Cambridge Handbook of Experimental Political Science

Chapter 7 Experiments and Game Theory's Value to Political Science

In recent decades, formal models have become common means of drawing important inferences in political science. Best practice formal models feature explicitly stated premises, explicitly stated conclusions, and proofs that are used to support claims about focal relationships between these premises and conclusions. When best practices are followed, transparency, replicability, and logical coherence are the hallmarks of the formal theoretic enterprise.

Formal models have affected a broad range of scholarly debates in political science – from individual-level inquiries about why people vote as they do, to large-scale studies of civil wars and international negotiations. The method's contributions come when answers to normative and substantive questions require precise understandings about the conditions under which a given political outcome is, or is not, consistent with a set of clearly stated assumptions about relevant perceptions, motives, feelings, and contexts. Indeed, many formal modelers use mathematics to sort intricate and detailed statements about political cause and effect by the extent to which they can be reconciled logically with basic premises about the people and places involved.

Formal models in political science have been both influential and controversial. Although no one contends that explicitly stated assumptions or attention to logical consistency are anything other than good components of scientific practice, controversy often comes from the content of formal models themselves. Many formal models contain descriptions of political perceptions, opinions, and behaviors that are unrealistic. Some scholars, therefore, conclude that formal models, generally considered, are of little value to political science. Yet, if we can offer a set of premises that constitutes a suitable analogy for what key political actors want, know, and believe, then we can use formal models to clarify conditions under which these actors will, and will not, take particular actions.

In this chapter, we address two questions that are particularly relevant to debates about formal models’ substantive relevance. We present each question in turn and, in so doing, explain how experiments affect the value of formal modeling to political science.

One question is, “Will people who are in the situations you describe in your model act as you predict?” This question is about the internal validity of a model. Experiments permit the creation of a specialized setting in which a model's premises can be emulated, with the test being whether the experiment's subjects behave as the model predicts (akin to physicists studying the action of falling objects in a laboratory-created vacuum and thus as free from air resistance as possible). Lupia and McCubbins (1998, chapter 6), for example, devote an entire chapter of their book to pinpointing the correspondence between the experimental settings and the models that the experiments were designed to evaluate. Furthermore, if a modeler wants to claim that a particular factor is the unique cause of an important behavior, then he or she can design treatments that vary the presence of the presumably unique causal factor. If the focal behavior is observed only when the presumed factor is present, then he or she will have greater evidence for his or her claim. Generally speaking, this way of thinking about the role of experiments in formal theoretic political science is akin to Roth's (1995) description of experiments as a means of “speaking to theorists” (22).

A second question is, “Are your theoretical predictions representative of how people will act in more realistic circumstances?” This question speaks to the ecological validity of models and is akin to Roth's (1995) description of experiments as “whispering in the ears of princes” (22). Experimental designs that address these questions should incorporate elements that audiences would see as essential to proffering a substantive explanation, but that are not necessarily included in the model. Cross-national experiments are an example of designs that address such concerns. As Wilson and Eckel's chapter in this volume explains, for models whose predictions are not culture specific, it is important to evaluate whether experimental subjects in different regions or countries will really play given games in identical ways. When experiments reveal cross-cultural differences, theorists who desire broadly applicable conclusions can use these findings to better integrate cultural factors into their explanations.

Indeed, a key similarity between what formal modelers and experimentalists do is that neither simply observes the environments they want to explain. Instead, both seek to create settings that emulate the environments. When used in tandem, formal models can help experimentalists determine which settings are most critical to a particular causal hypothesis and experimenters can inform formal modelers by evaluating their theoretical predictions’ performance in relevant environs.

Given the emphasis on logical precision in formal modeling, it is also worth noting that many model-related experiments follow practices in experimental economics, which includes paying subjects for their participation as a means of aligning their incentives with those of analogous actors in the formal models. As Palfrey (2007a) explains,

[R]esearchers who were trained primarily as [formal] theorists – but interested in learning whether the theories were reliable – turned to laboratory experiments to test their theories, because they felt that adequate field data were unavailable. These experiments had three key features. First, they required the construction of isolated (laboratory) environments that operated under specific, tightly controlled, well-defined institutional rules. Second, incentives were created for the participants in these environments in a way that matched incentives that existed for the imaginary agents in theoretical models. Third, the theoretical models to be studied had precise context-free implications about behavior in any such environment so defined, and these predictions were quantifiable and therefore directly testable in the laboratory. (915)

For formal modelers, these attributes of experimentation are particularly important because a comparative advantage of formal theoretic approaches is precision in causal language.

