Third, the relevant reference agents may be a person’s colleagues, relatives, trading partners or neighbors, depending on the situation (Fehr and Fishbacher, 2005).

The concept of fairness is central to understanding social preferences, since it determines people’s beliefs regarding how both the costs and benefits of people’s behavior should be distributed. These beliefs in turn affect how people value the payoffs, beliefs and intentions of others. It is not proposed here to discuss what is fair and what is not. Indeed that would be contrary to the approach of this book, which takes the view that ‘fairness is in the eye of the beholder’. A society’s view of what is fair can change hugely over the course of centuries and even decades; 200 years ago slavery and hanging people for stealing a sheep were acceptable in many countries. Some societies today regard the stoning of adulterers to death and ‘honor killings’ of family members for unapproved love affairs as being acceptable, or even as moral obligations. Even over relatively short periods of time people tend to adjust their values of fairness as circumstances change. The purpose of this section is to examine the factors that determine judgments of fairness in general terms. It is useful to follow the approach of Kahneman, Knetsch and Thaler (hereafter KKT) (1986), who identify and describe three of these, based on empirical research. Although their discussion relates to the context of profit-seeking by firms, the factors can be applied to more general situations. The key concept in this approach is dual entitlement, meaning that both parties in a transaction are entitled to certain considerations. If we extend the KKT approach, these transactions do not have to be monetary in nature, but can incorporate any kind of cost and benefit. There are three main elements in this concept of dual entitlement:

1 Reference transactions

Market transactions can relate to a price, a wage or a rent. However, we should also consider the broader context of non-market transactions, where some non-monetary cost or benefit is involved, for example where it is customary to bring a bottle of wine to someone’s house for dinner. The reference transaction is normally determined by the past history of a particular type of transaction, or by prevailing competitive rates. Thus it may not be regarded as fair for a landlord to increase the rent of an existing tenant, unless rents for similar properties in the area are also increasing, but it may be acceptable to charge a higher rent for a new tenant. The new tenant does not have the same entitlement as an existing one. The basis for this judgment may involve the concept of moral hazard, or post-contract opportunism. Once a transactor has made a commitment, like renting a property or taking a job, it may be regarded as unfair if the other transactor takes advantage of this commitment. Sometimes this is referred to as the ‘holdup’ problem.

Conflicts may arise in particular when there is more than one reference point. For example, in a wage dispute a union may claim that their wage is unfair because workers of a similar skill in another industry are higher paid, but an employer may claim that their wages have risen faster in recent years than similar workers.

Two observations can be made regarding the reference transaction factor. First, it is in line with prospect theory’s emphasis on reference points as far as the perception of gains and losses is concerned. Second, it illustrates that fairness judgments are based on what is normal, or ‘norms’, rather than what is ‘just’. The consequence of this is that not only does the yardstick of what is fair change over time, but also that agents tend to perform, and be expected to perform, fairly in the marketplace. For example, a majority of people tip around 15% in restaurants. An interesting sidelight on this issue is that ‘ticket touting’, or charging above the standard ticket price in the secondary market, is generally regarded as unfair, and indeed criminal. Theatre tickets in London’s West End are regularly sold at below a market-clearing price, resulting in continuing shortages for popular shows. In 2006 a tout was fined £9000 for selling tickets at a 500% markup. Even though people are obviously willing to pay the higher price, and may not have been able to purchase tickets earlier at the standard price, the below-equilibrium standard price is regarded as the reference price and the huge excess causes outrage. We will say more about social norms in the next section, in terms of their nature, origins and functions.

2 Outcomes to the transactors

The general principle of dual entitlement means that it is usually regarded as unfair if one transactor makes a gain by imposing a similar loss on the other transactor, Thus if there is a shortage of snow shovels after a big snow fall, an increase in the selling price may be regarded as ‘gouging’, since such a gain comes at the expense of the buyer. However, it is usually perceived as fair to pass on any increase in cost to the customer, since the seller is not perceived to make a gain in this case. It should be noted that empirical findings suggest that there is an asymmetry here, since reductions in cost are not necessarily expected to be passed on to the customer; the seller’s gain is not perceived to be at the buyer’s expense.

Once again concepts from prospect theory are relevant here, along with concepts from mental accounting theory. The phenomenon of loss-aversion means that overall welfare is reduced if gains are made at the expense of equal losses in monetary terms, since losers tend to lose more in utility than winners gain. The accounting rules used to make judgments also suggest a lack of fungibility between different types of expense. Out-of-pocket costs, for example paying higher prices, are not judged in the same way as opportunity costs, like not receiving a price reduction. Furthermore, framing effects are important in terms of how the transactors code gains and losses. A loss is perceived as worse than the cancellation of a gain. For example, firms may prefer to offer a discount in a low season rather than reduce prices, since later on it is more acceptable to customers to remove the discount than increase the price. Similarly it is more acceptable for firms not to pay bonuses to employees, however much these were expected, than to cut wages.

3 Circumstances of changing transaction terms

KKT discuss these in a price-setting situation, classifying occasions for change into the three categories of profit reductions, profit increases and increases in market power. However, a more useful general classification, which would fit the empirical findings equally well, may relate to controllable and uncontrollable factors. For example, if a firm has an increase in demand that may increase both profit and market power, this may have occurred because of factors outside the control of the firm, and in this case it may be perceived as unfair to increase price. However, an increase in demand caused by the firm producing a better quality product or providing better service may justify a price increase. Similarly increases in cost outside the firm’s control causing a fall in profit may justify a price increase, but increases in cost due to inefficiency may not. The same rules apply to changes in wages and rents.

In general exploitation of market power is judged to be unacceptable. What may be relevant to the judgment here is how a transactor gained such market power. Market power based on a superior product or technology may be acceptable, while market power gained by restrictive practices may not. Research findings are limited on this aspect, but it appears that some forms of price discrimination are not regarded as fair, even when substitutes are available.

Reciprocity

We will see that the concept of strong reciprocity is very important in social preferences, and has fundamental consequences for both private and public policy. Strong reciprocity can be distinguished from ‘standard’ reciprocity in that, in addition to involving conditional cooperation, it also involves a willingness to punish other players at a cost to the punishing player. An important implication of this is that purely self-interested players will never punish another player, because there are no benefits, only costs. We will also see that there are different reasons for punishment. ‘Strategic’ punishment relates to situations where there is an expected material payoff from punishment. This may occur because punishment has a deterrent effect, causing other players to cooperate more in the future in repeated games, or because if a player does not punish defectors he may in turn be punished. However, for strong reciprocators punishment need not have a material payoff; the benefit may be purely in psychic terms, increasing the player’s utility by making them feel better. A strongly reciprocal player therefore responds kindly toward actions that are perceived to be kind and hostilely to actions that are perceived to be hostile. Whether an action is perceived to be kind or hostile depends on the fairness or unfairness of the intention underlying the action (Fehr and Fishbacher, 2005). The existence of strong reciprocators in a multi-player game has far-reaching implications for behavior and equilibrium, because not only is their behavior different from purely self-interested players, and conditional cooperators, but also their strategies affect the behavior of the purely self-interested players, in particular by making them more inclined to cooperate. We will examine models of reciprocity, the evidence relating to them, and the policy implications, in later sections.

Fairness games and the standard model

Much insight can be gained into people’s perceptions of fairness by examining the results of various games in an experimental setting. Common games that are used to investigate fairness and social preferences are ultimatum bargaining games, dictator games, trust games, prisoner’s dilemma games and public goods games. We have seen a number of examples of these games in the previous chapter. Some games are one-shot games and some are conducted on a repeated basis, and the importance of this distinction will be discussed later, since it is a source of debate and confusion. Games can be varied in a number of ways to observe differences in behavior, and this aspect is discussed in the next section. The purpose here is to observe differences between the predictions of ‘analytical’ game theory in the standard model and empirical findings. With these empirical results in mind we can then move on to consider how social preferences can be modeled into a game-theoretic analysis in such a way that the findings can be predicted. The different game situations are now discussed.

1 Ultimatum bargaining games

These are two-player games, and, as with most games, involve a proposer (P) and a responder (R). An example was given in the previous chapter. We saw that, in its standard form, a certain sum of money, frequently $10, represents a value of the gain to exchange, or surplus, that would be lost if no trade was made. P offers the sum x to R, leaving themselves $10 – x. R can either accept the offer, or reject it, in which case both players receive nothing.

The basic form of the game is so simple that it does not faithfully represent the more complex bargaining situations in real life, which often involve several stages, but it does offer some important insights as far as fairness is concerned. The standard model, based on ‘pure’ self-interest, predicts that R will be happy to receive even the smallest amount of money rather than nothing, and that therefore P will propose the smallest amount of money possible (maybe one cent), with R accepting this offer. However, the original study by Güth, Schmittberger and Schwarze (1987) observed that proposers sometimes offered 50% of the surplus and that responders often rejected positive offers. Empirical findings in experiments have consistently confirmed this result, contradicting the predictions of the standard model. Some of these studies use the method of eliciting responses described above, while others have asked responders to state a minimal acceptable offer (MAO). The latter method has the advantage that more exact information can be provided, particularly regarding infrequent low offers; a possible disadvantage is that this method may cause an upward bias in responses, meaning that people may demand more (there is a lack of evidence here).

These studies generally indicate that between 60% and 80% of offers are between 0.4 and 0.5 of the surplus, and that there are almost no offers below 0.2. Furthermore, low offers are frequently rejected, with offers below 0.2 being rejected about half of the time. The above findings are also robust as far as increased stakes are concerned. For example, an experiment was conducted with Arizona students where the stakes were $100, and a couple of students rejected offers of $30 (Hoffman, McCabe and Smith, 1996). A similar result has been found with a $400 stake (List and Cherry, 2000), and in countries with low disposable income where the stake was equivalent to three months’ expenditure for a typical subject (Cameron, 1999).

In summary, the results can be interpreted as showing that responders are angered by proposals that they regard as unfair, and are prepared to punish such unfair behavior at a cost to themselves (being ‘spiteful’). At this point we will not explore the issue of what causes such feelings of unfairness, and how much they are innate or determined by culture. This is better left until later in the chapter, after a discussion of variations of this game, other games and empirical findings.

2 Dictator games

These are games where the responder’s ability to reject an offer is removed, and thus are even simpler. In a one-shot situation they do not even involve strategic thinking (at least in the standard model), since the proposer does not have to consider the reaction of the responder. However, the value of such games is that they establish whether proposers make generous offers because they fear rejection, or whether they are altruistic. Any positive offer by a proposer is altruistic rather than strategic, meaning caused by the fear of rejection. The first comprehensive comparison of ultimatum and dictator games (Forsythe et al., 1994) indicated that dictators offered on average about 20%, much lower than proposers in ultimatum games. Early studies also indicated that average offers are close to the offer that maximizes expected payoffs given the actual pattern of rejections in ultimatum games (Roth et al., 1991), suggesting strategic behavior, but later more sophisticated analyses showed that offers were more generous than payoff-maximizing offers, even allowing for risk-aversion (Hoffman, McCabe and Smith, 1996; Heinrich et al., 2001). In the Hoffman et al. study ‘dictators’ still shared their wealth in about 40% of the observed bargains when the anonymity of the offerer was preserved.

However, these results have also been called into question, on the basis that the wealth of the dictators was not earned. In real-life situations earned wealth may be the more likely situation. Cherry, Frykblom and Shogren (2002) controlled for this factor in an experiment involving three treatments: baseline (unearned wealth), earned wealth and double-blind with earned wealth. Subjects, who were undergraduate students, ‘earned’ wealth by answering a sample of Graduate Management Admission Test (GMAT) questions correctly. In the baseline situations a zero offer was only made in an average of 17% of the bargains. In contrast, in situations where wealth was ‘earned’, zero offers occurred in about 80% of the bargains. This increased to around 96% in the double-blind situations where the dictators acted in complete anonymity from both the other transactor and the experimenter. The authors therefore concluded that strategic concerns and not fairness were the motivation for other-regarding behavior.

In some experiments dictator games are observed by third parties, who have no monetary interest in the game, but who are in a position to punish proposers at a cost to themselves. Fehr and Fischbacher (2004) find that 60% of observers are willing to punish under these conditions, punishing more the lower the proposer’s offer. In this case the reason for punishment is different from the reason in ultimatum games, since reciprocity is not involved.

In summary, it appears that positive offers are mainly strategic, but there is some altruism involved. Again, variations on these games and a more detailed discussion of the implications are given later in the chapter.

3 Trust games

Trust is the basis of any transaction that does not involve a complete contract that specifies all possible outcomes of the transaction, i.e. the vast majority of transactions. This is because most transactions involve costs and benefits in the future where there is always an element of uncertainty. When we buy a good, we assume that it will provide the benefits that we expect; the seller assumes that he will be paid in full. Other types of transaction, like renting a property, taking a job or hiring an employee, or lending money involve similar assumptions. Other activities, not normally considered as relating to economic behavior, such as leaving one’s front door unlocked, parking on the street, giving to charity and getting married, also are based on an element of trust. Economists regard trust as a means of reducing transactions costs, since engaging in legal contracts or other forms of commitment is costly; thus it can be viewed as being ‘social capital’. Some economists believe that countries and cultures that are more trusting have higher rates of growth and development; certainly there appears to be a strong correlation here (Knack and Keefer, 1997), but the causation is more complex, because we will see that the existence of trust does not just reduce transactions costs, it also affects behavior in fundamental ways, in particular increasing investment.

The essence of all these activities, and games relating to them, is that some kind of investment by the truster (I) in the trustee (T) is involved. This investment is risky because it may not be repaid by the trustee. However, if the return from investment is sufficient, and the investment is repaid sufficiently, the investor will benefit in terms of making a net gain compared with not investing. A typical investment game involves I having an amount x which they can choose to invest or keep. If I invests the amount y (and keeps x – y) this earns a return so that it becomes y(1 + r). T must then decide how much of this amount to share with I, playing a dictator game at this stage. If T keeps z and returns y(1 + r) – z to I, then the total payoffs are z to T and (x – y) + y(1 + r) – z, or x – z + ry, to I. It is therefore possible to measure the amount of trust and the amount of trustworthiness: trust is measured by the size of investment y, while trustworthiness is measured by the amount returned, x – z + ry.

The standard model predicts that there will be no trust, for the reason that trustees will never return anything. Empirical findings have invariably contradicted this. A study by Berg, Dickhaut and McCabe (1995) used an initial amount x of $10 and a rate of return r of 2. On average investors invested about 50%; 16% of investors invested the entire amount, and only 6% invested nothing (zero trust). The average amount repaid was about 95% of the amount invested (or a third of the tripled amount), although there was a wide variation. This indicates that the return to trust is around zero, and this result has been confirmed by later studies. There appear to be some cross-cultural variations, and these are discussed in the following section.

Trust games are interesting since they allow reciprocity, or at least positive reciprocity, to be measured. This is because the second stage of the game is, as we have seen, a dictator game on the part of the trustee. Therefore, if trustees repay more than they would pay in an ordinary dictator game, any excess must be related to reciprocity. The concept of reciprocity is discussed in detail in Section 10.5, but at this point we can think of positive reciprocity as arising from some feeling of moral obligation on the part of the trustee. In terms of empirical findings, a study by Cox (1999) found that repayments were significantly larger than allocations in a similar dictator game, but that the difference was small, about 10%. Dufwenberg and Gneezy (2000) also found that returns were larger than allocations in a similar dictator game, but in this case the difference was insignificant. Thus it seems that positive reciprocity is not a major factor in trust games.

As with the other games described above, there are variations on trust games, in particular involving many persons or groups. These are discussed in the next section, and also in the section on policy implications related to social and market norms.

4 Prisoner’s dilemma games

The prisoner’s dilemma (PD) is perhaps the most well-known game of all, and was discussed in some detail in the last chapter. The classic PD situation involves two prisoners who are held in separate police cells, accused of committing a crime. They cannot communicate with each other, so each does not know how the other is acting. If neither confesses, the prosecutor can only get them convicted on other minor offences, each prisoner receiving a one-year sentence. If one confesses while the other does not, the one confessing will be freed while the other one receives a ten-year sentence. If both confess they will each receive a five-year sentence. The normal form is shown in Table 10.1, which is a repeat of Table 9.1.

Table 10.1 Prisoner’s dilemma

The values in the table represent payoffs, in terms of jail sentences; the payoffs for Suspect A are the left-hand values, while the payoffs for Suspect B are the right-hand values. The objective for each suspect in this case is obviously to minimize the payoff in terms of jail time. The problem that they have in this case is that the best combination payoff for the pair of them is for them both not to confess, in other words to ‘cooperate’ with each other; in this case each suspect will receive a one-year sentence. However, as was shown in the last chapter, this is not an equilibrium strategy according to the standard game theory of the standard model. The equilibrium is for both suspects to confess, or to ‘defect’, since this is a dominant strategy for players. This equilibrium situation represents a paradox, since they will both end up receiving longer sentences, five years, than if they had cooperated. The equilibrium still applies even if the suspects had agreed to cooperate beforehand; they will still tend to defect once they are separated and do not know how the other is acting.

The reader may wonder at this stage how the type of situation described above relates to social preferences. This is more easily understood if we examine the payoff structure. In any PD situation there is a hierarchy of payoffs, which are frequently labeled as temptation, reward, punishment and sucker’s payoff. The relationship between strategies and payoffs is shown in Table 10.2.

Table 10.2 Structure of payoffs in prisoner dilemma

Strategy pair (self/other)	Name of payoff
Defect/Cooperate	Temptation (0)
Cooperate/Cooperate	Reward (1)
Defect/Defect	Punishment (5)
Cooperate/Defect	Sucker’s Payoff (10)

In this light we can see that the PD situation is more related to reciprocity than with fairness. Extensive empirical studies have been conducted for over two decades, and they generally show that in one-shot situations players cooperate about half of the time. Although this plainly contradicts the predictions of standard game theory, it is not clear whether the cooperation is caused by altruism or the expectation of matching cooperation. Therefore the analysis of PD games is a blunt tool for predicting real-world behavior. One interesting finding is that pre-play communication, which according to the standard model should not affect outcomes at all, has a significant effect in terms of increasing cooperation.

As with other games, there are many variations of the standard PD situation. The game as described above involves simultaneous play, or at least each player determines their action without knowing what the other player has decided. If the game is transformed into a sequential play, it resembles a trust game, with the second player acting as a dictator. As we shall see later, many experiments have also been conducted with repeated PD games, sometimes using the same pair of players each time, and sometimes changing the pairs.

