Narrator: Listen to part of a lecture in a business management class.
Professor: All right, last week we started talking about game theory, and how it applies to management of companies. Does anyone remember the name of the example we talked about?
Male Student: Was it the prisoner’s dilemma?
Professor: Yes… and what did it prove?
Female Student: Rational agents sometimes may not cooperate with each other.
Professor: That’s right. And why is that?
Male Student: It’s because, um… it might be in their interest to not cooperate.
Professor: Exactly. In a prisoner’s dilemma, each prisoner has an incentive to cooperate with the police—in other words, to not cooperate with each other—because if they do, they will receive a lighter punishment. So, cooperating with police basically means confessing. But if neither confesses, they will be much better off than if both of them confess. The worst case for either prisoner is to not confess, when the other prisoner does confess.
So it leads to a dilemma. Do I confess, or do I honor my commitment to the other prisoner not to confess? This requires, absolutely, that the prisoners trust each other entirely. They each trust that the other one will not confess. Otherwise, there’s no point—both sides will confess and both sides will be ruined. But, if the trust is there, then there is still incentive to cheat on the agreement to cooperate—to go ahead and confess when the other prisoner doesn’t. Because in that case, the prisoner who confesses may get off scot-free.
So now, today, we are going to pivot to a new way of looking at game theory situations, and how this impacts business decision-making. Today, we will talk about zero-sum games.
OK, so can anyone tell me what a zero-sum game is? Yes?
Female Student: It’s a game in which the total profit is fixed.
Professor: OK… and?
Female Student: And?
Professor: Listen, you’re right, the total profit is fixed. So what does that—
Female Student: It means that… let’s say I make a decision that improves my profit…
Professor: Right, so you’re acting in your own best interest, trying to maximize your own profit. What does that do to the other player in the zero-sum game? And when would this come up?
Female Student: It reduces that other person’s by the same amount.
Professor: Yes, that’s true... Also, I asked… I asked when this would come up. I wanna know what this has to do with business decision-making. Yes.
Male Student: Well, for example, if we’re talking about acquiring a customer, and there’s only one possible customer, then whichever firm gets that customer… the other firm loses that potential customer.
Professor: OK. And… the point is—a zero-sum game—it–it is a “winner and loser” game. If someone gains, someone else has to lose something. So these games model highly competitive situations. Ones in which you cannot gain without someone else taking a hit.
Female Student: So this would be like, say, poker or trading in the stock market?
Professor: Yes, that’s exactly… that’s exactly what I’m getting at. If I win a pot in a poker game, it must be because someone else failed to win that pot. In a sense, I can only profit by taking someone else’s money. Likewise, in the stock market, I can only make a profit in a stock by buying it from someone at a low price, and selling it to someone else at a high price—thereby denying the original holder of the stock of the profit he could have made by selling it to the other party at the price I sold it. Now, these are interesting games because in both cases, there can be transaction costs. Say I’m playing poker in a casino. How does the casino make money?
Male Student: Don’t they take a small amount out of every pot?
Professor: That’s precisely what happens. So in effect, the casino does not care who wins the pot. They care about…
Female Student:…They want to play as many hands as possible.
Professor: Right. So, is that still a zero-sum game?
Female Student:…No.
Professor: Well, it depends on how you frame it. If you’re only talking about the poker players at the table, then no, it is no longer a zero-sum game. But what if we include the casino as a player in this game?
Then in that case, it still is a zero-sum game, but the number of players has increased by one. A couple of game-theory experts named von Neumann and Morgenstern proved years ago that any non-zero-sum game can be modeled as a zero-sum game by adding one additional player. This player represents the net profits, or losses, of the other players.
In business, zero-sum games occur frequently. They can be dangerous. And recent research has shown that over time, zero-sum games can cause damage to society as a whole. Think about two businesses that spend all their resources fighting to steal customers from each other, rather than focusing on higher goals, such as innovation of products, or environmental sustainability. How do we avoid falling into the short-term, zero-sum trap? We’ve run out of time, so we will get into this discussion next week.