In the rest of this chapter, we highlight ways in which experiments have affected the value of formal modeling in political science. Because the range of such activities is so broad, we focus our attention on a type of formal modeling called “game theory.” Game theory is a way of representing interpersonal interactions. Premises pertain to specific attributes of individual actors and the contexts in which people interact. Conclusions describe the aggregate consequences of what these actors do, or the properties of the individuals themselves, that result from interactions among the actors.

The next two substantive sections of this chapter pertain to the two main types of game theory, respectively. Section 1 focuses on experiments in the domain of cooperative game theory. Political scientists have used cooperative game theory to address key theoretical and normative debates about preference aggregation and properties of common decision rules. As the first game-theoretic experiments in political science tested results from cooperative game theory, many of the standard protocols of experimental game theory were developed in this context. Section 2 focuses on experiments in the domain of noncooperative game theory. Most game-theoretic treatments of political science topics today use some form of noncooperative game theory. This type of theory can clarify how actors pursue their goals when they and those around them have the ability to perceive and adapt to important attributes of their environment. Influential models of this kind have clarified how institutions affect individual choices and collective outcomes, and how strategic uses of communication affect a range of important political outcomes.

In the conclusion, we speak briefly about how experiments may affect future relationships between formal modeling and political science. We argue that, although the psychological realism of many current models can be questioned, research agendas that integrate experimental and formal modeling pursuits provide a portal for more effective interdisciplinary work and can improve the applicability and relevance of formal models to a wide range of important substantive questions in political science.

1. Cooperative Game Theory and Experiments

Game theory is often divided into cooperative and noncooperative game theory, and it is true that most results can be fit into one or the other division. However, both formal definitions are at the extreme points on a continuum, and thus virtually the entire continuum fits in neither category very precisely. The basic distinction is that in cooperative game theory, coalitions may be assumed to form, whereas in noncooperative game theory, any coalitions must be deduced from the model itself rather than assumed a priori. In the early days of game theory, which we can mark from the publication of Von Neumann and Morgenstern (1944) to approximately the late 1970s, when the Nash-Harsanyi-Selten revolution in noncooperative game theory carried the day (and won them a Nobel prize in 1994), this now-critical distinction was much less important. Theoretical results, for example, were not often identified as one or the other, and theorists (including Nash [1997]) moved back and forth across this division easily.

This early blurring of the distinction between the two is relevant here because experimental game theory began very early in the history of game theory, and experiments would at times include and intermingle results from cooperative and noncooperative game designs. This is perhaps most evident in the truly vast experimental literature on prisoner's dilemma (PD) games. The PD played an important role in game theory from the beginning because it was immediately evident that the strong prediction of rational players both (or all) defecting with or without communication being possible was simply empirically false. Whether presented as a teaching device in an introductory undergraduate course or tested in the most sophisticated experimental setting, people simply do not follow the predictions of game theory (particularly noncooperative game theory) in this regard. Therefore, game theorists naturally turned to experimentation to study play by actual players to seek theoretical insight (see, e.g., Rapoport and Chammah [1965] for a review of many early PD game experiments). This case is thus very similar to the experimental work on the “centipede game,” which is discussed in Section 2, in that both endeavors led scholars to question key assumptions and develop more effective modeling approaches.

Coalition Formation

As noted, game theorists conducted experiments from the earliest days of game theory (see, e.g., Kalish et al. [1954], on which John Nash was a coauthor). A common application was to the question of coalitions. Substantively, Riker (1962) argued for the centrality of coalitions for understanding politics. Theoretically, cooperative game theory was unusually fecund, with a diverse set of n-person games and many different solution concepts whose purposes were to characterize the set of coalitions that might form.

This set of solution concepts has three notable attributes. First, one concept, called the core, had the normatively attractive property that outcomes within it did not stray too far from the preferences of any single player. In other words, the core was a set of outcomes that were preferred by majorities of voters and not easily overturned by attempts to manipulate voting agendas. Unfortunately, such core outcomes have the annoying property of not existing for a very large class of political contexts. As Miller's chapter in this volume details, the general nonexistence of the core raises thorny normative questions about the meaning and legitimacy of majority decision making. If there is no structure between the preferences of individuals and the choices that majority coalitions make, then it becomes difficult to argue that preference-outcome links (e.g., the will of the majority) legitimate majority decision making.