5 Public goods games

Economists define public goods as those goods which have the characteristics of nonexclusivity and nondepletion. This means that they cannot be easily provided to one person without automatically being provided for others, and the consumption of the good by one person does not reduce the amount of the good available to others. Street lighting is a common example. There are also many examples of semi-public goods, like libraries, stadiums, hospitals, roads and fish stocks, which satisfy these characteristics up to a point. In each case one person’s consumption or activity causes a negative externality on others. Essentially public goods games are multiple-player PD situations, where the Pareto-optimal solution is for all players to contribute to the maximum (cooperation), but the equilibrium solution according to the pure self-interest of the standard model is to contribute nothing and defect.

Therefore these goods present a problem for public policy, since few people will volunteer to pay for them, or refrain from consumption, hoping to get a ‘free ride’ by enjoying the goods that others have paid for. The situations can be easily modeled in experimental games as follows: each of N players has an endowment of x_i and invests y_i of this resource in a public good that is shared by everyone, and has a total per-unit value of m. Player i receives the benefit x_i – y_i + mΣy_j/N, where Σy_i represents the sum of the contributions of all the other players. The dominant strategy is to defect by making no contribution, in spite of the fact that all players could collectively benefit most by cooperating and contributing the maximum to the common pool of resources. A number of assumptions are made in this simple model regarding the value of m and the shape of the common utility function.

Empirical evidence again contradicts the standard model, since generally subjects in experiments contribute about half of their resources. There is however a wide range of responses, with a majority of players contributing either all their resources or nothing (Sally, 1995; Ledyard, 1995). As with PD games it is difficult to conclude whether people contribute from altruism or because of expectations of cooperation. Furthermore, it is impossible to say whether people defect out of self-interest or whether they have reciprocal social preferences but expect others to free ride. In order to draw sharper conclusions the structure of the game needs to be tweaked and the consequences examined, as will be seen in the next section. In particular it is interesting to introduce the possibility of punishment at a cost; as we have seen, this allows us to see the role of strong reciprocation. A detailed example of a public goods experiment with such variations is given in Case 10.2. We will see that punishment changes the whole playing of the game in experimental studies: without punishment people tend to ‘free ride’ and contribute little, this trend increasing as the game continues; with punishment people contribute far more, with this trend increasing as the game continues.

Another aspect of punishment is often observed in public goods games, referred to as anti-social punishment. Unlike the punishment of free riders, who are punished for contributing too little, anti-social punishment involves the punishment of those who contribute more than average. There are two possible reasons for such an action: (1) low or non-contributors may retaliate in turn against those punishing them; and (2) low contributors may want to deter high contributors from giving large amounts, because this establishes a social norm that makes the low contributors look bad. This second factor is discussed in Case 10.4.

10.3 Factors affecting social preferences

The different games described in the last section have been studied under a wide variety of different conditions that help to shed light on a number of issues related to social preferences. These conditions relate to three main categories of factor: methodological and structural, descriptive, and demographic. These factors and their effects are now discussed.

Methodological and structural factors

These change how experiments are conducted, and include the following factors: repetition and learning, stakes, anonymity, communication, entitlement, competition, available information, number of players, intentions, and the opportunity and cost of punishment. These constitute the most important single variable, particularly since they are to a large extent controllable. This means that, by using clever variations in experiments, individual factors and their effects can be isolated.

1 Repetition and learning

When ultimatum games are repeated with strangers, there is mixed evidence whether there is a learning effect. Bolton and Zwick (1995) report no learning effect, but other studies have found a slight but usually insignificant tendency for both offers and rejections to fall over time (Roth et al., 1991; Knez and Camerer, 1995; Slonim and Roth, 1998; List and Cherry, 2000).

Learning can also occur when players know the offers and MAOs of other players. A study by Harrison and McCabe (1996) indicated that providing such information reduces offers and MAOs to around 15% by the fifteenth round of play. There may be several reasons for this: responders may cease punishing unfair proposers if they see that others are not doing so; they may ‘tire’ of punishing, if the desire to punish is a visceral impulse that can be satiated; or they may adjust their perceptions of what is fair. Although it is possible in principle to test if there is a ‘tiring’ effect by pausing the game for a while and then restarting it, there is at present a lack of research regarding the contributions of any of the above factors.

The success of different strategies in repeated PD situations can be tested by computer simulation, the method pioneered by Axelrod (1985). More recent studies have introduced further complications related to real-life situations, such as playing the game sequentially as opposed to simultaneously, and allowing players to have the option of choosing which other players to play with. Successful strategies tend to be easily understood, ‘nice’ (tending to cooperate), but prepared to punish (defecting where necessary as a deterrent). Stability over time is not easy to achieve, given the dynamics of different strategies. For example, in a population of players using different strategies against different players, the nastiest strategy, ‘always defect’ (AD), will do well at first, but then starts to fail, as more AD players play each other and get low payoffs. TFT then gains ground, but because of the weakness of tending to spiral into mutual defection mentioned above, it also starts to lose out to more ‘forgiving’ strategies, like ‘generous’ TFT, which occasionally (but unpredictably) forgives defection. ‘Generous’ in turn allows the rise of even more forgiving strategies, like ‘always cooperate’ (AC). However, as such strategies spread, this in turn allows the return of the parasitic AD strategy, and a cycle may be initiated (Nowak, May and Sigmund, 1995).

What can be concluded from existing research regarding PD, trust and public goods games in a repetitive context? The general consensus is that in environments where people (1) have frequent interactions with others; (2) recognize these others; (3) remember the outcomes of these interactions; and (4) are in a position to punish these others either by defection or by refusing to play with them (social ostracism in real life), successful strategies tend to be ‘nicer’ or more cooperative. It should be noted that the threat of being excluded from playing (and not receiving any payoff at all) may be enough to force people to cooperate. We have to be seen to be nice to get people to trust us.

There is one final observation to be made regarding repetition and learning. It has been assumed so far that players are human, and therefore intellectually capable of calculating the effects of strategies in terms of outcomes. It is important to understand that this is not a necessity. As we saw in the last chapter, there is a branch of game theory in biology, commonly called evolutionary game theory, where the players do not have to be intelligent beings in the normal sense. This aspect of game theory was pioneered by Maynard Smith (1976, 1982). For example, bats (Wilkinson, 1984) and fish (Milinski, 1987; Dugatkin, 1991) have been observed to behave according to the predictions of the theory. In the words of Ridley (1996):

… there is, in fact, no requirement in the theory that the fish understand what it is doing. Reciprocity can evolve in an entirely unconscious automaton, provided it interacts repeatedly with other automata in a situation that resembles a prisoner’s dilemma – as the computer simulations prove. Working out the strategy is the job not of the fish itself, but of evolution, which can then program it into the fish (p. 79).

Thus in evolutionary biology it is the blind mechanistic force of natural selection, not the purposeful behavior of intelligent forward-thinking individuals, which leads to equilibrium. The significance of this phenomenon will be discussed more fully in Section 10.7 related to evidence from evolutionary psychology.

2 Stakes

The importance and effect of size of stakes has been discussed before, in both this chapter and earlier ones. One might expect based on this previous discussion that, in ultimatum games, as stakes rise, the amount that responders reject should rise, but the percentage of the surplus they reject should fall. For example, responders should reject $4 out of $50 more often than $4 out of $10, but should accept 20% out of $50 more often than 20% of $10.

In fact there is mixed evidence that stakes have such an effect, with most studies indicating no significant effect (Roth et al., 1991; Forsythe et al., 1994; Hoffman, McCabe and Smith, 1996; Straub and Murnighan, 1995). Even in the study by Cameron (1999), where stakes were as high as one month’s spending, there was little effect. Only a few studies (Slonim and Roth, 1998; List and Cherry, 2000, 2008) find fewer rejections for larger stakes. Furthermore, the studies also indicate little effect on proposers’ offers with higher stakes. The probable reason for this is that subjects may offer closer to 50% rather than much less than 50%, for fear of costly rejection. This fear may well be justified: in the study by List and Cherry (2000) a quarter of the subjects rejected offers of $100 out of $400.

In trust, PD and public goods games the effects of increasing stakes, in terms of the relative size of monetary payoffs, are predictable. When the ‘temptation’ (defect when other player cooperates) payoff is reduced, and the ‘sucker’ (cooperate when other player defects) payoff is increased, there is a greater tendency to cooperate. Similarly, when m, the marginal rate of social return, is increased in public goods games, contributions increase.

3 Anonymity

One recurring problem with experimental studies in general is that the behavior of the subjects can be influenced by lack of anonymity. The knowledge, or suspicion, that their identity may be known either to the investigator or to other subjects may cause subjects to want to appear ‘nice’ or to please the investigator. Hoffman et al. (1994) found that dictator allocations averaged only about 10% in a double-blind study, significantly less than in other dictator games where the protocol did not involve double-blindness. A similar result was found in Hoffman, McCabe and Smith (1998), although Bolton, Katok and Zwick (1998) did not find any significant difference between double-blind and other conditions. In ultimatum games it appears that anonymity may reduce rejections slightly but not significantly (Bolton and Zwick, 1995). These findings have been generally supported by a more recent study by Charness and Gneezy (2008), which reports that when players know the family name of their counterparts, dictators allocated a significantly larger portion of the pie. However, this information did not have a significant effect on offers in the ultimatum game, where it appears that strategic considerations crowd out tendencies to be generous.

4 Communication

Several studies show that in dictator games communication by recipients, for example talking about themselves, increases allocations (Frey and Bohnet, 1995; Bohnet and Frey, 1999). In the later study average allocations rose to half, and 40% of dictators gave more than half. Even simply being able to identify their recipients had some effect, in terms of reducing the number of dictators leaving nothing. However, in three-person games where there are two recipients for each dictator, but communication only occurs with one of them, dictators are generous only to the recipient with whom they have communicated (allocations being around twice as large). This indicates that communication elicits a target-specific sympathy rather than a general feeling of generosity (Frey and Bohnet, 1997). A study by Xiao and Houser (2005) proposes that people have a strong desire to express negative emotions, and that this is a reward in itself; thus people are less likely to reject offers from unfair proposers if they are able to write a message to them.

5 Entitlement

We have already seen that entitlement has important effects on behavior, for example the endowment effect. When dictators or proposers in ultimatum games feel entitled in some way, for example by winning a contest, they make less generous offers (Hoffman et al., 1994; List and Cherry, 2000; Cherry, Frykblom and Shogren, 2002; Jakiela, 2011). In the Hoffman et al. study the right to propose an offer was allocated to the person who answered more general knowledge questions. Offers in ultimatum games were reduced by about 10%, while dictators’ allocations fell by about half. The Cherry et al. study found that the tendency of dictators to make zero offers increased from about 17% to around 80%, with the proportion rising still further in double-blind studies to around 96%. However, it is interesting that recipients did not appear to share the entitlement attitudes of proposers in ultimatum games, since rejection rates increased, even with $100 stakes. There may be a self-serving bias here as far as legitimacy of entitlement is concerned. The Jakiela (2011) study is significant, since it indicates that the relative effects of earned versus unearned status vary between different cultures. Cultural effects are discussed in more detail shortly.

6 Competition

We have already observed that competition has significant effects on judgments of fairness. For example, it is judged to be fair for firms to cut wages if their survival is threatened by competition, but not otherwise (KKT). Furthermore, in ultimatum games proposer competition increases offers significantly. Roth et al. (1991) conducted a market game where nine players proposed offers (as sellers), and a single recipient (buyer) had the right to refuse the highest offer. Only one offer could be accepted, as is the case where a buyer only wants to buy a single unit. After five or six rounds of play, proposals converged on 100%, meaning that all the surplus from trade goes to the buyer. This is in fact the equilibrium according to the standard game theory of the standard model. In a study of responder competition Güth, Marchand and Rullière (1997) found a similar result, but with the effect working in the opposite direction. When a single proposer (seller) was selling a single unit to many competing recipients (buyers), the MAO was found to fall to below 5% of the surplus by the fifth round, while the average offer had fallen to 15%. The gap between offer and MAO indicates that the game had still not found its equilibrium by this fifth stage. Again this confirms the prediction of standard game theory, where the equilibrium is zero, or the smallest unit of money available. These results are discussed further in the following sections.

Some experiments have added outside options to ultimatum games, meaning that players earn nonzero payoffs if offers are rejected (Knez and Camerer, 1995). For example, if a proposer’s division of a $10 pie was rejected, the proposer earned $2 and the responder earned $3. A variation of this game awarded half of the surplus ($10 minus the sum of the gains of $2 and $3) to each player. The main result was that the rate of disagreement between proposer and responder rose considerably, to nearly 50% compared with the range of 10–15% in most experiments. It appears that this change in the game’s structure affects the players’ perceptions of fairness in different ways, with self-serving bias again causing the conflict.

7 Available information

Another structural variable that can be manipulated in experiments concerns the information possessed by the players. In ultimatum games, for example, respondents may be in any one of three situations in terms of knowledge about the size of the pie to be divided: (1) perfect information – they know for certain the amount to be divided; (2) incomplete information – they know the possible payoff sizes and their probability distribution; and (3) no information at all. Most studies indicate that responders tend to accept less under conditions of incomplete or zero information (Mitzkewitz and Nagel, 1993; Straub and Murnighan, 1995; Croson, 1996; Rapoport, Sundali and Potter, 1996). This can be interpreted as giving proposers the benefit of the doubt, since low offers could indicate a small pie. Proposers also tend to take advantage of the situation by offering less. However, a study by Camerer and Loewenstein (1993) found a contrasting result. In this case some respondents had perfect information, while others only knew that the possible pies were $1, $3, $5, $7 and $9, with equal probabilities. In the perfect information situation the average MAO was a typical 30%, but in the incomplete information situation the average MAO was $1.88, which represents about 38% of the average pie of $5. Disagreements were therefore much more common in the imperfect information case.

Information can also be provided regarding the past history of players in terms of their previous offers or behavior. This can provide a reference point as far as judgments of fairness are concerned. In both ultimatum games (Knez and Camerer, 1995) and dictator games (Cason and Mui, 1998) there was some positive correlation between the size of offers made by others and own offers, indicating some social influence. In PD games knowledge of the previous behavior of other players has an important effect, particularly if players can choose which other players to play with. As we have seen, a ‘bad record’ of defection is likely to cause social ostracism in these circumstances, so ‘nasty’ players will not get a chance to play much and will therefore earn little after a few rounds of play.

8 Multiperson games

The addition of other players to games that normally involve only two players provides a number of new insights regarding reciprocity and fairness. One general result is that players tend to be mainly concerned with fairness or equality in terms of their own payoffs relative to those of a proposer, rather than compared with the payoffs of third parties. Thus allocations of only 12–15% to other players who are inactive recipients in a three-person game do not seem to concern active responders; overall rejection rates of around 5% have been recorded, showing that they do not care much about how inactive third parties are treated (Güth and Van Damme, 1998). Furthermore, when trust games are played in three-person groups, groups give and repay less, and appear to be disproportionately influenced by the least trusting and trustworthy members (Cox, 1999). In multi-person PD games the likelihood of defection increases, since there is often a race to defect first. This is essentially a ‘tragedy of the commons’ situation, which can result in global problems like pollution and the depletion of fish stocks. At a more mundane level it can explain why at parties common resources of food and drink are often soon exhausted. If a player trusts some players but not others, he may defect to pre-empt defection by others. These findings, in both experiments and real-world situations, do not present an optimistic outlook for cooperation. However, and fortunately, they are counterbalanced by the following two factors.

9 Intentions

Humans, and human institutions like legal systems, place great importance on the intentions behind a person’s actions as well as on the consequences. Harm caused by accident is not punished as harshly as harm caused deliberately. Furthermore, the intention to cause harm (‘conspiracy’) is usually punished even if there is no harmful consequence. This view is a universal one in different societies, and therefore appears to be deeply rooted in evolutionary psychology. Simple game theory experiments have established that in ultimatum games MAOs are lower when players are paired with random devices like computers, rather than human proposers (Blount, 1995). Thus it appears that there is a difference in attitude toward inequality compared with attitude toward inequity. It is the latter, meaning a person’s perception of being treated unfairly, which seems to cause outrage, more than the perception of inequality. The importance of this distinction will be examined in the next two sections, when inequality-aversion models are compared with reciprocity models that incorporate intentions.

10 Opportunity and cost of punishment

Punishment is a vital method of enforcing social norms, in particular cooperation. Some writers distinguish between punishment as negative reciprocity and punishment as retaliation (Fehr and Gächter, 2001). Retaliation is described as relating to situations where players or agents expect future material benefits from their actions. Negative (and positive) reciprocity on the other hand does not entail any expected material benefits. For example, rejecting offers in an ultimatum game represents negative reciprocity on the part of the responder. We have seen that the rewards here are psychological and neurophysiological, as evidenced by neural scanning. A number of studies have shown that a large proportion of subjects, between 40% and 66%, exhibit reciprocity in one-shot situations; the one-shot nature of the situation indicates that this behavior is reciprocal rather than retaliatory (Berg, Dickhaut and McCabe, 1995; Fehr and Falk, 1999; Gächter and Falk, 1999; Abbink, Irlenbusch and Renner, 2000). Furthermore, studies also show that the desire to punish harmful behavior is stronger than the desire to reward friendly behavior (Offerman, 1999; Charness and Rabin, 2002), indicating that negative reciprocity is stronger than positive reciprocity. This has important consequences for multiperson games.

We have seen that public goods games are particularly prone to defection, or free riding. Defection may occur out of self-interest, or it may arise because reciprocal types want to punish self-interested types, and this may be the only practical way of doing so. However, as Fehr and Gächter (2000) have shown, if the behavior of players is observable, and if the direct punishment of individual players is possible (at a cost to the punisher), the results of public goods games are radically different. In this study there were four different protocols, all involving four players:

perfect strangers in each game and no punishment
perfect strangers with punishment
same players in repeated game and no punishment
same players with punishment

In the punishment protocols players could punish any other player by reducing the number of their tokens by x, at a cost of x/3 to themselves. The existence of a cost is important, not only because it is realistic, but because it enables a distinction to be made between reciprocal and self-interested players. Purely self-interested players will never pay a cost to punish others when there is no material reward.

The results of the four different protocols were vastly different. In the first case, perfect strangers and no punishment, cooperation falls to very low levels in later rounds, with average contribution levels being only 10% of available tokens, and 79% of subjects free riding and contributing nothing. Even when games were played repeatedly with the same players cooperation tended to fall, with contributions averaging only about 30% for the last five rounds of the ten-period game. However, when the opportunity for punishment existed, contributions increased throughout the rounds, even with perfect strangers. In this case contributions started at 50% and increased to 60%. When games were repeated with the same players, contributions started at 65% and rose to 90% by the end of ten rounds. This is a clear and dramatic demonstration of the power of punishment to enforce cooperation by self-interested individuals. Fehr and Schmidt (1999) have shown theoretically that even a minority of reciprocal subjects is capable of inducing a majority of selfish subjects to cooperate.

There are a number of important policy implications that arise from the above observations that will be discussed at the end of the chapter.

Descriptive factors

As we have seen at some length in previous chapters, framing effects are a common phenomenon. It should therefore be no surprise that they play a part in causing differential responses in various games. For example, when ultimatum games are framed in terms of a buyer-seller transaction, where sellers ask a price for a good that buyers can take or leave, offers are reduced by almost 10%, while rejection rates remain unchanged (Hoffman et al., 1994). When ultimatum games are framed as dilemmas where resources are shared, with players making sequential claims on a common pool of resources and receiving nothing if the claims add up to more than the pool, then players tend to be more generous, with rejections less frequent (Larrick and Blount, 1997). This may be because the language of ‘claiming’ creates a sense of common ownership, thus inducing a greater tendency to cooperate. It also appears that prompting proposers to consider the likely reactions of responders reduces offers, possibly by increasing the fear of rejection. Hoffman, McCabe and Smith (2000) found that this reduction was in the order of 5–10%.

Framing effects can also be observed in PD and public goods games. For example, when a PD game is framed as a ‘social event game’, as opposed to an ‘investment game’, this engenders more cooperation (Pilutla and Chen, 1999). It appears that different terms can trigger different expectations regarding the behavior of other players, leading to reciprocal behavior. This framing effect is particularly noticeable in the case of the Wason Test situation, described in Case 10.1.

Demographic variables

A considerable body of research has examined the effects of various demographic variables on social preferences. The variables most frequently studied are gender, age, academic major, culture and social distance.

1 Gender

Although there are a number of significant differences between the genders in terms of fairness and social preferences, there is no simple pattern. Instead there are complex interactions with a number of other factors. Here are some of the main findings:

In ultimatum games both sexes make similar offers (Eckel and Grossman, 2001).
In ultimatum games women reject less often.
In dictator games there appear to be no differences (Frey and Bohnet, 1995; Bolton, Katok and Zwick, 1998).
Both sexes demand more from women and offer more to men (Solnick, 2001).
Women generally punish more (Eckel and Grossman, 1996b).
Women are cost-conscious punishers; they punish more than men when it is cheap, but less when it is expensive.
Women are more generous than men in dictator games when recipients have to exert effort to earn rewards as opposed to receiving them as gifts (Heinz, Juranek and Rau, 2011).
In investment games where subjects can select partners, people tend to prefer to invest in partners of the opposite sex. This cannot be explained by the amount returned, but appears to be caused by tastes and beliefs regarding the trustworthiness of the opposite sex (Slonim and Guillen, 2010).
While men are not especially generous to attractive women, women offer about 5% more to attractive men than to unattractive men. In fact Schweitzer and Solnick (1999) report that the average female offer to good-looking men was over 50% of the pie, with 5% of females offering almost the whole pie! This last interaction is particularly interesting, since it supports field data that looks, and in particular height, are positively correlated with income.
Men tend to be more competitive and overconfident than women. This may apply in particular to certain professions, like business (Kamas and Preston, 2011), and appears to be true even in professional sports, like tennis, where one might expect all players to be highly competitive (Wozniak, 2011).

2 Age

Although few studies have been conducted in this area, it appears that children go through three main stages of development as far as social preferences are concerned (Damon, 1980; Murnighan and Saxon, 1998). Before the age of five, they are highly self-interested. Between five and seven they become very concerned with equality, mainly as a method of preventing conflict. After seven they become more interested in equity, for example by relating rewards to inputs or some other measure of entitlement. Some researchers have indicated that this constitutes evidence against the evolutionary psychology approach. For example, Camerer (2003) states:

These facts cast doubt on a strong version of the hypothesis that an instinct for acting tough in repeated interactions evolved because it was adaptive in our ancestral past (p. 67).

As we shall see, this conclusion can cause misunderstanding, and it is the ‘weaker’ version of the hypothesis that is important. This is discussed in the section on the role of evolutionary psychology.

3 Academic major

The evidence appears somewhat mixed in this area. A study by Carter and Irons (1991) found that Economics majors offered 7% less and demanded 7% more in ultimatum games than other majors. This difference applied to both first and final year undergraduates, causing the authors to conclude that Economics majors are born self-interested rather than made that way by the subject matter. A side issue is raised here: is this conclusion an example of self-serving bias by economists who want to defend their subject against the alternative conclusion that studying economics makes people more selfish?

Other studies indicate that economics and business students are no different from other majors in terms of offers and MAOs (Eckel and Grossman, 1996a; Kagel, Kim, and Moser, 1996), and a couple of studies have even indicated that economics and business students are more generous in their offers (Kahneman, Knetsch and Thaler, 1986; Frey and Bohnet, 1995). It is therefore impossible to come to any definite conclusion on this issue at present.

4 Culture

Cultural effects are notoriously difficult to test for, because of problems related to language, experimenter interaction and confounds with other factors. Most cross-cultural studies have involved ultimatum bargaining games. The first detailed study in 1991 by Roth et al. examined subjects in four countries: the US, Japan, Israel and Yugoslavia. The main finding was that offers were on average about 10% lower in Japan and Israel, yet rejection rates were also lower. The conclusion was that there appeared to be a different conception in these countries regarding what constitutes a ‘fair’ offer. It is interesting that a study by Buchan, Johnson and Croson (1997) found an opposite result as far as Japan was concerned, with average offers being higher than in the US. This may be due to methodological variations, since the latter study used the MAO method whereas the earlier study used the specific-offer method. However, there may be confounding factors here related to the two samples of students.

The most interesting studies of cultural differences in social preferences have been conducted by Henrich et al. (2001, 2004, 2005), which examined 20 different cultures, including many primitive cultures in Africa and Asia. An important aspect of this research is that it involved an interdisciplinary approach, with contributions from both anthropologists and economists. The research found some very different results regarding average offers in ultimatum games. The Machiguenga in Peru had the lowest average offer rate, with 26% of the pie, whereas two cultures actually had average offer rates above 50%: the Ache in Paraguay and the Lamelara in Indonesia.

How can such large differences be explained? It appears that two variables explain the variations to a considerable extent, with a multiple R² of 68%. These variables are:

a) The amount of cooperative activity or economies of scale in production

For example, when members of a society hunt in a group this factor is high, and offers tend to be higher. It is notable that The Machiguenga have a very low level of such cooperation, since the most important social group is the family, and business transactions outside the family are rare.

b) The degree of market integration

Markets are integrated when there is a national language and national or large-scale markets for goods and labor. Such integration is also associated with higher offers. There is an important conclusion here: well-developed markets that are more likely to be efficient are less likely to be dominated by pure self-interest.

One final point regarding the Henrich et al. findings is worthy of comment, and that concerns the two cultures with average offers above 50%. This appears to involve the ‘potlatch syndrome’. A potlatch is essentially an exhibition or competition of gift-giving which is designed to cause embarrassment or a feeling of obligation in the receiver, and it is, or has been, a feature of some primitive societies in both the South Pacific and Pacific North-west. There are also aspects of the same syndrome in many advanced countries. In this case gifts are used as weapons, and what may appear to be positive reciprocity is actually negative reciprocity. The reason why the practice is effective, however, is because it relies on the basic psychological mechanism of the feeling of reciprocity, which appears to be universal in all societies.

This double aspect of reciprocity is also relevant as far as punishment is concerned, and again cultural factors have a large influence. We have already seen that most punishment in public goods games is aimed at low or non-contributors, but sometimes high contributors are punished, this phenomenon being referred to as anti-social punishment. A recent study by Herrmann, Thöni and Gächter, (2008) finds that in western cities this type of punishment appears to be rare, but in other cities, notably Muscat, Athens and Riyadh, high contributors were punished as much as low contributors. There appear to be a number of correlated factors here: anti-social punishment is associated with a lack of trust and weak social norms of cooperation. Furthermore, there is evidence that lack of trust in strangers is correlated with strong family ties (Ermisch and Gambetta, 2010), which the authors argue is causal; in large families there is less motivation to deal with strangers, and less experience in such dealings, creating more uncertainty. Since larger, extended family networks are more common in developing countries, it may not be surprising that there is also evidence that lack of trust and weak social norms are negatively correlated with economic growth (Knack and Keefer, 1997). The importance, nature and origins of social norms are discussed in the next subsection.

5 Social distance

Most studies have found that people have more empathy and therefore more positive social preferences towards those others who are closer socially and geographically. However, there have been some recent observations that modify this generality. A study by Charness, Haruvy and Sonsino (2007) examined positive reciprocity in internet interactions pairing people in different countries or different states in the US, and found in all cases that a substantial minority displayed positive reciprocity, albeit declining with social distance. There has also been a recent natural experiment that relates to this phenomenon, which may have important policy implications. The UK has the third highest level of shoplifting in the world behind the US and Japan. CCTV is now widely used to detect this crime, and many shops in the UK pay £20 ($32) per week to have a CCTV linked up to the Internet Eyes website, while viewers pay a £13 ($21) annual subscription to access the footage. If a viewer detects a shoplifting incident in real time they can alert the shopkeeper by a simple click of a mouse, and they earn points for flagging up suspicious incidents. The highest scorer each month wins a prize of up to £1000 ($1600). Thus this natural situation resembles a public goods game, with the additional factor that people can gain a material reward from punishing free riders. However, material reward may not be the main incentive. A recent shoplifting incident in southern England was reported by a man living in northern Italy; he claimed he was not motivated by money, saying: ‘I feel what I’m doing is ultimately helping someone who lives far away. That can only be a good thing’ (The Sunday Times, November 21, 2010, p. 9). This is obviously anecdotal evidence, and may not represent average behavior, but it could indicate that there is at least a minority of people with social preferences that extend to others who are far removed from them socially and geographically.

Social norms

Fehr and Gächter (2000) define social norms in terms of the following three characteristics: (1) behavioral regularities; (2) based on a socially shared belief regarding how one ought to behave; and (3) enforcement is by informal social sanctions.

The role of social norms in determining social behavior is a highly controversial one. For Binmore and Shaked (2010a) they are fundamental in determining behavior:

We think it likely that people enter laboratories primed with a variety of social norms, one of which is triggered by the manner in which the experiment is framed (p. 98).

They go on to claim:

If the resulting behavior is close to a Nash equilibrium of the game (as in the Ultimatum game), then the social norm is stabilized in the laboratory experiment. If it is not (as in the prisoners’ dilemma), then the subjects’ behavior moves towards a Nash equilibrium (p. 98).

Binmore and Shaked also support the approach that regards social norms as being culturally determined, and, as we have seen from the Henrich et al. and other studies discussed earlier, there is much evidence for this.

However, there are two main problems with this approach. These problems do not relate to its correctness, but to the fact that it begs two questions, currently unanswered (Fehr and Schmidt, 2010, p. 103):

1 What is the origin of social norms?

2 What is it about the framing of a situation that triggers a particular social norm to operate?

Social norms appear to arise from a process similar to the ‘team reasoning’ process described in the last chapter in relation to the selection of appropriate focal points. It was seen that this process has been described by Crawford, Gneezy and Rottenstreich (2008) as follows:

Players begin by asking themselves, independently, if there is a decision rule that would be better for both than individualistic rules, if both players followed the better rule (p. 1448).

It is now suggested that such a process applies in a broader context, for example situations where there may be a rule that is not a Nash equilibrium at all, as far as the original game is concerned, but instead represents a correlated equilibrium of the type described in the previous chapter. This appears to apply particularly to iterated and repeated games, and an example was given in the repeated prisoners’ dilemma game, where the rule of ‘tit-for-tat, starting off with cooperation’ results in a much better payoff than the Nash equilibrium and, in fact, is Pareto efficient. We have also seen that in trust games, like the centipede game, empirical studies indicate that players tend to cooperate for several rounds, and again end up with better payoffs than the Nash equilibrium, which is to defect at the first opportunity. Different players in different cultures may play different rules here in terms of how long to cooperate, but there appears to be a general realization that, particularly in games with a large number of stages, the strategy of early cooperation is beneficial. It is notable that the behavior of players does not necessarily move towards a Nash equilibrium with greater experience, either in the laboratory or in the field, although this may happen in some cases, like the repeated PD game.

It is also important to realize that the rules or norms that are developed are not themselves the product of game theory. As Gintis (2009) has argued, they are essentially an ‘emergent’ phenomenon that arises from the twin forces of gene-culture coevolution and complexity. A simple example will illustrate the point. When it comes to deciding which side of the road to drive on, a repeated game, there are two Nash equilibria, with drivers either always driving on the right or always driving on the left. There is no obvious focal point here, since in either case drivers have equal payoffs. However, in the UK drivers drive on the left and in the US (and most other countries) they drive on the right; so why have these different norms evolved? There is much conjecture here, but common explanations are as follows:

UK – most people found it easier to mount a horse from the left-hand side, thus making it more natural to ride on the left-hand side of the road, and later to drive on that side.

US – many people rode in horse-driven carts or carriages, using a whip. Since the majority of people are right-handed it was safer to ride on the right side of the road, otherwise there was a danger of whipping passers-by.

Even if these conjectures are incorrect or incomplete they illustrate the point that social norms are determined by factors other than game theory itself, although they may be reinforced by game theory. The role of social norms in determining social preferences and decisions is discussed further in later sections.

10.4 Modeling social preferences

Objectives of modeling

We have now seen that the standard model, using standard game theory, fails to predict many empirical outcomes, both in real life and in experiments, and in some cases fails badly. It is important to emphasize again that this is not necessarily a failure of game theory as a technique of analysis. There are in general two possible reasons for failing to predict accurately: either people do not engage in strategic thinking in practice (meaning game theory is an inappropriate analytical technique), or the situations are not being modeled realistically, in particular by failing to incorporate social preferences into utility functions. We shall see that there is some truth in both of these factors. For example, we have already seen in the last chapter that there are some situations where empirical findings indicate a failure to think strategically, like in the ‘beauty contest’ game.

There is a further point to be made, or rather to be repeated, in this regard. Just as birds do not need to understand the theory of aerodynamics in order to be able to fly, people may behave according to the principles of game theory without necessarily following the logical steps involved. This kind of ‘as if’ behavior can evolve under the pressures of natural selection, as we have noted earlier in the discussion relating to repetition and learning; recall the apparent mathematical sophistication of woodpeckers. As we have also noted on several occasions, from the first chapter, this ‘as if’ justification is very commonly used in economics, particularly by supporters of the standard model. However, if standard game theory fails to predict accurately, we may conclude that the ‘as if’ inference is incorrect, and the model needs to be respecified. This point is further elaborated under the second feature below.

Although the absence of strategic thinking applies to some game situations where the standard model predicts badly, we will see in the remainder of this chapter that it is the existence of more complex strategic thinking that accounts for many anomalies. In these situations improved modeling of situations can lead to accurate predictions of many of the empirical findings, indicating that game theory is still useful as a predictive and explanatory tool.

In the modeling context, the challenge that is posed is that a good model must have two main features, in keeping with other behavioral models in general:

1 Explanation and prediction – it must be able to explain the results of a wide variety of different games in terms of endogenous parameters. As we have seen earlier in this section, changes in the structure of games can lead to very different empirical results. For example, the introduction of proposer competition and responder competition in ultimatum bargaining games has drastic effects on responses. A good model must be able to account for such differences in a parsimonious way, without resorting to ad hoc complications. A further related feature of such a model is that it can make interesting new predictions.

2 Psychological basis – this means that models must be based on known psychological mechanisms. It does not necessarily mean that the model actually explicitly incorporates psychological or neurological processes in its mathematical formulation, but it must at least be compatible with such processes, and also be compatible with the results of other studies. This issue will become clearer as we move on to discussing particular models.

In general we will see that all models have certain advantages and disadvantages; the models with more realistic features have a greater psychological richness and predictive power, but their added complexity tends to make them less tractable. Thus a researcher’s choice of model will ultimately be determined by the purpose in mind (Falk and Fischbacher, 2005).

Issues in modeling

Falk and Fischbacher (2005) describe four main questions that models incorporating social preferences need to address:

1 What is the reference standard as far as equitable transactions are concerned?

A common standard here is an equal distribution of payoffs.

2 How important are intentions?

In inequality-aversion (IA) models these are not important at all, but in reciprocity models they are an essential component. This means that it is not just the consequences of a player’s actions that are important but their beliefs, and the alternative possibilities of action that are open to them.

3 What is the purpose of punishment?

In IA models the only purpose of one player reducing another player’s payoffs is to reduce inequality, but in reciprocity models the motive is retaliation for an unkind act. Thus with the latter model one should observe both punishments and rewards even when inequality is not reduced.

4 Who is the relevant reference agent?

This issue arises in multi-player games. In some models players evaluate fairness towards individuals separately, while in other models the reference agent is the group as a whole (pp. 194–5).

The empirical findings relating to these questions are discussed in Section 10.7.

Psychological game theory

We have seen that social preferences are concerned with the distributional consequences of people’s actions and people’s beliefs regarding underlying motives and intentions. There has been much research over the last 20 years that has shown that people very often care about these aspects, and the branch of behavioral game theory that examines these is now referred to as ‘psychological game theory’ (PGT). PGT models utilities as being based on beliefs as well as actions (Battigalli and Dufwenberg, 2007), and is used to conceptualize belief-dependent emotions like reciprocity, guilt aversion, regret and shame. The original development of PGT was proposed in a paper by Geanakoplos, Pearce and Stacchetti (1989). A few examples at this stage will help the reader to understand the nature of social preferences, fairness, reciprocity and PGT.

Ann takes a taxi ride, and tips the driver (Bill) as much as she believes he expects to get. She suffers from guilt if she tips less.

Carol is offered a piece of candy by a stranger (Dave) sitting next to her on a plane; she likes the candy but refuses to accept it because she believes that by accepting it she will be obligated to the stranger in some way, even if that only means making the effort to strike up some conversation during the flight. She prefers to forgo the candy rather than feel obliged to reciprocate. If she accepts the candy but does not reciprocate she would again feel guilty, because she believes that the stranger would believe that the acceptance of the candy indicates that she is disposed to be friendly and she would be letting him down by not conforming to his expectation. Dave would then also have a lower opinion of her.

Ellen is worried about her health and consults her family doctor, Frank, who is also a friend. Frank diagnoses a serious illness. Frank realizes Ellen is distressed by her worry, and also realizes that if he prescribes her the most appropriate medicine for her disease, this will also reveal to Ellen the severity of the disease and increase her anxiety. Because Frank cares about Ellen he is reluctant to prescribe her the best medicine; to do so would make him feel guilty for causing her increased distress.