To address these and other normative concerns, scholars sought other solution concepts that not only described coalitional choices in cases where the core did not exist, but also retained some of the core's attractive properties. Second, theorists often developed these alternate concepts by adding assumptions that did not flow from the basic concepts of game theory as it was known at the time. It is fair to say, from a game-theoretic perspective, that many of the new assumptions needed to characterize coalition behavior were simply arbitrary. Third, many of these new ways of characterizing coalition behaviors offered vague (as in many outcomes predicted) or unhelpful (as in nonexistent) conclusions. Moreover, the diverse set of solution concepts often had overlapping predictions, making it difficult to distinguish between them in observational data.

So, although the multiplicity of solution concepts was part of an effort to clarify important attributes of coalition behavior, an aggregate consequence of such efforts was more confusion. Given his interest in the topic, and his substantive claim of the centrality of coalitions to politics, it is not surprising that the first published attempt to simulate a game-theoretic context in a laboratory setting was by William Riker (1967; Riker and Zavoina 1970). These simulations were important for several reasons. First, they established what became a standard protocol for conducting game-theoretic experiments. Preferences were typically induced by money. Communications between players were either controlled as carefully as possible by the experimenter or else were carefully and, as far as technology permitted, fully recorded. Assumptions were built into the research design to mimic the assumptions of the solution concept being examined. Behaviors were closely observed, with the observational emphasis being on whether the coalitions chosen were consistent with the concept or concepts being tested. Lessons learned were also reported in the text. For example, Riker discovered that students learned that they could, in effect, deceive the experimenter by agreeing outside (and in advance) of the simulation to exchange their university's food cards as a way of reaching binding agreements. This outcome taught the lesson that not only is the repeated use of the same subjects potentially problematic, but also that subjects – and therefore, at least potentially, people in real situations – will devise strategies to make binding commitments even when the situation precludes them formally.

The proliferation of solution concepts, such as those we describe, motivated many interesting and important extensions to the setting. With so many overlapping predictions, observational data were often of little help in selecting among competing accounts. For example, where Riker (1962) developed a theory of minimal winning coalitions, virtually every other cooperative solution concept that focused on coalition formation was also consistent with the observation of minimal winning coalitions. This overlap made it difficult to distinguish the power of various solution concepts. Riker's research designs varied the construction of subject preferences – preferences that one could induce with money – to distinguish competing causal mechanisms. These distinctions, in turn, clarified which solution concepts were and were not viable in important cases. By this careful construction, Riker could distinguish through lab design what was difficult to distinguish in real-world settings.

McKelvey and Ordeshook's research also captured theorists’ attention; they developed one of the last cooperative game-theoretic solution concepts, called the “competitive solution” (McKelvey and Ordeshook 1978, 1979, 1980, 1983; McKelvey, Ordeshook, and Winer 1978; Ordeshook 2007). They were very interested in evaluating their concept experimentally vis-à-vis other solution concepts. Their 1979 paper reports on a series of experiments that was able to establish predictive differences among nine solution concepts (some of which had noncooperative game-theoretic elements). In particular, they used the data to proffer statistical estimates of likelihoods that revealed support for two of the concepts (theirs and the minimax set of Ferejohn, Fiorina, and Packel [1980]), while effectively rejecting the other seven.

McKelvey and Ordeshook (1979) ended their paper with a conclusion that would turn out to be prescient. They write, “Finally, we cannot reject the hypothesis that [the competitive solution] succeeds here for the same reason that [other solutions] receive support in earlier experiments entailing transferable utility – namely that [the competitive solution's] predictions correspond fortuitously to some more general solution notion” (165). To see why this statement is prescient, it is important to note that the experimental protocol was developed to allow researchers to evaluate various solution concepts on the basis of coalition-level outcomes. The solution concepts they evaluated, however, derived their conclusions about coalition-level outcomes from specific assumptions regarding how players would actually bargain. McKelvey and Ordeshook soon began to use their experimental protocol to evaluate the status of these assumptions (i.e., the experiments allowed them to observe how subjects actually bargained with one another). In another of their papers (McKelvey and Ordeshook 1983), they reported on experiments that once again produced the results predicted by their competitive solution. However, they also observed players bargaining in ways that appeared to violate the assumptions of the competitive solution. Such observations ultimately led them to abandon the competitive solution research agenda for many years (Ordeshook 2007) and to devote their attention to other explanations of collective behavior (see Section 2 of this chapter, as well as Morton and Williams’ chapter in this volume, for descriptions of that work).

This idea of using the lab setting as a way of sorting among solution concepts reached an apogee in Fiorina and Plott (1978), in which they develop sixteen different sets of theoretical predictions. Some are from cooperative game theory and others from noncooperative game theory. Some focus on voting, whereas others focus on agenda control. Some are not even based in rational actor theories. The beauty of their use of the lab setting (and their own creativity) is that they are able to design experiments that allow for competing tests between many of the pairs of theories, and sometimes tests that uniquely discriminate one account from virtually all others. In addition to differentiating outcomes in this way, they examined the effect of varying treatments – in particular, whether the payoffs were relatively high or low to the players and whether there was open exchange of communication or no communication at all among the players.

They found that when there is a core (a majority-preferred outcome that is not easily undone by agenda manipulation), it is almost always chosen. High payoffs yielded outcomes even closer to those predicted points than lower payoffs, and, to a much lesser extent, communication facilitated that outcome. Comparing these outcomes to those where no core exists allows the authors to conclude more sharply that it is indeed the existence of a core that drives the results. In contrast, the absence of a core also yielded an apparent structure to the set of coalition-level outcomes rather than an apparently unpredictable set of results, as might have been expected by some readings of McKelvey's (1976) and Schofield's (1978) theoretical results about the unlimited range of possible outcomes of majority decision making in the absence of a core. Rather (as, indeed, McKelvey argued in the original 1976 article), there seems to be structure to what coalitions do, even in the absence of a core. Hence, the correspondence between individual intentions and coalition-level outcomes in the absence of a core is not totally chaotic or unstable, and this correspondence provides a basis for making normatively appealing claims about the legitimacy of majority rule (see Frohlich and Oppenheimer [1992] for a broader development of links among models, experiments, and important normative considerations). However, these structures, although observed by Fiorina and Plott (1978), were not the result of any theory then established. Hence, one of the lasting contributions of the work by Fiorina and Plott, as is true of the other work described in this section, is that it set the stage for other experiments on political decision making, such as those discussed in Section 2 and by Morton and Williams’ chapter in this volume.

2. Noncooperative Game Theory and Experiments

Noncooperative game theory is a method of formal modeling that allows researchers to draw logically transparent conclusions about how individuals adapt and react to the anticipated strategic moves of others. It uses the Nash equilibrium concept, or well-known refinements of the concept, as a criterion for identifying behavioral predictions. In recent decades, noncooperative games using the extensive form have been formal modelers’ primary instrument in attempting to make contributions to political science. The extensive form outlines, in order, the decisions to be reached, actor by actor, from the opening move to the final outcome. It thus offers a rich perspective for analyzing strategic decision making, as well as the roles of beliefs and communication in decision making. These games have informed our discipline's attempts to clarify the relationship among political institutions, individual choices, and collective outcomes. They have also been the means by which scholars have examined positive and normative implications of the strategic use of information (see Austen-Smith and Lupia [2007] for a recent review). As the field evolves, these games increasingly serve as a portal through which implications of substantive premises from fields such as economics and psychology can become better understood in political contexts.

Key moments in the evolution of such understandings have been experimental evaluations of these games. In this section, we review three examples of where the combination of noncooperative game-theoretic models and experiments has produced new insights about important social scientific matters. The examples are voter competence, jury decision making, and the centipede game.

Voter Competence

A conventional wisdom about mass politics is that candidates and their handlers seek to manipulate a gullible public and that the public makes inferior decisions as a result (see, e.g., Converse 1964). In recent decades, scholars have used formal models and experiments in tandem to examine when seemingly uninformed voters do – and do not – make inferior decisions. In this section, we review two examples of such work. In each case, scholars use formal models to understand whether claims about the manipulability of voters are, and are not, consistent with clearly stated assumptions about voters’ and candidates’ incentives and knowledge. Experiments then clarify the extent to which subjects will act in accordance with focal model predictions when they are placed in decision-making environments that are similar to the ones described in the models.