Gene applies for promotion in his firm. His boss, Henry, writes him an unfavorable report, and his application is rejected. Gene believes that this was partly due to Henry’s ignorance regarding the quality and quantity of his work, but was also due to professional jealosy, in that Gene believes that Henry believes Gene is a superior worker and is threatened by him. Gene therefore complains about Henry’s conduct to Henry’s boss, although this involves more work for him and the risk of retaliation when Henry discovers his disloyalty.

Irene shares a cake she has bought with Jim and Kayla. Kayla notices that Jim’s portion is bigger than hers. She suspects that Irene deliberately gave her a smaller portion, but believes this may be because Irene believes Jim has a greater fondness for cake than she does, so she is not upset. Jim however thinks that the unequal portions were accidental, and offers to give Kayla some of his portion, because he would feel guilty for being given the larger portion and accepting it without saying anything.

A number of factors emerge from these quite different situations. First, outcomes or utilities are largely non-monetary, except for the tip, but instead are belief-dependent. Second, people’s utilities depend not just on their own beliefs but also on others’ beliefs and on other’s beliefs about their own beliefs; thus PGT models can be considered as involving a hierarchy of beliefs. Third, emotions such as anger, envy, disappointment, blame, pride, shame, gratitude and guilt, or the desire to avoid guilt, are relevant in affecting people’s utilities (Geanakoplos, Pearce and Stacchetti, 1989; Battigalli and Dufwenberg, 2007). These emotions crucially depend on our expectations and prior beliefs, which obviously vary from situation to situation. For example, we often care if we cause other people distress, or if they have a lower opinion of us. However, in other situations we may want to cause others distress, or may not care about their opinion of us. All of these factors mean that PGT involves more complexity than standard game theory.

More recently there have been attempts to expand the scope and complexity of PGT further in order to handle many plausible forms of belief-dependent motivation that are illustrated in the examples above. In particular, Battigalli and Dufwenberg (2009) propose four further aspects of development:

1 Updated beliefs – PGT originally only allowed initial beliefs to affect a player’s utility.

2 Others’ beliefs – PGT originally only allowed a player’s own beliefs to affect his utility, but we can see that sometimes the beliefs of others, for example their respect for him, affects his utility.

3 Dependence on plans – PGT, and other traditional game theory, assumes that utilities are affected only by actual outcomes, but unrealized intentions may also influence utility. For example, if we believe another player intended to do us harm, even if their plans were thwarted and the harm was averted, this would still affect our beliefs regarding the other player and our utility.

4 Nonequilibrium analysis – PGT, like other game theory, only considers equilibrium situations, but in reality players may not coordinate to reach an equilibrium.

Some of these aspects will be considered further in the next subsection.

Nature and features of models

In general, current models of social preferences fall into the two main categories referred to above: inequality-aversion models, and reciprocity models. Both of these models maintain the basic assumption in the standard model that players aim to maximize utility, and that players also assume that other players do the same. The models both differ from the standard model in that they enrich or modify the utility function to take into account social preferences. IA models are simpler, because they only incorporate players’ first-order beliefs regarding inequality of distribution. They are not PGT models because they do not incorporate a hierarchy of beliefs as discussed earlier, and they take no account of players’ emotions beyond a desire for reducing inequality. Reciprocity models are more complex and varied in nature, and can take into account a variety of emotions such as anger, envy, disappointment, blame, pride, shame, gratitude and guilt.

At this stage a couple of simple examples will help to give the reader a flavor of PGT models and some of the implications:

1 ‘Surprise gift’ game

This is a two-player game in which only player 1 moves. Player 1 has two options: he can send player 2 flowers, or he can send chocolates. He knows that player 2 likes either gift, but he enjoys surprising her. Thus, if he thinks player 2 is expecting flowers more than chocolates, he will get more utility from sending chocolates, and vice versa (adapted from Geanakoplos, Pearce and Stacchetti, 1989). In standard game theory there is always an equilibrium in pure strategies if only one player moves; in this game, if we ignore the enjoyment from surprise factor, the pure strategy equilibrium would involve giving the gift which player 1 believes will give player 2 the most utility. However, given the surprise factor, there is a unique mixed strategies equilibrium, where player 1 sends each gift with equal probability.

2 Disappointment/retaliation game

This is a sequential game, again adapted from Geanakoplos, Pearce and Stacchetti. It is shown in extensive form in Figure 10.1.

Figure 10.1 Disappointment/retaliation game

Player 1 only cares about physical outcomes, but player 2’s payoffs at two of the terminal nodes depend on his initial expectations. If he is resigned at the start of the game to the idea that 1 will choose down, then A = 1 and B = 5 (these can be regarded as monetary payoffs); therefore 2 chooses down if 1 chooses down, so (down, down) is one credible equilibrium. On the other hand, if 2 is confident that 1 will play up, 2 will be disappointed if 1 plays down, and this alters the values of his payoffs A and B, so that A = 2 and B = 0. In this situation playing up gains utility from harming 1, while playing down loses utility from frustration at 1’s betrayal. Therefore, under this belief by 2, the equilibrium is (up, no move). One important implication here is that the backward induction method, used to solve sequential games in SGT, does not work with psychological games. This finding is discussed in later sections.

More specific aspects and concepts related to modeling will be examined in the next two sections, where the psychological foundation and the resulting differences in structure of different models are discussed in more detail. The abilities of the models in terms of explaining empirical results are then discussed in Section 10.7.

10.5 Inequality-aversion models

These models assume that people care about their own payoffs, and the relative size of these payoffs compared to the payoffs of others. It should be noted that sometimes such models are referred to as ‘inequity-aversion’ models. The latter term is less appropriate. The distinction between inequality and inequity was touched on earlier, in the discussions of both intentions and the age factor. The most important point here is that inequality is a neutral term and implies no value judgment, while inequity is a value-laden or normative term involving the subjective notion of fairness. Thus, if a human proposer offers less than 50% of the pie in an ultimatum game, this may be rejected by the responder either because of inequality aversion or because of inequity aversion. As we have seen, this ambiguity can be removed by using a random proposer, like a computer. If rejections occur in this situation, the cause must be inequality aversion.

Before examining inequality-aversion (IA) models in detail, it is useful to consider the nature of altruism more closely, since altruism is sometimes regarded as the basis of social preferences. This will also aid an understanding of the relevance of the terms ‘endogenous’, ‘parsimonious’ and ‘ad hoc’, used in the previous section in the description of the characteristics of a good model.

As we have already seen, some authors distinguish between pure altruism, where a player’s utility increases as the utility of other players increases, and impure altruism, where a player’s utility increases from the act of contributing to others (Margolis, 1982). Thus, if I am made happier by lending you my car (and thus making you happier), but not if my neighbor lends you his car, this is impure altruism.

Two fundamental points need to be made at this stage. First, neither of the above types of altruism constitutes pure altruism in the sense that it is sometimes used in psychology (Batson, 1991). Psychological altruism refers to the objective of increasing the welfare of others without any increase in one’s own welfare, either material or psychological. Such a phenomenon is alien to economics, since it cannot be incorporated into any utility maximization model, whether standard or behavioral. In any kind of economic model no factor can affect an individual’s behavior unless it can be incorporated in some way into that person’s utility function, although Amartya Sen (1977) seems to envisage the reality of psychological altruism. However, current neurological research tends to support the economic model, as illustrated in the last case study in the first chapter.

The second point is that altruism, as defined above, can only explain positive reciprocity; it cannot explain the widespread negative reciprocity observed in empirical findings reported earlier. Any model explaining empirical findings only in terms of altruism would have to incorporate ad hoc complications like changing signs related to the utilities of others. These complications are not explained within the structure of the model itself, meaning that they are exogenous rather than endogenous. This would also make the model lack parsimony, since the model would have to be adjusted to explain different situations.

Therefore any successful model of social preferences must go beyond altruism, since it also has to able to explain spiteful behavior, like the various forms of punishment we have already observed in different types of game.

The Fehr–Schmidt model

Fehr and Schmidt (1999) proposed a model (FS model), sometimes referred to as a ‘guilt/envy’ model, but which the authors actually referred to as a model of inequity aversion. They use the term inequity on the basis that fairness judgments are based on some ‘neutral’ reference point. They refer to the literature in social psychology regarding social comparisons (Stouffer et al., 1949; Festinger, 1954; Homans, 1961; Adams, 1963), noting that a key insight in this research is that relative material payoffs affect people’s wellbeing and behavior. They also note a number of empirical findings that directly support their hypothesis (Loewenstein, Thompson and Bazerman, 1989; Agell and Lundborg, 1995; Clark and Oswald, 1996; Bewley, 1998). In real-life situations the determination of the relevant reference group and outcome tends to pose modeling problems, but in experimental situations it seems justifiable to assume that the relevant reference group is the other subjects in the study, and that the reference outcome is the average income of these subjects.

In the FS model it is therefore assumed that, in addition to purely selfish subjects, some subjects will also dislike inequitable outcomes. Such inequity could arise from being either worse off or better off than others. An individual’s utility function therefore depends not only on their own monetary payoff, but on differences between this payoff and those of others.

This situation can be modeled mathematically as follows:

In a set of n players the social allocation is given by the vector of payoffs

x = (x₁, x₂,…,x_n)

The utility function of player i is a function of this vector and is given by

U_i (x) = x_i – α_i/(n–1) max (x_j – x_i, 0) – β_i/(n–1) max (x_i – x_J, 0)

(10.1)

Where α_i is a measure of player i’s aversion to disadvantageous inequality, and β_i is a measure of his aversion to advantageous inequality. Thus the second term in (10.1)

measures the utility loss from disadvantageous inequality and the third term measures the utility loss from advantageous inequality. Three further assumptions are involved:

1 β_i ≤ α_i, meaning that players suffer less from advantageous than disadvantageous inequality. This certainly seems a reasonable assumption in the light of direct empirical evidence (Loewenstein, Thompson and Bazerman, 1989).

2 0 ≤ β_i < 1, the lower boundary meaning that players do actually suffer from advantageous inequality, rather than feeling a benefit from it. This assumption is certainly questionable (Frank, 1985; Wilkinson, 2004), and Fehr and Schmidt admit the possibility of status-seeking players with negative values of β_i, but they justify the assumption on the grounds that such players ‘have virtually no impact on equilibrium behavior’. The upper boundary β_i = 1 can be interpreted as meaning that a player is willing to throw away a dollar in order to reduce his relative advantage over player j of the same amount, which seems unlikely.

3 The population of players is heterogeneous, meaning that different players have different values of α and β. Thus α and β have distributions rather than single values for the whole population.

Using the utility function in (10.1), Fehr and Schmidt then apply game-theoretic analysis (similar to that used in the last chapter in relation to continuous strategies) to derive average values of α and β, sometimes referred to as the ‘envy’ and ‘guilt’ coefficients, which are necessary to explain the various empirical results.

The FS model derives a number of conclusions regarding different variations of ultimatum and public goods games. While the standard model predicts complete free riding in public goods games (zero contributions), and no willingness to engage in costly punishment, the FS model predicts that both contributions and punishment will occur if players are sufficiently envious and guilty. The model derives specific conclusions regarding (1) the conditions under which people will free ride (β_i ≤ 1 – m, where m is the marginal return to the public good), (2) how many free riders (k) it takes to cause everyone to free ride (k > m(n – 1)/2), and (3) how much guilt and envy are necessary for an equilibrium to emerge where there are some positive contributions and punishment (again determined in terms of the endogenous parameters α_i,β_i, m, and c, the cost of punishment).

The twin strengths of the FS model are:

1 Simplicity

The model is simple in form, in terms of the number of parameters involved, and the linearity of the function (although the latter feature can easily be modified).

2 Robustness

This characteristic refers to the ability to explain the wide variation in results that are observed from different games. For example, it fits the normal ultimatum game, and the variations with both proposer and responder competition. As far as competition is concerned, the model produces an interesting prediction: in proposer competition, the number of proposers does not affect the equilibrium offer of almost zero, while in responder competition a greater number of responders will reduce the highest equilibrium offer. These contrasting predictions have yet to be confirmed empirically. The nature of empirical evidence and how this relates to different models is discussed in Section 10.7, along with criticisms of the methodology involved.

The Bolton–Ockenfels model

This model (BO), proposed by Bolton and Ockenfels (2000), is often referred to as an ERC model, because it relates to equity, reciprocity and competition. It is similar to the FS model in many respects, since players care about their own payoffs and their relative share. It is assumed that players prefer a relative payoff that is equal to the average payoff, meaning that they will sacrifice to move their share closer to the average if they are either above or below it.

This situation can be modeled mathematically as follows:

U_i (x) = U(x_i, x_i/Σx_j)

(10.2)

The BO model, like the FS model, uses game-theoretic analysis to derive specific conclusions regarding equilibria in various different games. For example, it predicts that in ultimatum games responders will reject zero offers all the time, and that the rejection rate will fall with increasing percentage offers. It also predicts that ultimatum offers will be larger than dictator offers, and that in three-person games the allocation to inactive recipients will be ignored. These predictions are largely confirmed by empirical findings.

There are three main differences between the BO model and the FS model:

1 The BO model is concerned with relative shares, whereas the FS model is concerned with absolute differences.

2 The BO model only makes a comparison between an individual’s payoffs with the average payoff of all the other players. It does not compare each player’s payoffs with the maximum and minimum of the other payoffs, like the FS model does.

3 The BO model proposes a symmetrical attitude towards inequality, where guilt and envy are equal in force (α_i = β_i), whereas the FS model proposes that envy is stronger than guilt.

In all three respects the FS model appears to be superior, in terms of both fitting empirical findings and psychological foundation. A simple demonstration can be given by using a three-person game where the payoff allocation is given by According to the BO model the preferences of the first player should be independent of ∊, since the sum of the payoffs will be constant and therefore the relative share of the first player is not affected. However, according to the FS model, as ∊ increases, envy of the third player’s payoff and guilt regarding the second player’s payoff both increase, causing the first player’s utility to fall. A study by Charness and Rabin (2002) has confirmed this prediction, and similar empirical findings are reviewed in Section 10.7. However, this conclusion does not mean that the FS model can explain all empirical results in such games, or that it is complete in capturing all the relevant psychological factors, as we shall now see.

10.6 Reciprocity models

Reciprocity is based on the idea that people’s conception of fairness depends not only on equality or inequality but on people’s intentions. As explained in the previous section, altruism only explains positive reciprocity, but any realistic model must also be able to explain and predict the negative reciprocity that is widely observed empirically. In general people can have either ‘kind’ or ‘unkind’ intentions toward other people, depending on what we believe are their intentions toward us. Thus intentions depend on beliefs and possibilities. For example, if we have no alternative but to make an unequal offer to someone this is not judged as being as unfair as when we have a choice between making an equal offer and an unequal offer. Empirical evidence relating to this is presented in the next section.

A good starting point for the discussion of reciprocity models is the model proposed by Rabin (1993), since this was the first formal model of this type and the simplest.

The Rabin model

The central basis of the Rabin model is expressed by the statement:

If somebody is being nice to you, fairness dictates that you be nice to him. If somebody is being mean to you, fairness allows – and vindictiveness dictates – that you be mean to him (p. 1281).

The model is a two-player model, in which utilities depend upon beliefs. Player 1’s strategy, a₁, depends on his belief about the strategy of the other player, b₂, and his belief about player 2’s belief regarding player 1’s strategy, c₁. A similar description can be applied to player 2’s strategy. On the basis of these beliefs two important constructs can be determined: (1) player 1’s ‘kindness’ to player 2, and (2) player 1’s perception of player 2’s ‘kindness’ toward him. The determination and interpretation of these constructs requires a certain amount of intellectual effort, and a fairly detailed exposition of the relevant analysis follows, using a prisoner’s dilemma situation as an illustration.

1 Player 1’s kindness to player 2

Given that player 1 has belief b₂ regarding player 2’s strategy, his own strategy consists of allocating a payoff to player 2 out of a set of possible payoffs. Let the highest and lowest of these payoffs for player 2 be π₂^max (b₂) and π₂^min (b₂). We then need to define a fair payoff, , which Rabin does by taking an average of the highest and lowest payoffs (although this particular definition does not affect the basic analysis). Player 1’s kindness to player 2 can now be expressed as follows:

(10.3)

This can be interpreted by saying that player 1’s fairness to player 2 is a function of his own strategy (a₁) and his belief regarding player 2’s strategy (b₂), and is determined by the fraction of the way above or below the fair point that player 2’s actual payoff lies (the numerator), scaled by the range of payoffs player 1 could have dictated (the denominator). Thus if player 2 received a higher payoff than the fair one, the numerator is positive and player 1 is being kind. If on the other hand player 2 receives a lower payoff than the fair one, the numerator is negative and player 1 is being unkind.

2 Player 1’s perception of player 2’s kindness

This perception depends on what player 1 believes player 2 believes player 1 will do (c₁). It can therefore be written as follows:

(10.4)

Rabin then assumes that player 1’s social preferences are given by a three-component utility function:

U₁ (a₁, b₂, c₁) = ₁(a₁, b₂) + f~₂ (b₂, c₁) + f~₂ (b₂, c₁) f₁ (a₁, b₂)

(10.5)

The first component of the function, π₁(a₁, b₂), represents player 1’s direct monetary payoff. The second component, f~₂ (b₂, c₁), represents the utility of player 1’s perception of player 2’s kindness, where is a weight showing how fairness converts into money utility (players with no social preferences have α =0). The third component, f~₂ (b₂, c₁) f₁ (a₁, b₂), represents the utility of reciprocity; it is a function of the product of the kindness they expect and their own kindness. It should be noted that this term is positive if player 1’s generosity is reciprocated by player 2, or if their meanness is reciprocated by player 2. Thus both positive and negative reciprocity yield positive utility, unlike an altruism model.

An equilibrium for the model can then be derived on the basis that players maximize social utilities, assuming rational expectations, a₁ = b₂ = c₁. This means that beliefs about the other player’s strategy are correct, and that beliefs about the other player’s beliefs are also correct. An illustration of the operation of the model can be given in terms of a PD situation, assuming the monetary payoffs are those shown in Table 10.3.

Table 10.3 Prisoner’s dilemma – monetary payoffs

It can be seen that the monetary payoffs correspond to the conditions described in Table 10.2, so that the dominant strategy for each player is to defect, if social utilities are ignored. We now have to calculate social utilities by adjusting the monetary payoffs to incorporate fairness or ‘kindness’ factors, according to the utility function in (10.5). These calculations are shown for each of the four possible pairs of strategies confronting player 1 (player 2’s strategies are identical since the monetary payoffs in Table 10.3 are symmetrical).