McKelvey and Ordeshook (1990) focus on a spatial voting model in which two candidates compete for votes by taking policy positions on a unidimensional policy space. Voters have spatial preferences, which is to say that they have an ideal point that represents the policy outcome they most prefer. A voter in these models obtains higher utility when the candidate whose policy preference is closest to his or her ideal point is elected.

If the game were one of complete information, then the outcome would be that both candidates adopt the median voter's ideal point as their policy preference and the median voter's ideal point becomes the policy outcome (Black 1948). The focal research question for McKelvey and Ordeshook (1990) is how such outcomes change when voters know less. To address these questions, they develop a model with informed and uninformed voters. Informed voters know the policy positions of two candidates. Uninformed voters do not, but they can observe poll results or interest group endorsements. McKelvey and Ordeshook examine when uninformed voters can use the polls and endorsements to cast the same votes they would have cast if completely informed.

In the model's equilibrium, voters make inferences about candidate locations by using poll results to learn how informed voters are voting. Uninformed voters come to correctly infer the candidates’ positions from insights such as “if that many voters are voting for the [rightist candidate], he can't be too liberal.” McKelvey and Ordeshook (1990) prove that the greater the percentage of informed voters represented in such polls, the more quickly uninformed voters come to the correct conclusion about which candidate is closest to their interests.

McKelvey and Ordeshook (1990) evaluate key aspects of their theoretical work experimentally. As Palfrey (2007a, bracketed caveat inserted by authors) reports,

Perhaps the most striking experiment…used a single policy dimension, but candidates had no information about voters and only a few of the voters in the experiments knew where the candidates located. The key information transmission devices explored were polls and interest group endorsements. In a theoretical model of information aggregation, adapted from the rational expectations theory of markets, they proved that this information alone [along with the assumption that voters know approximately where they stand relative to the rest of the electorate on a left-right scale] is sufficient to reveal enough to voters that even uninformed voters behave optimally – i.e., as if they were fully informed. (923)

Of course, uninformed voters in the McKelvey-Ordeshook (1990) model do not cast informed votes in all circumstances. The caveat inserted into the Palfrey quote highlight key assumptions that contribute to the stated result. However, it is important to remember that the conventional wisdom at the time was that uninformed voters could seldom, if ever, cast competent votes – where competence refers to whether a voter casts the same vote that he or she would have cast if he or she possessed full information about all matters in the model that are pertinent to his or her choice (e.g., candidate policy positions). The breadth of conditions under which McKelvey and Ordeshook proved that 1) uninformed voters vote competently, and 2) election outcomes are identical to what they would have been if all voters were informed prompted a reconsideration of the conditions under which limited information made voters incompetent.

Lupia and McCubbins (1998) pursue these conditions further. They examine multiple ways in which voters can be uninformed and incorporate focal insights from the psychological study of persuasion. By using formal models and experiments, they could clarify how conditional relationships among psychological, institutional, and other factors affect competence and persuasion in ways that the dominant approach to studying voter competence – conventional survey-based analyses – had not.

The starting point for Lupia and McCubbins (1998) is that citizens must make decisions about things that they cannot experience directly. For voters, the task is to choose candidates whose future actions in office cannot be experienced in advance of the election. Relying on others for information in such circumstances can be an efficient way to acquire knowledge. However, many people who provide political information (e.g., campaign organizations) do so out of self-interest, and some may have an incentive to mislead. For voters who rely on others for information, competence depends on whom they choose to believe. If they believe people who provide accurate information and ignore people who do otherwise, then they are more likely to be competent.

A key move in the development of the Lupia-McCubbins (1998) model is to follow the arguments of empirical scholars of voting behavior and public opinion who linked this question to the social psychological study of persuasion. O’Keefe (1990) defines persuasion as “a successful intentional effort at influencing another's mental state through communication in a circumstance in which the persuadee has some measure of freedom” (17). Seen in this way, the outcomes of many political interactions hinge on who can persuade whom. Social psychologists have generated important data on the successes and failures of persuasive attempts (see, e.g., McGuire 1985; Petty and Cacioppo 1986).

Although psychological studies distinguish factors that can be antecedents of persuasion from factors that cannot, they are typically formulated in a way that limits their applicability to questions of voting behavior. The typical social psychological study of persuasion is a laboratory experiment that examines how a single variation in a single factor corresponds to a single attribute of persuasiveness. Such studies are designed to answer questions about the conditions under which some attributes will be more important than others in affecting the persuasive power of a particular presentation. In a formal model, it is possible to conduct an analysis of the conditions under which a range of factors has differential and conditional effects on whether persuasion occurs. Lupia and McCubbins (1998) do just that, examining the logical consequences of mixing a range of assumptions about beliefs and incentives to generate precise conclusions about the conditions under which 1) one person can persuade another, and 2) persuasive attempts make voters competent – that is, help them choose as they would if fully informed.

Their models and experiments also show that any attribute causes persuasion only if it informs a receiver's perceptions of a speaker's knowledge or interests. Otherwise, the attribute cannot (and experimentally does not) affect persuasion, even if it actually affects the speaker's choice of words. Experiments on this topic clarified how environmental, contextual, and institutional variables (e.g., those that make certain kinds of statements costly for a speaker to utter) make learning from others easier in some cases and difficult in others.

These and other subsequent experiments demonstrate that the knowledge threshold for voting competently is lower than the normative and survey-based literatures at the time had conjectured (see Boudreau and Lupia's chapter in this volume for more examples of such experiments). Instead of being required to have detailed information about the utility consequences of all electoral alternatives, it can be sufficient for the voter to know enough to make good choices about whom to believe. So, when information about endorsers is easier to acquire than information about policies, voters who appear to be uninformed can cast the same votes that they would have cast if they had known more. In sum, there appears to be logic to how uninformed voters use information. Formal models have provided a basis for discovering it, and experimentation offers one important way for testing it.

Jury Decision Making

Experiments have also clarified implications of a visible game-theoretic claim about jury decision making. Many courts require a unanimous vote of a jury in order to convict a defendant. A common rationale for this requirement is that unanimity minimizes the probability of convicting the innocent.

Feddersen and Pesendorfer (1998) identify an equilibrium in which unanimity produces more false convictions than was previously believed. The logic underlying their result is as follows. Suppose that all jurors are motivated to reach the correct verdict. Suppose further that it is common knowledge that every juror receives a signal about a defendant's status (i.e., courtroom testimony and/or jury room deliberation) that is true with a known probability.

In this case, a juror is either not pivotal (i.e., his or her vote cannot affect the outcome) or is pivotal (i.e., his or her vote does affect the outcome). Under unanimity, if at least one other juror is voting to acquit, then a juror is not pivotal, and the defendant will be found not guilty regardless of how this juror decides. Likewise, a juror is pivotal under unanimity rule only if every other juror is voting to convict. Hence, a juror can infer that either his or her vote makes no difference to the outcome or that all other jurors are voting to convict. Feddersen and Pesendorfer (1998) examine how such reasoning affects the jurors’ assessments of the defendant's guilt. They identify conditions in which the weight of each juror's conjecture about what other jurors are doing leads every juror to vote to convict – even if every single juror, acting solely on the basis of the signal he or she received, would have voted innocent. False convictions come from such calculations and are further fueled by jury size (as n increases, so does the informational power of the conjecture that “if I am pivotal, then it must be the case that every other juror is voting to convict.”) Feddersen and Pesendorfer use these results to call into question claims about unanimity's convictions of the innocent.

A number of scholars raised questions about whether making more realistic assumptions about jurors could yield different results. Some scholars pursued the question experimentally. Guernaschelli, McKelvey, and Palfrey (2000) examine student juries of different sizes (n = 3 and n = 6) that were otherwise in the type of decision environment described by Feddersen and Pesendorfer (1998). Guernaschelli et al. report that where “Feddersen and Pesendorfer (1998) imply that large unanimous juries will convict innocent defendants with fairly high probability…this did not happen in our experiment” (416). In fact, and contrary to Feddersen and Pesendorfer's claims, this occurred less frequently as jury size increased.