1 Cooperate/cooperate

U₁ = 4 + α(4 – 2)/(4 – 0) + α(4 – 2)/(4 – 0) × (4 – 2)/(4 – 0) = 4 + 0.5α + 0.25α = 4 + 0.75α

The second term above (0.5α) is positive because it is perceived that the other player is being kind, and the third term (0.25α) is also positive because there is positive reciprocity.

2 Cooperate/defect

U₁ = 0 + α(0 – 2)/(4 – 0) + α(0 – 2)/(4 – 0) × (6 – 3.5)/(6 – 1) = 0 – 0.5α – 0.25α = 0 – 0.75α

In this case both the second and third terms are negative. Not only is the other player mean, but they are not reciprocating player 1’s kindness.

3 Defect/cooperate

U₁ = 6 + α(6 – 3.5)/(6 – 1) + α(6 – 3.5)/(6 – 1) (0 – 2)/(4 – 0) = 6 + 0.5α – 0.25α = 6 + 0.25α

The second term is positive since the other player is perceived to be kind, but the third term is negative because player 1’s meanness is not reciprocated.

4 Defect/defect

U₁ = 1 + α(1 – 3.5)/(6 – 1) + α(1 – 3.5)/(6 – 1) × (1 – 3.5)/(6 – 1) = 1 – 0.5α + 0.25α = 1 – 0.25α

The second term is negative because the other player is perceived as mean, but the third term is positive since player 1 is reciprocating the other player’s meanness.

We can now construct a new payoff table with the social utilities for each pair of strategies. This is shown in Table 10.4.

Table 10.4 Prisoner’s dilemma – social utilities

In the revised situation the dominant strategy for each player need not necessarily be to defect. The payoff for cooperation given that the other player cooperates is greater than the payoff for defection if 4 + 0.75α 6 + 0.25α, i.e. if α > 4. The implication here is that if people have sufficiently strong social preferences related to fairness there will be a Nash equilibrium situation with two equilibria in pure strategies: cooperate/ cooperate and defect/defect. Alternatively the situation could be viewed in terms of a mixed strategy equilibrium.

The Falk–Fischbacher model

Falk and Fischbacher (FF hereafter) (1998) constructed another reciprocity model, which proposes a social utility function that incorporates four elements as opposed to the three in Rabin’s model. As well as including monetary or ‘material’ payoffs, kindness and reciprocity, it also takes into account how intentional the kindness of a player is. The FF model has two important variations from the Rabin model: (1) kindness is measured in terms of differences between the payoffs of the different players, rather than in terms of possible payoffs for a single player, and (2) intentions are treated as being dependent on available allocations, both chosen and unchosen. These two variations are now explained in more detail.

1 Measurement of kindness

In the Rabin model kindness is judged in terms of how much players receive relative to some ‘fair’ payoff for themselves, which in turn depends on the range of their own possible payoffs. In contrast, the FF model proposes that players judge fairness in terms of the difference between their own expected payoffs and the other player’s payoff.

2 Measurement of intentions

In the FF model there is an intention function, which compares a set of possible payoffs with alternative payoffs. In this case the opportunity cost to the decision-maker is relevant in terms of judging the fairness of their allocation. For example, in an ultimatum game, offering 80%/20% may be regarded as unfair in some situations, but fair in others, depending on what alternatives were open to the decision-maker. If the only alternative was 90%/10%, then the 80%/20% split is likely to be judged fair.

Further details of the FF model are not given here, since it was developed to analyze sequential or extensive-form games, rather than the simultaneous normal-form games illustrated in the tables we have so far used. We saw in the last chapter that the analysis of extensive form games was more complicated than the analysis of simultaneous games. In standard game theory this involves the use of the foldback method, but as we have seen in the section on PGT, this cannot be applied in psychological games.

The Dufwenberg–Kirchsteiger model

Dufwenberg and Kirchsteiger (DK hereafter) (2004) propose a variation of the FF model. Like the FF model and unlike the Rabin model, the DK model relates to sequential reciprocity and also measures fairness in terms of the difference between a player’s own expected payoff and the other player’s payoff. The DK model is also based on PGT, but extends the analysis to situations where players’ beliefs and expectations can change throughout the game, whereas in the original paper by Geanakoplos, Pearce and Stacchetti (1989) initial conditions or beliefs remain constant throughout the game. One consequence of this extension of the analysis is that preference reversals can occur due to a change in the players’ beliefs. The DK analysis of a sequential prisoners’ dilemma game comes to similar conclusions to the Rabin model: if players have high reciprocity sensitivities a twin Nash equilibria solution may result. Both players may cooperate for both material and reciprocity reasons; or they may both defect because of self-fulfilling expectations, with each player believing the other is unkind and being unkind in return.

The DK model also makes some interesting predictions regarding the centipede game, a trust game discussed in the last chapter. In the DK version of the game, at every node the decision-making player can take (defect) or pass on, in which case their material payoff is reduced by 1 while the material payoff of the other player is increased by 2. A 4-stage game is represented in Figure 10.2.

Figure 10.2 Centipede game with reciprocity

The most interesting prediction here is that it is enough that just one of the players is sufficiently motivated by reciprocity for both players to stay to the last or to the last but one mode. For example, even if A suspects that B will take at the last mode, A may still pass to him at the previous node if B has cooperated up until that point and therefore has established a regular pattern of kindness. The consequence of this is that B may cooperate until the last mode even if he is entirely selfish. Another prediction that follows from this is that the greater the number of stages in the game the more likely the players are to cooperate, since it allows a greater build-up of kindness between them. Dufwenberg (2002) has referred to this process in a psychological game based on motivation by guilt aversion as ‘psychological forward induction’.

We can now see that there are a number of differences between the Rabin and DK models, the most important of which can be summarized below:

1 The DK model applies to sequential games as well as simultaneous games.

2 The DK model applies to games with more than two players.

3 The DK model measures kindness in the same units as material payoffs, whereas the Rabin model measures kindness as a ratio.

4 The DK model defines the efficiency of strategies as being belief-independent, whereas in the Rabin model the efficiency of a strategy depends on the beliefs of players.

One of the implications of these differences is that Rabin’s model assures the existence of an equilibrium in any game where no player is kind. In many games there may also be ‘happy’ equilibria where both players are kind, but in these cases there must be multiple equilibria, including at least one where no player is kind. We have already seen in the Centipede game that the DK model is not so ‘gloomy’ in its implications, although in other games a ‘happy’ equilibrium is not guaranteed.

The main advantage that reciprocity models in general have over inequality-aversion models is that they capture an important psychological factor omitted from the latter type of model. However, as Dufwenberg and Kirchsteiger (2004) themselves admit, their model still omits many of the other psychological factors mentioned earlier in the context of PGT, such as a concern for equality, envy, disappointment and guilt-aversion. These omissions have been addressed by more recent papers by Battigalli and Dufwenberg (2007, 2009). However, the added complexity of the models proposed renders their examination outside the scope of this text.

10.7 Empirical evidence

We have already discussed in Section 10.2 some aspects of empirical evidence in relation to some of the basic games described in the previous chapter, such as PD games, ultimatum games, dictator games and public goods games. However, at that point we were only concerned with comparing empirical findings with the predictions of standard game theory. As in Chapter 8 when examining models of intertemporal choice, we now need to examine empirical evidence in terms of the light it sheds on the different behavioral models. The same general conclusion holds for games involving social preferences as for models of intertemporal choice: it is much easier to show anomalies in the standard model than to compare different behavioral models in terms of how their predictions fit empirical findings. It is important to understand the nature of these difficulties. In standard games, and even in many behavioral games discussed in the previous chapter, players can learn to play some equilibrium because with repetitive play they can come to hold correct beliefs about the opponents’ actions (Fudenberg and Levine, 1998). However, ‘this may not be enough for psychological games; since payoffs depend on hierarchical beliefs, players would have to be able to learn others’ beliefs, but unlike actions beliefs are typically not observable ex post’ (Battigalli and Dufwenberg, 2009). The consequence of this problem is that players could indeed have the same psychological preferences as proposed by a particular theory, but not behave according to the equilibrium prediction because of mistaken beliefs about beliefs.

Once again findings come from three main sources: behavioral studies, evolutionary biology and neuroscientific studies.

Behavioral studies

We can start by comparing the two IA models described earlier. We have already seen that empirical evidence supports the FS model rather than the BO model in terms of comparing a player’s payoffs with the maximum and minimum payoffs of other players rather than with their average payoff. Another advantage of the FS model is that it correctly predicts that in public goods games it is the biggest free riders who are punished, whereas the BO model makes no prediction regarding who is punished.

A final advantage to be mentioned here concerns predictions in variations of the ultimatum game, where rejections result in payoffs of 10% of the original offer. The BO model predicts that, since relative shares are not affected by acceptance or rejection, but payoffs are larger with acceptance, responders will never reject unequal offers, like 80%/20%. In contrast, the standard linear FS model predicts indifference, but modification of the model, to allow concave utilities for money, guilt and envy, can predict rejection. This is much more consistent with empirical results, where the rejection rate by responders of 80%/20% offers may be as high as 50%.

However, there has been heavy criticism of the FS methodology from Binmore and Shaked (BS hereafter) (2010a,b). These authors report that the FS model has been cited in 2390 works with uncritical acceptance of the methods, and ‘is thought so unproblematic that it is even taught to undergraduates’, with a reference to this text. First, it should be noted that virtually all the models described in this text are ‘problematic’ in some way or other, including prospect theory. This does not mean that they should not be taught to undergraduates, provided the problems are described. Where BS make a valid point is that in the first edition of this text, although certain limitations of the FS model were described, there was no comment on the methodology. It is not appropriate to discuss the details of BS’s paper here, and the student is referred to the original work, and to the various responses to it, but the four main grounds of their criticism are summarized below:

1 Calibration of parameters

It is claimed that the distributions of and cannot be estimated from ultimatum game data alone, which leaves the parameters under-identified.

2 The distribution of parameters is not kept constant

It is claimed that FS sometimes alter their assumptions about the joint distribution of and without drawing attention to this in order to accommodate or fit new data. In particular BS points out that the distribution used in the FS papers relating to employment contracts (Fehr and Schmidt 2004, 2005, 2007), which involves 60% of the population behaving according to the standard model (with α= β = 0) and 40% being inequality-averse (with α = β > 0.5), is not consistent with the original ultimatum game data. The FS response to this is that the later 40/60 distribution is essentially a simplification of the one originally used.

3 Predictions are not quantitatively accurate

The BS paper claims that the FS predictions in various games, including public goods games with and without punishment, auction games and contract games, are no more accurate in general than the predictions from the standard model that do not take into account other-regarding preferences.

4 Cherry-picking of data and results

This is really the most serious criticism, and has been touched on above. BS claim that FS throughout their series of papers on inequality aversion focus on data and predictions that support their model, ignore data or predictions that do not, and fail to make appropriate comparisons with the standard model (or ‘money-maximizing’ model in BS terms) when such comparisons are not favorable.

BS go to pains to state that their criticisms are not leveled especially at the FS inequality-aversion model, but are aimed more generally at the current state of experimental economics. However, Fehr and Schmidt (2010) have defended their methodology against the above claims, and Eckel and Gintis (2010) have also defended the general approach in experimental economics as well as the FS papers specifically. The response to this by Binmore and Shaked (2010a,b) has further polarized and broadened the debate. Not only do they claim that FS have not answered any of their criticisms in any substantive way, but they also criticize the work of Gintis (2009), which they claim adopts a similar cherry-picking approach to data and predictions. There is no doubt that this debate will continue for some time.

Having examined and compared the different IA models we can now broaden the discussion and compare IA models in general with reciprocity models. This means we need to address the four issues described in the previous section related to modeling.

1 What is the reference standard as far as equitable transactions are concerned?

There appears to be little controversy here that an equal distribution of payoffs is generally regarded as being fair when these payoffs are regarded as being unearned (Loewenstein, Thompson and Bazerman, 1989; Falk and Fischbacher, 2005). However, as we have already seen, it is rare in reality that payoffs appear as ‘manna from heaven’, and when there is an element of ‘merit’ or entitlement involved we find that preferences can be highly heterogeneous, both within and between cultures.

2 How important are intentions?

This second issue is of fundamental importance in evaluating and comparing IA models with reciprocity models. There is an abundance of empirical evidence that suggests that people do not just care about inequality, they also care about reciprocity and intentions. For example, responders in an ultimatum game may reject 80%/20% offers by a human proposer who stands to gain by making such an offer, but may accept the same split if it is determined by a random process. This clearly shows that the ‘consequentialistic’ perspective that proposes that people only consider payoffs, not beliefs and intentions, is inadequate. This finding is supported by a number of studies. For example, Falk and Fischbacher (2005) conducted an experiment based on the ultimatum game, comparing rejections of an (8/2) split when there were different alternatives for the proposer. If the proposer had an alternative of offering an even (5/5) split then 44% rejected the less advantageous (8/2) offer. However, if the alternative was an even less advantageous split of (10/0) then only about 9% of the subjects rejected the offer. Furthermore, if the alternative was a split of (2/8) that was disadvantageous to the proposer, only 27% rejected the (8/2) offer, showing that the majority of subjects did not expect proposers to choose splits that were disadvantageous to themselves.

A more recent study by Falk, Fehr and Fischbacher (2008) confirms some of these findings. This study involved a ‘moonlighting game’, where proposers can either give tokens to a responder (which are tripled in value) or can take them away. The responder in turn can then reward or punish the proposer by giving tokens or taking them away at a cost. The game thus combines elements of the ultimatum game, public goods game with punishment, and trust games. What is particularly significant is that in one treatment the proposals were generated randomly by a computer, which allows us to see the relevance of intentions. As expected, responders rewarded giving and punished taking, showing strong reciprocity. In the standard treatment there was a slight asymmetry here, in that there was a greater amount of punishment than reward for a given amount of giving or taking by the proposer. Thus on average responders rewarded a gift of six tokens by returning six tokens, but punished a taking of 6 tokens by taking away eight tokens. So far these results are consistent with an IA model, where people are more averse to negative inequality than positive inequality. However, when the random treatment was used the rewards and punishment were both much smaller, not exceeding two tokens in either direction. Thus, although there is still some evidence of inequality aversion, the large reduction in rewards and punishment shows that people place a great importance on intentions, not just outcomes.

In summary one can say that reciprocity models are more realistic than IA models, although they are analytically more complex since they have to take into account unchosen options as well as those selected. However, the greater mathematical complexity of the analysis may well be worth the trouble, in the light of the greater accuracy of explanation and prediction.

3 What is the purpose of punishment?

Again there is a distinction between IA models and reciprocity models here. According to IA models punishment will only occur if this has the effect of reducing inequalities of material payoffs, while reciprocity models propose that the motive is retaliation for an unkind act, regardless of whether this reduces inequalities. Experiments by Falk, Fehr and Fischbacher (2001) using both ultimatum and public goods games show that inequality aversion cannot explain much punishment that takes place.

4 Who is the relevant reference agent?

This issue was again investigated by Falk, Fehr and Fischbacher (2001). Their experimental results show clearly that people tend to punish individual defectors rather than the group as a whole, which would include both defectors and cooperators. This represents another refutation of IA models, since these predict that cooperators want to improve their situation relative to the group average, which involves punishing cooperators when this is cheaper than punishing defectors.

Various other significant findings emerge from empirical studies, with a common theme being some kind of asymmetry:

1 Asymmetry in reciprocity

People tend to punish unkindness more than they reward kindness. Croson and Konow (2009) propose two reasons for this: first, an asymmetry in underlying preference that even impartial spectators display, and second, a moral bias in that stakeholders punish more and reward less than spectators.

2 Asymmetry in attitudes to punishers and cooperators

A study by Kiyonari and Barclay (2008) finds that people are more willing to support or reward those who reward cooperators than support those who punished noncooperators. People did not reward punishers or punish nonpunishers. This appears to indicate that people are more inclined to support positive sanctions than negative sanctions.

3 Asymmetry in desire to contribute

We have already seen that in public goods games there is a tendency for contributions to gradually decline, unless there is a possibility for punishment. However, there are various possible reasons for this: (1) people might change their beliefs over time regarding the willingness of others to contribute; (2) people have heterogeneous preferences regarding contributions; and (3) people wish to contribute less than others, so that as the contributions of others decline, their own contribution declines in a ‘race to the bottom’. Fischbacher and Gächter (2010) propose that the third explanation is responsible.

4 Asymmetry of effects of spiteful preferences

While we have seen that strong reciprocators have a desire to punish free riders, and these spiteful preferences promote cooperation, there are also a significant number of free riders who have a desire to punish cooperators, and this reduces cooperation. These free riders are not purely selfish, because they are prepared to pay a cost to reduce the payoffs of others, with the purpose of increasing the payoff difference between themselves and cooperators. Falk, Fehr and Fischbacher (2005) find that 13% of the subjects in their study were in this category in a one-shot public goods game. Fehr, Hoff and Kshetramade (2008) conducted an experiment involving a one-shot trust game in India, and find a particularly high proportion of high-caste subjects with spiteful preferences who punish cooperative behavior. When both defection and cooperation are punished, free riders have less incentive to cooperate, a conclusion also reached by Gächter and Hermann (2007) from experiments in Russia.

5 Consistent contributors are vital to group cooperation

Whereas the previous finding has somewhat pessimistic implications for human societies, the finding that a hard core of consistent contributors promotes the development of general cooperation within groups has optimistic implications. This has been recognized by social researchers for some time (Elster, 1985a), but recent experimental studies have supported these conclusions. Furthermore, they suggest that consistent contributors, who basically have an ‘always cooperate’ strategy, tend not to suffer any cost from their actions and sometimes gain, at least in repeated multi-player situations similar to actual societies (Weber and Murnighan, 2008). This has been somewhat of a puzzle in the past, since such contributors can never receive a higher payoff than other players, and can always be exploited by defectors in the short run according to standard game theory. Hence they have been labeled ‘suckers’. However, it appears that consistent contributors may receive other payoffs, such as prestige and perhaps sexual access to more partners, which are ignored in SGT, and this may enable them to survive and prosper. Warriors who exhibit self-sacrificial bravery tend to be valued in many societies (Chagnon, 1988; 1990), and an explanation of this phenomenon has been proposed in terms of costly signaling theory (Gintis, Smith and Bowles, 2001; Smith and Bird, 2005). Costly signals act as a credible commitment, in a similar manner to the handicap theory in evolutionary biology (Zahavi, 1975), whereby only meritorious individuals can afford to give a certain signal. It appears that a number of political systems endow prestige on individuals on this basis (Boone, 1998). The effect of such individuals on the group is vital in generating general cooperation, since their behavior encourages conditional cooperators to cooperate more often, by promoting cooperation as the social norm. In this situation punishers of free riders may be giving a credible signal that only they can afford to pay the cost of punishing. This may in turn cause observers to reward them in ways not considered in SGT. However, in such a system punishment may not even need to be explicit, since people may be shamed into cooperation (Elster, 1985b). The policy implications of social norms are discussed in the next section.

6 Consensual punishment promotes cooperation most effectively

In an experiment to compare the effects of a consensual punishment institution versus autonomous individual punishment, Casari and Luini (2009) find that the former promotes a higher level of cooperation. Again social norms appear to be relevant here.

7 Cooperation in repeated games only tends to evolve if a number of conditions are satisfied

In experiments involving infinitely repeated games, or simulations of such games where the end of the game is determined randomly, evidence suggests that cooperation is not guaranteed even if an equilibrium involving cooperation exists, and this equilibrium is both Pareto efficient and risk dominant (Bó and Fréchette, 2011). This is best illustrated by means of an example, and we can use a simple one from the previous chapter to do this, in Table 10.5, which is a repeat of Table 9.4.

Table 10.5 Pareto efficiency and risk dominance

We have seen that in the above situation there are two Nash equilibria: both suspects confess; and both suspects do not confess (this is obviously not a prisoners’ dilemma situation, since there are no dominant strategies). The second of these equilibria, involving cooperation, is Pareto efficient, since both players are made better off by not confessing compared with both players confessing. However, the first equilibrium is risk dominant. A risk dominant equilibrium in a 2 × 2 symmetrical game occurs when the equilibrium strategy is a best response to a mixed strategy where the other player plays each strategy with equal probability (Harsanyi and Selten, 1988). In Table 10.5 the average payoff from confessing is 3.5 years in jail, while the average payoff from not confessing is 5.5 years. Thus the equilibrium of both players confessing, i.e. defecting, is risk-dominant in this case, mainly because the ‘sucker’ payoff from not confessing when the other player confesses is very high. Bó and Fréchette (2011) find that even when equilibria are both Pareto efficient and risk dominant, these conditions are not sufficient for cooperation to evolve in infinitely repeated games. Only when the payoff from cooperation and the probability of future interactions are high enough do subjects tend to achieve a high level of cooperation.

8 Overly selfless players are disliked

This counterintuitive finding emerged from a recent study by Parks and Stone (2010). These researchers reported that players in public goods games who contributed more than they withdrew from the common pool were not liked by other players. This may partly explain the phenomenon of anti-social punishment discussed earlier. The other players also did not want to play another game with the selfless players (who were actually computer programs, but were anonymous in the game), even though this should be to their material advantage. Further experiments established that this refusal was not because of the perceived incompetence or unpredictability of the selfless players. Instead two reasons appeared relevant: first, the selfless players were seen as deviating from a social norm (that giving and taking should match), and second, they made the other players look bad. Thus once again, social norms, self-image and reference points are important here. Do-gooders beware.

There is finally one general conclusion here, which resembles a general conclusion earlier in the book relating to decision-making under risk and uncertainty: it appears that there may be two types of situation where people have to make decisions involving social preferences. In one kind of situation people tend to automatically apply some kind of social norm, as Binmore and Shaked (2010) claim, whereas in other situations they play strategically, taking into account beliefs and intentions of other players. Of course, as mentioned earlier, this begs the questions regarding what situations trigger social norms, and which norms are triggered.

Evolutionary psychology

As we have seen in other areas of economic behavior, evolutionary psychology plays an important role in understanding social behavior. As far as social behavior is concerned, evolutionary psychology (EP) proposes that the human brain developed significantly as people started to live in hunter-gatherer bands or tribes over the last few million years. Cooperation yielded significant advantages in such an ancestral environment, since repeated interactions between people in the same group were frequent, and people learned to recognize others and remember debts. Cooperation was also necessary to provide public goods, including food from big game hunting. Punishment of defectors and free riders, often in the form of exclusion from the group, or ostracism, was also important in enforcing cooperation. As mentioned above, consistent cooperators may have been rewarded in terms of prestige and access to sexual partners. However, there are a number of misunderstandings concerning the role of EP, and it is important to clarify these.

1 Competing versus underlying theories

The most fundamental misunderstanding is that evolutionary explanations are an alternative to the theories described in the preceding sections. Evolutionary theory is in no way a substitute for these theories; rather it has a complementary role, in terms of explaining how underlying social preferences are formed in the first place. All the theories discussed so far make certain assumptions regarding how conceptions of fairness are determined, and how these conceptions affect our choices in terms of other concepts such as reciprocity and intentions. The fundamental role of EP is to explain how such conceptions developed in our intellectual decision-making processes. EP therefore is best regarded as an underlying theory rather than a competing theory as far as theories of social preferences are concerned. In terms of the hierarchical reductionism explained in Chapter 2, an EP explanation is at a lower level in the hierarchy than the theories described in this section.

2 Questionable status as a scientific theory

Related to the first criticism is the accusation that EP suffers from an inability to be falsified or to make precise predictions. These are two basic requirements for any scientific theory. However, although EP can be difficult to falsify in some cases, this is because of a lack of available evidence in practice, not because of any principle (unlike for example string theory in physics, or religious ‘theories’ like the existence of heaven and hell). As far as precise predictions are concerned, EP does indeed lead to some very precise, and surprising, predictions, as will be seen in the first case study, on the Wason Test.

3 Individual development variations

One line of criticism of EP is that people are not born with a sense of social responsibility. As we have seen, this takes a number of years to develop, and in the first few years of life infants are almost entirely ‘purely’ selfish. This is often taken as evidence that the capacities of judging fairness and calculating strategic behavior are inculcated by cultural factors rather than being innate. The falsehood of this argument can be seen by making a direct comparison with sexuality. Most modern psychologists agree that human sexuality does not really develop until puberty (although Freudians dispute this to some extent). However, it is absurd to argue that this is evidence that sexuality is a cultural concept and is not innate. It must be recognized that not all our innate instincts are present at birth; even innate instincts may take some time to fully develop.

4 Cross-cultural variations

We have also seen that there are considerable variations between cultures as far as certain characteristics like offers and rejections in ultimatum games are concerned. Such variations are also often seen as evidence that EP is not a powerful predictor of social behavior. The essential point here is that EP should not always be seen as a competing explanation for behavior compared with cultural factors (although it may often be). It is not always a case of ‘nature versus nurture’; frequently phenomena are best explained in terms of ‘nature via nurture’, as Matt Ridley (2004) has proposed. Thus, although our brains may be hardwired with certain innate propensities and preferences, these are to some extent malleable by culture. The phenomenon of suicide bombing is an extreme case, where an evolved psychological mechanism geared to improve survival (belief in purpose and supernatural powers) has been hijacked into serving an entirely opposite purpose.

5 One-shot and repeated games

It is sometimes argued that the tendency to cooperate or reciprocate in one-shot games is evidence against EP. For example, Camerer (2003) makes the point that ‘subjects are usually well aware that one-shot games are strategically different than repeated ones’, implying that this awareness should discourage them from cooperating in such one-shot games. This implication overlooks the fact that awareness is not sufficient to deter certain behavior in all cases. To take an extreme example, an alcoholic may be very aware that indulgence after a long period of abstinence may cause a relapse into self-destructive behavior, but this does not deter them, any more than the knowledge that fatty foods cause heart disease discourages people from going to McDonalds. As Camerer also states: ‘when our caveman brains play one-shot games in modern laboratories, we cannot suppress repeated-game instincts’. The point to recognize here is that repeated-game instincts involve guilt and envy, anger and indignation, all emotions that are now hardwired into our psychological make-up. Such emotions cannot be simply disengaged in one-shot situations, even when we are aware of their one-shot nature.

The real challenge for EP, in analyzing social behavior as in other areas, is to produce precise and testable predictions. EP is certainly capable of meeting this challenge, and often produces surprising and interesting results, as seen in Case 10.1.

An example of a prediction based on EP involves a phenomenon called assortative matching. This is essentially an application of evolutionary game theory, incorporating signaling, where cooperators are more likely to interact with other cooperators than with noncooperators. The evolutionary story here is that it is important for cooperators to be able to detect defectors or cheaters, to avoid being suckered. Thus they need to be able to send signals relating to their willingness to cooperate. To be credible these signals tend to be costly. However, it then pays defectors to be able to simulate such signals, and this puts selective pressure on cooperators to become better detectors, so an evolutionary arms race begins. The result of this is that signaling a willingness to cooperate becomes more and more complex, and may well lead to self-deception (Pinker, 1997); it is easier to fake a cooperative signal if we really believe we will cooperate, even if we ultimately defect.

Other indirect evidence relating to EP comes from studies of primates. Certainly there is evidence that both capuchin monkeys and chimpanzees respond negatively to disadvantageous inequity. On the other hand, the evidence regarding whether these species exhibit prosocial attitudes in response to advantageous inequity is ambiguous (Brosnan, 2008), since non-human primates seem mainly concerned with their own payoffs rather than the payoffs of others. However, the evidence that primates exhibit feelings of reciprocity seems beyond doubt. Like humans, other primates appear to be more concerned with the actions of their social partners than with the payoffs of these partners. Thus intentions seem to matter to primates too. Furthermore, their reactions to inequity appear to show several factors related to the emotions that are common to humans. For example, they are prepared to incur a cost to punish ‘unfair’ treatment, by throwing food back at an investigator, or refusing to cooperate in paired tasks where their partner routinely claims the better reward in an unequal payoff situation (Brosnan and de Waal, 2003). These actions cannot be explained in terms of inequality-aversion, since they actually result in an increase in inequality. Thus reciprocity in primates is a complex issue, and appears to involve the same kind of emotional commitment devices as with humans. Obviously more research is needed here, perhaps aided by neuroeconomic studies of primate brains in this kind of decision situation. We can now turn our attention to neuroeconomic studies in general.

Neuroscientific studies

When discussing altruistic and spiteful behavior earlier we were careful to distinguish between material and non-material benefits. Until the beginning of this century the measurement and even the identification of non-material benefits and costs was highly speculative and introspective. Furthermore, many people are reluctant to admit that they actually get a kick out of punishing or reducing the welfare of others; this contravenes social norms in societies with a Judaeo-Christian morality. However, over the last few years, and with the benefit of various types of neural scanning, both identification and measurement of psychic costs and benefits are possible, and this has added significantly to the science of economics in terms of both theory and empirical evidence. We can now consider the implications of certain neuroscientific studies regarding some of the games described above.

First of all, researchers need to know where in the brain to look as far as the recording of rewards from decisions is concerned. O’Doherty (2004) found that not only was the dorsal striatum activated in decisions involving expected monetary rewards, but also that this activation increases as the expected monetary gain grows. Therefore we would expect rewards from punishment or cooperation to be associated with a similar activation. A study by de Quervain et al. (2004) examined rewards from punishment in trust games. They used a PET scanning technique and three treatments:

1 Free punishment (F), where player A can punish player B for defecting at the rate of $2 per point at no cost to themselves.

2 Costly punishment (C), where A can still punish B at the rate of $2 per point, but at a cost of $1 per point to themselves.

3 Symbolic punishment (S), where there is just an assignment of punishment points, but no monetary cost to either A or B.

The last treatment was important as a baseline control measure, since neuroimaging scans always measure brain activations in one condition relative to another condition.

The study found that the dorsal striatum was strongly activated in both the F–S contrast and the C–S contrast, indicating that subjects experienced rewards in both situations. Furthermore, subjects in the C condition who exhibited higher dorsal striatum activation also tended to punish more. The authors concluded that the level of stratum activation was related to the anticipated satisfaction from punishment, rather than from the actual punishment. This was because subjects who experienced higher striatum activation in the F condition, even though they were punishing to the same maximal level as subjects with less activation, were willing to spend more on punishment in the C condition.

The de Quervain et al. study also found that the ventromedial prefrontal cortex (VMPFC) is activated in the processing of rewards from punishment. It appears from a number of studies that the VMPFC is involved in the integration of separate benefits and costs in the pursuit of behavioral goals (Ramnani and Owen, 2004; Knutson et al., 2007), and the VMPFC is also activated by rewards related to charitable donations (Moll et al., 2006).

Other studies relating to rewards from cooperation as opposed to punishment have been revealing. Rilling et al. (2002, 2004) have examined mutual cooperation with a human partner compared to mutual cooperation with a computer in repeated and one-shot social dilemma games. Results were essentially the same in both studies, but the one-shot situation gives more reliable results, since the repeated game involves a number of confounding influences. The studies show that mutual cooperation with a human partner promotes more striatum activation than cooperation with a computer; the use of the computer partner controls for other influences like the size of reward and effort, so it can be concluded that the observed reward arises entirely from mutual cooperation in the normal sense, meaning with another person.

As far as fairness is concerned, various brain areas are implicated. Two recent studies (Fliessbach et al., 2007; Golnaz et al., 2007) have provided evidence that the fairness of a bargaining offer is associated with activity in the ventral striatum. Studies have also examined the neural processes involved when negative feelings are aroused, for example with unfair offers. Sanfey et al. (2003) conducted a study of the ultimatum game using fMRI and found that there was greater activation in the insula, the anterior cingulate cortex (ACC) and the dorsolateral prefrontal cortex (DLPFC). A later study by Knoch et al. (2006) corroborates these results to some extent. This study used the rTMS technique to disrupt the DLPFC, and found that when the right (but not the left) DLPFC was disrupted this increased people’s propensity to accept unfair offers, thus implicating this area of the brain in the judgment of fairness. It appears from this study, and also later studies by Knoch et al. (2008) and Spitzer et al. (2007), that the DLPFC along with the orbitofrontal cortex (OFC), play a role in moderating self-interested impulses in games where people are tempted to violate social norms and fear punishment. People whose brains show more activation in these areas are more inclined to abide by social norms. The opposite side of this coin is that people with antisocial personality disorder have been shown to display deficient activation in these areas, as well as deficient insula activation (Veit et al., 2002; Birbaumer et al., 2005).

We have seen in an earlier chapter that the insula is implicated in the processing of unpleasant emotions, such as pain, hunger and disgust; it is also activated when we experience negative social feelings, like seeing a price charged that we think is excessive. A study by Harle and Sanfey (2007) sheds further light on people’s tendency to reject unfair offers; when negative emotions such as sadness and disgust have already been primed, engaging the insula, this leads to a higher rejection rate of unfair offers.

Neuroscientific studies also shed some light on inequality aversion. A study by Tricomi et al. (2010) created one ‘rich’ subject and one ‘poor’ subject, the first with $80 and the second with $30. The subjects were then asked to evaluate future payments to the other player. Rich subjects valued payments to themselves only slightly more highly than payments to the other subject, while poorer subjects valued payments to themselves much more highly, and valued payments to the other subject negatively. These valuations were closely correlated with activation in the nucleus accumbens (NAcc), an indication of anticipated reward, but there was a different pattern of activity in the VMPFC. Thus it appears once again that separate areas of the brain react differently to social situations: the NAcc is concerned with inequality aversion, while it appears that the VMPFC has a moderating role in terms of reconciling the conflict between the social preference to equalize payoffs and the purely selfish desire for gain.

In addition, it has been shown that when people’s emotions are primed by either fair or unfair behavior in a trust game, this affects their empathy with the player if that player is then subjected to pain (Singer et al., 2006). When the player previously treated them fairly, returning their trust, there was evidence of empathy for their pain in terms of activation of the ACC and anterior insular cortex (AI). When the player had treated them unfairly previously, a difference in reaction between the sexes was observed: while women continued to show some empathy, men no longer showed activation in the ACC or AI, on the contrary showing activation in the NAcc. It seems men may be more likely to take revenge on unfair players than women, while women are more likely to be prosocial. This finding is echoed in some other studies mentioned in the next section. However, a note of caution is in order here: the term prosocial is used in different senses; in economic studies it is usually related to fairness, while in psychology studies it is often related to helping others, or empathy, and the two characteristics are not perfectly correlated. People who value fairness more do not necessarily display more empathy.

A final area of note in this area of social interaction is the influence of the mirror neuron system (MNS) and the neuropeptide oxytocin on trust and social behavior. It has been known for some time that the MNS allows monkeys to mimic actions by others, since the same neurons are activated when they observe specific actions by others as when they perform the same actions themselves. More recently it has been found that the MNS is responsible for producing empathy, since it allows people, and some other animals, to experience the emotions of others. Zak, Kurzban and Matzner (2004) and Zak (2011) propose the existence of a human oxytocin mediated empathy (HOME) system, whereby mirror neurons are activated by the release of oxytocin, in turn causing people to be either generous or to punish.

Neurobiologists have suspected for some time that this chemical promotes bonding behavior, including maternal care and trust, in a variety of species. Studies by Fehr et al. (2005) and Kosfeld et al. (2005) supported this hypothesis; it was found that the percentage of players who trusted maximally in a social dilemma game increased from 21% to 45% after treatment with oxytocin. The issue then raised was whether oxytocin operated at the level of subjects’ beliefs about others’ trustworthiness, or whether it operated at the level of the subjects’ preferences. The authors concluded that oxytocin does not significantly affect beliefs about the trustworthiness of others, but instead renders subjects less averse to being exploited, thus changing their preferences. A more recent study by Zak, Stanton and Ahmadi (2007) sheds further light on the effects of oxytocin. This study found that the administration of oxytocin increased offers significantly in ultimatum games, but not in dictator games. The authors explain this result by proposing that oxytocin increases empathy related to the mental states of others, rather than by increasing altruism per se. If the increased offers in the ultimatum games are purely strategic, then this result could be seen to conflict with the Kosfeld et al. study, since it would seem that beliefs were being affected rather than preferences.

There appear to be a number of conflicts in terms of how oxytocin and empathy affect behavior. First, if people witness a distressing scene, such as a car accident, the experience of distress associated with empathy can inhibit generous behavior, so they may be less likely to help victims or people in need of aid in spite of feeling empathy with them (Batson et al., 1987). Second, mimicry and understanding do not necessarily go together (Khalil, 2011). Thus people may imitate the actions of others who are violent, without performing a rational appraisal of the situation, an unfortunate phenomenon all too often observed in scenes of mob violence. Mob psychology is the flip side of the MNS-oxytocin coin. Obviously, further research needs to be done in this area to clarify the role of both the MNS and oxytocin.

10.8 Policy implications

As with other areas of behavior the factors discussed in this chapter have important policy implications, for individuals, firms and governments. In all cases the implications point to different courses of action compared to those suggested by the standard model. Furthermore, we often find that policies designed by firms and governments to achieve certain ends may actually prove to be counterproductive, because of the phenomenon of crowding out of intrinsic incentives. In general terms this means that the provision of external market-based norms in a transaction may replace pre-existing social norms and change the incentive structure for behavior in an unintended way. Evidence of this phenomenon comes both from field studies and experiments.