Experimental results such as these imply that the frequency at which unanimity rule convicts the innocent requires additional knowledge of how jurors think. These experiments helped motivate subsequent modeling that further clarified when strategic voting of the kind identified by Feddersen and Pesendorfer (1998) causes unanimity requirements to produce false convictions. With a model whose assumptions are built from empirical studies of juries by Pennington and Hastie (1990, 1993) and psychological experiments on need for cognition by Cacioppo and Petty (1982), Lupia, Levine, and Zharinova (2010) prove that it is not strategic voting per se that generates Feddersen and Pesendorfer's (1998) high rate of false convictions. Instead, driving the increase in false convictions is the assumption that all jurors conjecture that all other jurors are thinking in the same manner as they are. Lupia et al. (2010) show that strategic voting under different, and more empirically common, beliefs can cause far fewer false convictions. Collectively, experiments and subsequent models show that using more realistic assumptions about jurors generates equilibria with many fewer false convictions.

More generally, we believe that the pairing of formal models and experiments can be valuable in improving political scientists’ efforts to pursue psychological explanations of behavior. Models can help scholars determine whether claims being made about citizen psychology must be true given a set of clearly stated assumptions, or whether the claim is possibly true given those foundations. These types of questions are now being asked with increasing directness (e.g., Lupia and Menning 2009) and are serving as the foundations for several exciting new research agendas, such as Dickson's chapter in this volume describes.

Contributions to Other Fields

Political scientists have also used combinations of game theory and experiments to make contributions whose relevance extends well beyond political science. Eckel and Wilson's discussion of trust (see their chapter in this volume) and Coleman and Ostrom's discussion of collective action (see their chapter in this volume) provide prominent examples. Other such examples are experiments by McKelvey and Palfrey (1992, 1995, 1998). Their experimental and theoretical efforts provide a focal moment in the emergence of behavioral economics.

Behavioral economics is a movement that seeks to derive economically relevant conclusions from premises with increased psychological realism. The evolution and gradual acceptance in economics of a behavioral approach was motivated by an important set of experiments. These experiments revealed systematic divergence between the predictions of several well-known game-theoretic models and the behavior of laboratory subjects in arguably similar decision contexts.

One such model is called the centipede game. In a centipede game, two players decide how to divide an object of value (say, $10). One player can take a very unequal share of the object for him- or herself (say, “I get $7 and you get $3”), or the player can pass on that opportunity. If he or she takes the larger share, the game ends and players are paid accordingly. If he or she passes, the object doubles in value and the other player can take the larger share (say, “I get $14 and you get $6”). An important part of the game is that payoffs are arranged so that a player gets slightly more from taking in the current round ($7) than he or she will if the other player takes in the next round ($6). The game continues for as long as players pass. In every subsequent round, the object continues to double in value after each pass and players alternate in their ability to take.

It is easy to imagine that both players could earn very high payoffs by passing for a while to let the object grow in value. The game, however, has a unique Nash equilibrium (Rosenthal 1981), and it does not involve such behavior. Instead, it predicts that players will take at the first opportunity. A number of scholars raised questions about the applicability of this prediction. Two political scientists, McKelvey and Palfrey (1992), ran experiments to address these questions. As Palfrey (2007b) describes their experimental efforts,

[W]e designed and conducted an experiment, not to test any particular theory (as both of us had been accustomed to doing), but simply to find out what would happen. However, after looking at the data, there was a problem. Everything happened! Some players passed all the time, some grabbed the big pile at their first opportunity, and others seemed to be unpredictable, almost random. But there were clear patterns in the average behavior, the main pattern being that the probability of taking increased as the piles grew. (426)

Their efforts to explain such behavior evolved into the development of a new equilibrium concept, quantal response equilibrium (QRE). QRE is a variant of the Nash equilibrium concept that allows modelers to account for a much wider set of assumptions about what players believe about one another than did traditional concepts. As applied to the centipede game, the concept allowed players to adjust their strategies to varying beliefs that the other players would (or would not) play the strategies named in the game's unique Nash equilibrium. This concept allowed McKelvey and Palfrey (1998) to explain patterns of play in the centipede game far more effectively than other approaches.

Both McKelvey and Palfrey's (1992, 1995, 1998) experimental documentation of the problems with the applicability of the centipede game's Nash equilibrium and their use of these results to develop an alternate equilibrium concept now serve as models for why a more behavioral approach to economic topics is needed and how more realistic psychological content can begin to be incorporated.