Market norms and social norms

Market norms are extrinsic to the individual and are based on the assumption of the standard model that people act purely selfishly and have no social preferences in terms of reciprocity. Fines and monetary rewards are in this category. Social norms on the other hand involve intrinsic values that people have, and are shaped both by a person’s individual psychological make-up and by the culture in which the person operates. There is a considerable body of research that emphasizes the importance of social norms in the provision of public goods (Elster, 1989; Ostrom, 1998, 2000; Fehr and Gächter, 2000). An example of the application of the social norms is given in Case 8.3 relating to the desire for rising consumption profiles.

It is helpful at this stage to examine an example where implicit moral incentives are pitted against explicit economic incentives. A study that is often quoted in this respect was conducted by Gneezy and Rustichini (2000). This field study examined a situation at ten Israeli day-care centers, where there was a problem with parents being late picking up their children. The centers had a policy that children were supposed to be picked up by 4p.m., and delays caused anxiety among the children, and teachers had to wait around for parents to arrive. The study lasted for 20 weeks, and for the first 4 weeks the investigators simply recorded the number of late parents. On average there were eight late pick-ups per week per day-care centre. After week 4 a fine was introduced at six of the ten centers, which was the equivalent of $2.5 for a delay of 10 minutes or more. This fine was added to the monthly fee of about $380 per child. In the four centers with no fine, which acted as a control group, the number of late pick-ups stayed about the same. However, in the six centers where the fine was enforced the number of late pick-ups increased steadily for 4 weeks, and then stabilized at an average level of about 18 per week, more than twice the original level!

Another study regarding the relative importance of moral and economic incentives was conducted by Titmuss (1971) and related to blood donation. Most people donate blood for altruistic reasons, and are not paid a fee. When a small fee was offered, people tended to give less blood than without the fee. It has been hypothesized that the payment of a fee demeaned the act of donating blood, so that people no longer felt good about doing so.

A similar result has been reported in a study in Switzerland investigating people’s willingness to accept a nuclear waste repository in their community (Frey and Oberholzer-Gee, 1997). Initially about half (50.8%) of the respondents indicated a willingness to accept such a facility; however, when the same respondents were asked if they were willing to accept the facility if the Swiss parliament offered substantial compensation to all the residents of the community, the level of willingness dropped sharply to 24.6%.

It now appears that many governments have made serious policy errors by assuming that centralized control over key public resources is vital for efficient use. Standard economic theory predicts that in order to prevent a ‘tragedy of the commons’ involving overuse and free riding, common resources such as water supplies, grazing ground and irrigation systems need to be controlled by a central authority. However, there is now abundant evidence that such control frequently results in less efficiency and a worsening of environmental problems, by disempowering local groups who previously controlled such resources based on local knowledge and social relationships, and placing control in the hands of faceless bureaucrats who were often corrupt (Wunsch and Olowu, 1995; Finlayson and McCay, 1998; Shivakoti and Ostrom, 2002).

Experimental studies have produced similar findings to the field studies above. A meta-analysis of 128 laboratory studies that have explored the effect of extrinsic rewards on intrinsic motivation has found that tangible rewards tend to have a substantially negative effect on intrinsic motivation (Deci, Koestner and Ryan, 1999).

How can these findings be interpreted? A number of possible explanations have been proposed. One explanation is that the imposition of a fine changes the amount of information available to the players in the game. For example, parents may interpret the fine in terms of the economic and legal options that are feasible for the manager of the centre. They may infer from the low value of the fine that the actual cost to the centre of a late pick-up is low. Blood donors may interpret any fee paid to them in terms of the value of their donation, and therefore may be discouraged from making a donation if they perceive that this value is small.

However, a more likely explanation is that the introduction of fines and rewards causes a shift in the way that the activities in the game are perceived. Fines and rewards transform the meaning of activities into commercial commodities, to which people attach different monetary values than when such activities are performed out of moral incentives. It also appears that this shift in perception can only occur in situations where subjects had not previously considered monetary rewards and punishments as an option. Once subjects have had their perceptions changed in this direction, they cannot be unchanged. This conclusion is supported by the fact that, when fines were discontinued in the day-care centers after the 16th week, the number of late pick-ups remained at a high level.

We should not conclude from the findings above that monetary incentives in the form of fines and rewards are ineffective. In the day-care centre situation the fines were too low to be effective, and were simply seen as representing a low price for being late. To put this into perspective, we should consider the fine of $2.5, or 10 shekels, against the fine for illegal parking of 75 shekels, and the fine for not collecting dog droppings of 360 shekels. Monetary incentives may need to be larger in order to be effective. It should also be noted that being effective is not necessarily desirable; it simply means changing behavior in an expected direction. Levitt and Dubner (2005) note that, in the case of blood donation, large fees may indeed cause more donations, but they may also cause some highly undesirable side-effects, like taking the blood of others by force and donating the blood of animals. These effects have already been observed in the market for replacement body organs.

Another important conclusion relating to all the observed behavior is that incomplete contracts may be preferable to complete, or more complete, contracts in many situations. Such incomplete contracts would not specify fines and rewards, but would rely on moral or social incentives for changing behavior in the desired direction. For example, the original contract in the Israeli day-care centers was incomplete, since it did not specify any sanctions for late pick-ups. This issue is discussed further in Case 10.3.

What are the lessons to be learnt in terms of government policy? First of all it appears that policies that are perceived as controlling and treat people as untrustworthy are self-defeating, since they reduce people’s sense of self-determination and self-esteem, and are self-fulfilling. A second lesson, particularly related to government policies, is that bureaucrats do not necessarily know better than community residents, who may have much local knowledge gathered over a long period. It now seems that the UK government is learning from these mistakes, since it is trying a large-scale experiment in the opposite direction in terms of its police force. For nearly 50 years the police force has been a centralized authority. Over the last ten years there has been increasing criticism of the current target-based approach, such as catching a certain number of criminals and achieving certain crime detection rates. Many believe this has tied the hands of the police and crowded out intrinsic incentives, so that the police are no longer seen by people as public servants. A bill has been passed that proposes to put police forces in the hands of locally elected commissioners, who would be able to set priorities and budgets, and to hire and fire chief constables. This is intended as a return to real ‘community policing’.

When crime was largely dealt with by the community itself rather than by a centralized authority, a powerful punishment and deterrent was social ostracism. One main implication here for public policy is that a ‘naming and shaming’ policy may be effective. Some US cities fight prostitution by posting pictures of convicted ‘johns’ and prostitutes on websites or on local-access television. As Levitt and Dubner (2005) ask rhetorically in their popular book Freakonomics: ‘Which is a more horrifying deterrent: a $500 fine for soliciting a prostitute, or the thought of your friends and family ogling you on www.HookersAndJohns.com’.

Another implication for public policy is that a ‘whistle blowing’ facility may be beneficial. This is, however, a controversial issue, since it can lead to a ‘big brother’ state, with neighbors spying on each other. For example, the introduction of ASBOs (Anti-Social Behavioral Orders) in the UK in 1998 was greeted with mixed enthusiasm by the public.

Labor markets

Similar counterintuitive results to those discussed above have been found in labor markets. Since the seminal work of Akerlof (1982), behavioral economists have frequently modeled these in terms of gift exchange. A trust contract refers to a situation where the employer (principal) offers a high wage, trusting the employee (agent) to reciprocate by making a high effort. A bonus contract refers to a situation where the principal may reward the agent for making a high effort by making a voluntary bonus payment ex post. Both contracts actually involve one player trusting the other, who is in a position to exploit the other player, and both appeal to fairness and reciprocity. However, in spite of this symmetry, there is a distinct asymmetry in terms of the empirical findings. Fehr, Klein and Schmidt (2007) find that trust contracts do very badly and are not profitable, while bonus contracts do very well and are highly profitable. They explain this asymmetry in terms of the different risks involved. The employer faces a higher cost if employees defect by putting in little effort, compared to the employee’s cost of putting in a high effort and the employer defecting by not paying a rewarding bonus. Thus contracts work better when the risk of trusting lies with the player for whom the cost of trusting is lower. Fehr, Klein and Schmidt also make two other counterintuitive conclusions:

1 A higher proportion in the population of agents who value fairness makes trust contracts less acceptable, since fair agents have more to lose from trusting than purely selfish agents.

2 Incomplete contracts may be more efficient than contracts that are more complete, since they allow more flexibility for both employer and employee to act in a trusting and reciprocal way.

Experiments by Fehr and Gächter (2000) have examined different types of labor contract from those described above, relating to the work effort of workers under two conditions: one in which there were explicit incentives in the form of fines if workers were observed shirking, and another where there were no incentives. The relationship between work effort and offered rents was observed, where offered rents are defined as the wage minus the cost of providing a certain desired effort level. In the condition with explicit incentives, the actual work effort did not vary significantly with the rent offered, averaging about 2.5 on a scale of 1 to 10. However, when there were no explicit incentives in the form of fines, work effort increased steadily with the rent offered, reaching a level of 7. Only at low rent levels was work effort lower in the absence of incentives; at moderate and high rent levels work effort was higher than when incentives were offered. This result has been confirmed by a later study by Fehr, Klein and Schmidt (2004), as discussed in Case 10.3, where more than 80% of the principals preferred a bonus contract, and both principal and agent received higher payoffs as a result.

In a more recent study, Fehr and Schmidt (2007) investigated the effects of a contract that combined fines with bonuses (stick and carrot), comparing this with a contract that only offered bonuses. It might be thought initially that the combined contract would achieve the best of both worlds, being more general and adding more incentives. However, this was not the finding in their experimental study. Two-thirds of the principals preferred the pure bonus contract, and agents’ payoffs were significantly higher with the pure bonus contract.

In this situation, with both extrinsic and intrinsic incentives in operation in the combined contract, it cannot be argued that a simple crowding out of incentives is occurring here. Fehr and Schmidt propose two possible explanations, which are not mutually exclusive:

1 Threats of fines may be perceived by workers as a hostile act, with the result that negative reciprocity causes them to reduce work effort.

2 Threats of fines may send workers a signal that managers are untrustworthy and may pay a smaller bonus than the workers expect, so they react in a self-fulfilling manner, again reducing their work effort.

Sliwka (2007) arrives at similar conclusions. He proposes that when employers try to control employee behavior by using contracts relying on extrinsic incentives, this affects the behavior of employees by sending a pessimistic signal of distrust being the social norm, which may lead employees to conform to this norm and act selfishly. On the other hand, if employers do not rely on this type of contract, this sends a signal that trust is the social norm, and this may encourage conformist employees to act in a trustworthy manner. Thus the moral of these studies, noted in the previous section, appears to be that people respond to signals regarding the social norm: selfish behavior generates selfishness in others, while trust generates trust. Of course this does not apply to all persons, but it may apply to a majority. However, some caution must be urged with this conclusion, since some studies of single firms have indicated that incentive contracts can increase productivity (Gibbons, 1997; Lazear, 2000; Prendergast, 1999). More research is needed to investigate the precise conditions where incentive contracts may work, and when they are likely to be ineffective or even counter-productive.

Market clearing

According to the standard model markets tend to clear because any shortage or surplus will cause prices to change to eliminate any disequilibrium. Thus, if there is a shortage of shovels after a big snowfall, market forces will cause prices to rise as sellers take advantage of the situation to make additional profit. However, empirical evidence suggests that such an action may be judged unfair; in the survey by Kahneman, Knetsch and Thaler (1986) 82% of subjects responded in this way to this specific situation. Buyers may regard such temporary price rises as ‘gouging’, and boycott the seller in the future. As we have seen, anger and indignation are caused because the offending firm is seen as violating customers’ perceived entitlement to a particular reference price. Some states have laws against ‘gouging’, particularly for essential products like gasoline. In fact, such laws may not be necessary if firms are conscious of likely unfavorable public reactions. An example is given by Olmstead and Rhode (1985), relating to a severe gasoline shortage in California in 1920. SOCal, the dominant supplier, implemented allocation and rationing schemes, with the result that the price was actually lower in California than in the East where there was no shortage. It appears that management at SOCal was concerned about their public image and wanted to appear ‘fair’.

Similar considerations may apply when there are surpluses. Overproduction or seasonal factors, for example, may cause a temporary surplus of a product. Of course durable products may be withdrawn from the market and added to inventory, but there is a cost involved with such action. Rather than reducing the price in this situation, which would reduce the reference price, it may be better or more profitable for a firm to offer a discount. Later, when the surplus has disappeared, the discount may be revoked. Revoking a discount involves less hostile consumer reaction than raising price, since it is merely a case of returning to the previous reference price rather than exceeding it; therefore loss-aversion does not occur to the same extent.

Public goods

The main problem relating to public goods relates to free riding. According to the standard game-theoretic analysis of the standard model it is difficult to prevent free riding unless contributions are enforced by public authorities, usually in the form of taxes of some kind. The reason for this, as we have seen, is that it is the ‘pure’ self-interest of players in such a game situation to defect in terms of not contributing, while it is also in the ‘pure’ self-interest of other players to defect by not punishing free-riders, since punishment involves some type of cost. Behavioral models that incorporate social utility tend to be more optimistic regarding provision of public goods for two reasons:

1 People may contribute out of altruism, ‘pure’ or ‘impure’. They may also contribute because they expect others to contribute, and therefore they are prepared to contribute themselves out of positive reciprocity.

2 People may be prepared to punish others for not contributing. Such punishment may be in the form of ‘whistle blowing’ to the authorities in the case of social benefit fraud. Alternatively it may take the form of social ostracism, for example by yelling at people who throw trash on the street. Although there is a cost in punishing others, in the form of time spent or the threat of violent confrontation, this cost may be outweighed by a positive social utility of imposing negative reciprocity.

The empirical studies of Fehr and Gächter (2000), referred to earlier, and a more recent study by Carpenter et al. (2009), provide confirmation that the opportunity for punishment makes a big difference to the outcome of public goods games. Punishment, of course, does rely on the ability to observe behavior and contributions. The effectiveness of punishment may also depend on the ability to observe who is being punished.

It should be noted that punishment does not have to be in the form of a fine or material loss to be effective. As mentioned earlier in the context of social norms and public policy, ostracism, such as ‘naming and shaming’, may be at least as effective as material losses in deterring free riding (perhaps not the most appropriate term for describing consorting with prostitutes!), and ensuring cooperation. A recent study by Maier-Rigaud, Martinson and Staffiero (2010) supports this conclusion in finding that introducing ostracism increases contribution levels significantly in public goods games, with a net positive effect on the earnings of the group.

10.9 Summary

The standard model is based on the assumption that people are motivated by ‘pure’ self-interest. The main advantage to this model is its simplicity, but there are many empirical anomalies.

Behavioral models are also based on self-interest, but modify and extend this concept to include altruistic and spiteful behavior.

Altruistic behavior relates to behavior that confers a benefit to others, while involving a cost to the originator of the behavior, with no corresponding material benefit. Self-interest is still involved, since there is a psychic benefit.

Spiteful behavior can be viewed as the flip side of altruistic behavior. This is behavior that imposes a cost on others, while also involving a cost to the originator of the behavior, with no corresponding material benefit. Again the benefit is psychic. Such behavior may sometimes be seen as beneficial to society, since it aids the enforcement of social norms.

Game theory is an essential tool of analysis in understanding social behavior. This area of theory is involved when there is a strategic interaction between individuals, meaning that each individual has to consider the reactions of others to one’s own actions, and is aware that others are considering one’s own reactions to their actions.

Fairness must be regarded as a subjective concept not an objective one; different people and cultures have different attitudes towards fairness, and these attitudes can change greatly over time.

All attitudes regarding fairness involve the concept of dual entitlement regarding the transactors. Dual entitlement relates to three main factors: reference transactions, outcomes to the transactors, and the circumstances of changing transaction terms.

Reciprocity is fundamental to the concept of fairness and dual entitlement. In particular, many people are strong reciprocators, meaning that they are prepared to punish defectors at a material cost to themselves.

Experimental games are useful in establishing attitudes towards fairness; examples are ultimatum bargaining games, dictator games, trust games, prisoner’s dilemma games and public goods games. Empirical findings related to these games reveal extensive anomalies in the standard model.

There are three main categories of variable that affect social preferences: methodological and structural, descriptive, and demographic. The first category is particularly important since it relates to variables that can be manipulated experimentally to reveal the key factors involved.

Social norms play a vital part in affecting people’s attitudes regarding fairness and social preferences, and are determined by gene-culture coevolution in a complex environment.

When modeling social preferences, there are two main objectives: explanation and prediction, and a sound psychological basis.

Psychological game theory proposes that utilities are based not just on material payoffs but on beliefs.

Inequality-aversion models are based on the assumption that people are envious of others who have more utility than themselves, but also feel guilty if they have more utility than others.

Reciprocity models are more complex, taking into account how ‘kind’ people judge others to be, and basing their own kindness on the perceived kindness of other players. This approach has a stronger psychological foundation.

Behavioral studies indicate that spiteful preferences are asymmetrical in effect. When they result in punishing defectors they promote cooperation, but when they result in punishing cooperators then they cause cooperation to be reduced.

Consistent contributors, or unconditional cooperators, are vital to the development of a cooperative society. They may survive and prosper in spite of suffering material losses because they send a costly signal of credible commitment, which may result in them receiving rewards in terms of prestige and sexual partnerships.

Evolutionary psychology should not be viewed as an alternative approach to economic models; rather it is complementary to them, helping to lend understanding to the underlying psychological foundation of economic models. The real challenge for EP is to provide precise falsifiable predictions.

Neuroscientific studies support the hypothesis that we, and probably other primates, have areas in the brain that register negative emotions when we feel we have been treated unfairly, and that these negative emotions can result in spiteful preferences.

There are a number of important policy implications of the behavioral approach that differ from the standard model. In particular, these relate to the contrasts between market norms and social norms. If market norms are introduced in decision situations formerly governed by social norms, for example with fines or incentive contracts, this can result in the crowding-out of intrinsic incentives.

10.10 Review questions

1 What are social preferences?

2 What factors are relevant in determining the fairness of a transaction?

3 Explain the term ‘strong reciprocity’, and why it is an important concept.

4 Explain the differences between the Fehr–Schmidt and Bolton–Ockenfels models of inequality aversion.

5 Explain the difference between inequality-aversion models and reciprocity models. 6 Explain what is meant by the crowding-out of intrinsic incentives, giving two examples. 7 Explain the features of psychological game theory, giving two examples of situations where it is relevant.

8 What do behavioral studies indicate regarding inequality-aversion models versus reciprocity models in terms of explanation and prediction?

9 What is meant by costly signaling theory? What may it help to explain?

10 In what way are spiteful preferences asymmetrical?

11 Explain why the difference between social norms and market norms is important for public policy. What sort of mistakes do governments tend to make in this regard?

12 What do empirical studies indicate regarding the use of incentive contracts in the labor market?

10.11 Applications

The first case involves a detailed examination of the empirical findings regarding the Wason Test and the implications. This is designed to give the reader a better understanding of the role of evolutionary psychology. The other cases involve various policy implications of social preferences.

Case 10.1 The Wason Test

One of the main themes in this book is that the human brain is a highly fallible machine, but is fallible in certain predictable ways due to the manner in which it evolved. For example, we have seen that we tend to be bad at calculating and using probabilities, but work much better when probabilities are expressed in terms of frequencies. Similarly, the human brain is often bad at performing logic. Logic refers to inferring the truth of one statement from the truth of other statements based only on their form, not their content. A standard example that is normally used relates to the following reasoning: P is true, P implies Q, therefore Q is true. Being based on form rather than content, logic is not empirically based. Thus it does not matter what P means; to use the example of Pinker (1997), P could be ‘my car has been eaten by rats’.

Why do so many tests show that people are bad at problems involving logic? One factor concerns the ambiguity of certain logical words. For example, the word ‘or’ can either mean ‘and/or’, as in A or B or both, or it can mean ‘exclusive or’, as in A or B, but not both. The correct or intended meaning can only be inferred from the context, so our knowledge of the empirical world becomes relevant. For example, when we see a restaurant advertising ‘a free soda or hot beverage with your meal’, we immediately understand the ‘or’ in this context to mean ‘exclusive or’; we can have either a soda or hot beverage, but not both.

The psychologist Peter Wason was particularly interested in Popper’s criterion of scientific hypotheses, that they should be falsifiable. He wondered whether everyday learning was in fact hypothesis testing, in terms of looking for evidence that contradicts a hypothesis. In 1966 he devised a test that was designed to see how people perform when it comes to falsifying hypotheses. This well-known test can be described as follows. A set of four cards has letters on one side and numbers on the other. The objective is to test the rule ‘if a card has D on one side, it has a 3 on the other side’, in other words a simple P-implies-Q statement. Subjects are shown four cards, as in Figure 10.3, and are asked which ones they would have to turn over to see if the rule is true.

Figure 10.3 Wason Test

A hypothesis of the form ‘If P then Q’ is violated only when P is true and Q is false. This means that the first and the fourth cards must be turned over. However in numerous tests over the last 40 years only about 10% of subjects select the right cards. Most subjects pick either just the first card or the first and third cards. It should be seen that picking the third card cannot falsify the hypothesis; if the reverse side is not-D, this does not constitute a falsification, since the hypothesis does not say that only D cards have a 3 on the other side. Furthermore, the ambiguity factor mentioned above cannot account for the observed findings. If people interpreted the hypothesis as ‘if D then 3 and vice versa’, they would have to turn over all four cards.

According to Cosmides and Tooby (1992) the results can be explained in terms of evolutionary psychology: humans have not evolved to solve abstract logical problems, but rather to respond to problems structured as social exchanges when they are presented in terms of costs and benefits. More specifically, we have evolved to detect cheaters in social contract situations. A cheater can be defined as a person who receives a benefit without paying a cost (i.e. a free rider). They supported this hypothesis by performing a number of Wason-like tests with subtly designed variations. The basic variation was to pose the situation where the subject was a bouncer in a bar: their job is to eject under-age drinkers (cheaters). The problem can be posed logically as ‘if a person is drinking alcohol, they must be over 18’. In general terms this is again an ‘if P then Q’ statement, where P refers to drinking alcohol and Q refers to being of a legal age. The four cards in this case appear as shown in Figure 10.4.

Figure 10.4 Wason Test in terms of a social contract

Given the test in this form the vast majority of subjects (about 75%) picked the correct first and fourth cards, even though the logic is identical with the original problem. However, it should be noted that the Cosmides and Tooby hypothesis regarding social contracts is not the only explanation of these findings. There are two main alternative theories: availability and facilitation theories.

1 Availability theory

Although this theory comes in different forms, they all essentially argue that framing the logic of the problem in terms of a familiar real-world situation rather than in abstract terms accounts for the difference in performance. Therefore, Cosmides and Tooby performed various other experiments to test this alternative hypothesis.

The first kind of experiment involved using familiar real-world situations that did not involve social contracts. For example, subjects were asked to test the statement ‘if a person travels to Boston, then he takes a subway’. Performance on such descriptive/ causal tests was better than on the abstract form of the problem, with 48% of subjects responding correctly, but it was still well below the level of performance on the social contract version of the test. Furthermore, even when the social contract was expressed in unfamiliar terms, such as ‘if a man eats cassava root, he must have a tattoo on his face’, performance was still higher than in descriptive situations.

2 Facilitation theory

This essentially states that social contracts facilitate logical reasoning. The results of the experiments described above could still be explained by the fact that the correct answer in terms of evolutionary adaptation also happens to be the logically correct answer. In order to test this theory Cosmides and Tooby devised an experiment with a ‘switched’ form of social contract. In the standard form, a social contract can be expressed as ‘if the other party takes the benefit, then it pays the cost’; in switched form the contract becomes ‘if the other party pays the cost, then it takes the benefit’. For example, the same social contract is expressed in the following two statements:

If you give me your watch, I’ll give you $20 (standard form).
If I give you $20, you give me your watch (switched form).

In the first statement, from your point of view, taking the benefit (me receiving the watch) constitutes the logical category P, whereas in the second statement it relates to Q. However, in either case cheating (from your point of view) means that I receive the watch without paying you the $20. This experiment is represented in Figure 10.5.

Figure 10.5 Wason Test in terms of a switched social contract

In the standard social contract the first and fourth cards should again be selected, since they are required in order to detect cheating, and they also happen to be the logically correct answer. However, in the switched form of the contract, the logically correct answer involving P and not-Q means selecting the second and third cards. Thus there is a difference between the solution for cheater detection (first and fourth cards) and the logically correct solution, and it is this factor that allows the facilitation theory to be tested. It should be noted that EP supports the cheater detection hypothesis, since consistently altruistic persons who pay the cost without receiving a benefit would not have been likely to survive in our evolutionary past; there would thus have been no selection pressure for ‘altruist detection’, unlike the strong pressure for cheater detection.

Cosmides and Tooby found that, when presented with the switched form of social contract, about 70% of subjects gave the valid solution for cheater detection but logically incorrect answer. This result validates the prediction arising from EP, that we are not attuned to detect altruistic, or foolish, acts such as people paying costs and not receiving benefits in the same way that we are attuned to detecting cheaters. Other experiments by the same authors have confirmed these findings.

It is clear from the above example that the concept of cheating depends on whose perspective is taken, mine or yours. Gigerenzer and Hug (1992) utilized this difference in perspective to conduct further tests of facilitation theory against the cheater detection theory of Cosmides and Tooby. They asked subjects to test the statement ‘if an employee gets a pension, then that employee must have worked for the firm for at least 10 years’ (p. 155). The subjects were divided into two groups, one being told they were the employer and the other being told that they were the employee. For employers providing a pension is a cost, whereas getting the pension is a benefit to the employee. Likewise, working for at least ten years is a benefit to the employer but a cost to the employee. The situation is shown in Figure 10.6, assuming a standard form of contract where the logical construct P corresponds to the other party receiving the benefit.

Figure 10.6 Wason Test in terms of different perspectives

Thus, each group defined cheating in a different way: for employers cheating constituted paying a pension without the employee working for ten years (P and not-Q). However, for employees cheating relates to working for at least ten years and not being paid a pension (Q and not-P). The logically correct answer for either group is ‘P and not-Q’, as always, since this is independent of content or perspective. Facilitation theory predicts no difference between the two groups regarding the proportion of correct responses, while the cheater detection hypothesis predicts a higher correct response rate from the employer group. Gigerenzer and Hug found that for the employer group about 75% gave the correct ‘P and not-Q’ response, with a negligible proportion responding with ‘not-P and Q’. However, for the employee group, only about 15% gave the logically correct response, with about 60% giving the incorrect, but cheater-detecting, response ‘not-P and Q’. These results provide another strong vindication of the cheater detection hypothesis.

Questions

1 Give examples of familiar and unfamiliar social contracts. What does the cheater detection hypothesis predict regarding responses testing the breaking of such contracts?

2 Explain why using the switched form of social contract is a useful way of testing facilitation theory against the cheater detection hypothesis.

3 Explain why the use of different perspectives is a useful tool in testing the cheater detection hypothesis.

4 Explain why evolutionary psychology predicts cheater detection much better than altruist detection.

Case 10.2 Public goods and free riding

We have already seen that the provision of public goods presents problems in the standard model, both because people are unwilling to contribute, and because they are unwilling to punish other non-contributors due to the cost involved. This case study examines the results of a series of public goods experiments by Fehr and Gächter (2000), showing how reciprocity, both positive and negative, affects the situation.

The basic form of the experiment involves a group of four members, each of whom is given 20 tokens. All four people decide simultaneously how many tokens to keep for themselves and how many tokens to invest in a common public good. For each token that is privately kept there is a return of the same amount. For each token that is invested in the public good each of the subjects earns 0.4 tokens, regardless of whether they have contributed or not. Thus the private return for investing a token is 0.4 tokens, while the social return is 1.6 tokens (since there are four players). According to the standard model nobody will want to invest in the public good in this situation, since it is more profitable to keep the tokens privately (i.e. defect), and therefore each individual player will earn 20 tokens altogether. However, we can see that this is in effect a multi-player PD situation. If all the players cooperate, with each one contributing all their tokens to the public good, they will each end up with a return of 32 tokens (it is assumed in the simple model that there are constant returns to investment). This optimal solution cannot ever be an equilibrium in the standard model.

If we now introduce positive reciprocity into the model, this means that players are willing to contribute if others are also willing to contribute. However, in order to sustain such contributions there has to be a high proportion of players with such a motivation. In reality we know that there is a significant proportion of people who are motivated by pure self-interest, and this makes it difficult to achieve an equilibrium with positive contributions.

How does introducing negative reciprocity affect the situation? In this case negative reciprocity means retaliating against defectors or non-contributors who are free riding. In the simplest version of the game the only form retaliation can take is to free ride also. This punishes everyone else, whether they are free riding or not. Thus people may free ride either out of pure self-interest or because they are demonstrating negative reciprocity. The result is that negative reciprocity is even more likely to lead to a solution where there are no positive contributions, since ‘selfish’ players are inducing reciprocal players to defect.

This situation changes radically if players can observe the contributions of others, and punish specifically those who do not contribute. The experiment can be modified so that players can reduce the number of tokens of any other player, at a cost of 1/3 token for every token reduced. It is important to impose a cost here, not only for realism, but also because this allows a distinction to be made between ‘selfish’ players and reciprocal players. Selfish players will never be willing to punish others because of the cost involved, and the punishment opportunity will not affect the outcome of the game. However, those players with negative reciprocity may be willing to punish free riders, and this in turn may induce selfish players to cooperate and contribute. Thus the end result may be the opposite of that achieved without the punishment opportunity, with reciprocal types ensuring general cooperation rather than selfish types ensuring general defection.

In the experiments performed by Fehr and Gächter (2000) the various forms of the game described above were used, using two versions. One version was called the ‘Perfect Stranger’ version; this involved 24 subjects formed into 6 groups of 4 players each, with the game being repeated 6 times. Every time the game was repeated the groups were shuffled, so that no player ended up playing with any other more than once. This ensures that people treat the game as essentially a ‘one-shot’ game, so that their actions have no consequences for later games. In the ‘Partner’ version, on the other hand, the same four players played ten times; thus this was a ‘repeated’ game, where actions in one time period could have consequences in later periods. Both versions of the game were implemented with and without the punishment opportunity, and all interactions were anonymous. Where applicable, the punishment in each period occurred after observing the contributions in that period.

The results of the experiments are illustrated in Figure 10.7. NP refers to the ‘no punishment’ version, while WP refers to the version with punishment.

Figure 10.7 Evolution of cooperation in public goods game

Questions

1 Interpret the graph in terms of cooperation in the absence of a punishment opportunity.

2 Explain how the opportunity for punishment affects the development of cooperation.

3 What are the implications of the above findings as far as public policy is concerned?

4 Explain how public goods games are affected when free riders punish cooperators.

Case 10.3 Sales force compensation

The issue of determining the optimal structure for sales force compensation essentially involves a sequential game between manager and salesperson. It is an example of the principal-agent problem. The essential problem for the manager (as principal) is that, if the effort of the salesperson (as agent) cannot be contracted on or is not fully observable, a self-interested salesperson will always shirk, assuming that effort is costly. Therefore the manager has to design a contract that prevents moral hazard, or post-contract opportunism by the salesperson. The situation is complicated by inequality-aversion and reciprocity, which allows us to test the standard model against a behavioral model incorporating social preferences. If salespeople feel guilt about shirking, or repay kindness with reciprocal effort, they will not shirk as often as pure self-interest and the standard model would predict.

Fehr, Klein and Schmidt (2004) therefore propose a contract involving a bonus scheme (BC) as being more effective than a standard incentive contract that imposes a penalty for shirking (IC). The parameters of the situation are modeled as follows:

c(e) = f(e) cost of salesperson’s effort is a function of the level of effort, with rising marginal cost from 1 to 4 in the permissible range of e (1 to 10). This is shown in Table 10.6.

Table 10.6 Effort costs for salesperson

In the first stage the manager offers contract; in the second stage the salesperson decides whether to accept or reject. If they accept they receive w immediately, and choose effort e in the third stage. In the fourth and final stage the manager observes effort e accurately, and may impose a penalty in the IC or award a bonus in the BC.

Under the IC: effort can be monitored at the cost of K

w = g(e*, f ) where w = wage offered, e* is effort demanded, and f = penalty for being caught shirking, meaning that e < e* Probability of monitoring technology working = 1/3

Under the BC: w = h(e*, b*) where w = wage offered, e* is effort demanded, and b* = promised bonus for salesperson

neither e* nor b* are binding; the manager may award a bonus either greater or

less than b*.

The expected payoffs for both manager and salesperson can now be calculated for each contract.

Note that the bonus here is not necessarily the promised bonus of b*.

There is a large gain from exchange here if the salesperson gives high effort, because the marginal gain to the manager of a unit of effort is 10, while the marginal cost to the salesperson is only 1 to 4 units. Therefore the optimal outcome is for the manager not to invest in the monitoring technology and for the salesperson to choose e = 10, giving a combined surplus of 10 × e – c(e) = 80, since the cost of e = 10 is 20. However, this is not an equilibrium outcome.

Under the IC the optimal contract would be (w = 4, e* = 4, f = 13), resulting in π_M = 26 and π_S = 0.

Under the BC the purely selfish manager will never pay a bonus in the last stage, and the salesperson, knowing this, will only supply the minimum work effort, e = 1. Thus the optimal contract will be (w = 0, e* = 1, b*= 0), resulting in π_M = 10 and π_S = 0.

Under the above conditions managers will always choose the IC over the BC, according to the standard model. This is basically saying that, if managers realize that salespeople do not expect to get bonuses and are therefore likely to shirk, it is better to use an IC and set the demanded level of work at a moderate level, enforced by a probabilistic fine.

However, when Fehr, Klein and Schmidt (2004) tested this model empirically in an experiment, the results did not support the standard model. The investigators asked a group of subjects to act as managers and choose either a BC or IC. They then had to make offers to another group of subjects acting as salespeople, who then chose their level of effort. Managers chose the BC 88% of the time, and salespeople reciprocated by supplying a greater effort than necessary. Managers in turn reciprocated by paying higher bonus payments. As a result of the greater effort, payoffs to both manager and salesperson were higher under the BC than under the IC. The study concluded that the empirical findings supported the FS inequality-aversion model described earlier.

Questions

1 Explain how the empirical results could be interpreted as supporting the inequality-aversion model as far the behavior of the subjects was concerned.

2 The inequality-aversion model predicts that there will be a pooling equilibrium for managers under the BC, with both purely selfish and fair-minded managers offering the same wage. Why would this happen?

3 The inequality-aversion model predicts that fair-minded salespersons will put in less effort than purely selfish ones under a BC. Why would this happen?

4 What tends to happen when incentive contracts are combined with bonus contracts?

Case 10.4 Too much virtue is a vice

Selfishness is not a good way to win friends and influence people. But selflessness, too, is repellent. That, at least, is the conclusion of a study by Craig Parks of Washington State University and Asako Stone, of the Desert Research Institute in Nevada. Dr Parks and Dr Stone (2010) describe, in the Journal of Personality and Social Psychology, how and why the goody two-shoes of this world annoy everyone else to distraction.

In the first of their experiments they asked the participants – undergraduate psychology students – to play a game over a computer network with four other students. In fact, these others (identified only by colours, in a manner reminiscent of the original version of the film, The Taking of Pelham 123) were actually played by a computer program.

Participants, both real and virtual, were given ten points in each round of the game. They could keep these, or put some or all of them into a kitty. The incentive for putting points in the kitty was that their value was thus doubled. The participant was then allowed to withdraw up to a quarter of the points contributed by the other four into his own personal bank, while the other four ‘players’ did likewise. The incentive to take less than a quarter was that when the game ended, after a number of rounds unknown to the participants, a bonus would be given to each player if the kitty exceeded a certain threshold, also unspecified. When the game was over the points were converted into lottery tickets for meals.

The trick was that three of the four fake players contributed reasonably to the kitty and took only a fair share, while the fourth did not. Sometimes this maverick behaved greedily, because the experiment had been designed to study the expected ostracism of cheats. As a control, though, the maverick was sometimes programmed to behave in an unusually generous way.

After the game was over, the participants were asked which of the other players they would be willing to have another round with. As the researchers expected, they were unwilling to play again with the selfish. Dr Parks and Dr Stone did not, however, expect the other result – that participants were equally unwilling to carry on with the selfless.

Follow-up versions of the study showed that this antipathy was not because of a sense that the selfless person was incompetent or unpredictable – two kinds of people psychologists know are disliked in this sort of game. So the researchers organised a fourth experiment. This time, once the game was over, they asked the participants a series of questions designed to elucidate their attitudes to the selfless ‘player’.

Most of the responses fell into two categories: ‘If you give a lot, you should use a lot’, and ‘He makes us all look bad.’ In other words, people were valuing their own reputations in the eyes of the other players as much as the practical gain from the game, and felt that in comparison with the selfless individual they were being found wanting. Too much virtue was thus seen as a vice. Perhaps that explains why so many saints end up as martyrs. They are simply too irritating.

Source: The Economist, August 19, 2

Questions

1 What is meant in the study by being ‘over-generous’?

2 Why can we find over-generous people irritating?

3 Outline the different behavioral factors that are relevant in this case study.