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What is the lecture mainly about? |
Gist-content. The main discussion of this lecture is zero-sum games, although there is a substantial review of the prisoner’s dilemma at the beginning. |
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| ✗ | A A review of the “prisoner’s dilemma” game example |
While this takes up a fair portion of the lecture, this review is primarily used to pivot to a new topic—zero-sum games. |
| ✗ | B Contrasting the game of poker with stock market investing |
The lecture compares the two, rather than contrasting them. Furthermore, these are merely examples used to illustrate zero-sum games. |
| ✓ | C A topic within game theory called “zero-sum games” |
Correct. The main discussion of the lecture is about zero-sum games. |
| ✗ | D Explaining theories developed by von Neumann and Morgenstern |
The von Neumann and Morgenstern finding involved how to model non-zero-sum games as zero-sum games. This is not the main point of the lecture. |
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Why does the professor talk about poker and stock market investing? |
Organization. When a student brings up poker and stock market investing, the professor goes on to explain why they are good examples of zero-sum games. |
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| ✗ | A To avoid expanding on a topic brought up by a student |
On the contrary, while these examples were given by a student, the professor points out that they are good examples. He then furthers the discussion by explaining why they are good examples of zero-sum games. |
| ✓ | B To illustrate examples of zero-sum games |
Correct. The examples were given by a student, but the professor uses them as examples to illustrate what zero-sum games are and what characteristics they have. |
| ✗ | C To demonstrate different payouts to participants in a prisoner’s dilemma game |
Poker and stock-market investing are given as examples of zero-sum games, not prisoner’s dilemma games. |
| ✗ | D To explain why zero-sum games don’t exist in real life |
On the contrary, the professor explains that zero-sum games do exist, and that all non-zero-sum games can be modeled as zero-sum games by adding an additional player. |
Narrator: Listen again to part of the lecture. Then answer the question.
Professor: In a prisoner’s dilemma, each prisoner has an incentive to cooperate with the police—in other words, to not cooperate with each other—because if they do, they will receive a lighter punishment. So, cooperating with police basically means confessing. But if neither confesses, they will be much better off than if both of them confess. The worst case for either prisoner is to not confess, when the other prisoner does confess.
So it leads to a dilemma. Do I confess, or do I honor my commitment to the other prisoner not to confess? This requires, absolutely, that the prisoners trust each other entirely. They each trust that the other one will not confess.
Narrator: Why does the professor say this:
Professor: This requires, absolutely, that the prisoners trust each other entirely. They each trust that the other one will not confess.
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Why does the professor say this? |
Function of What Is Said. In this quote, the professor describes the structure of a prisoner’s dilemma situation in detail, explaining that each prisoner is better off confessing, but in total, the two prisoners are better off not confessing. The highlighted phrase is used to illustrate the importance of trust in achieving their ultimate goal, which is for neither of the prisoners to confess. |
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| ✓ | A To stress the level of mutual cooperation that the prisoners need to maintain |
Correct. The prisoners must trust each other strongly in order for both of them to overcome the temptation to confess. This is the only way to avoid a harsh penalty for one or both. |
| ✗ | B To note that each side individually is better off not confessing |
The opposite is true. Each side, individually, is better off confessing, irrespective of what the other party does. |
| ✗ | C To point out that without trust, neither side is likely to confess |
The opposite is true. Without trust, each side is likely to confess. |
| ✗ | D To indicate how the situation is likely to turn into a zero-sum game |
In this discussion, the professor is talking about a prisoner’s dilemma, not a zero-sum game. |
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What is an example of a zero-sum game? |
Detail. Zero-sum games are ones in which the total combined profit (or loss) of both sides is fixed. Therefore, one side cannot gain without the other side losing. |
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| ✗ | A A worker’s hourly wage is determined by his productivity in the prior quarter. |
This is not a “winners and losers” situation and thus not an example of a zero-sum game. |
| ✗ | B The stock market goes up, increasing the value of the holdings of most owners of company stock. |
This is an example in which nearly everyone profits, and thus not an example of a zero-sum game. |
| ✗ | C Two countries in a peace agreement each have an incentive to violate the terms of the agreement. |
This is a cooperative game with incentives to not cooperate. In other words, this is a prisoner’s dilemma example, not a zero-sum game example. |
| ✓ | D Only three gifts are available to be distributed among four children. |
Correct. Once three children get their gifts (the “winners”), the other child must necessarily not get one (the “loser”). This child cannot take a gift without causing an equivalent loss for one of the other children. Therefore, this is a standard example of a zero-sum game. |
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According to the professor, how can non-zero-sum games be modeled as zero-sum games? |
Detail. The professor explains that von Neumann and Morgenstern proved that non-zero-sum games can be modeled as a zero-sum game by adding an additional player. That player represents the net profits or losses to the other players. |
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| ✗ | A By turning the game into a prisoner’s dilemma |
This possibility is not mentioned in the lecture. |
| ✗ | B By increasing transaction costs |
If anything, any transaction costs must be reduced (to zero) to turn the non-zero-sum-game into a zero-sum game. |
| ✗ | C By temporarily removing a player from the game |
Removing a player is never mentioned in the lecture. |
| ✓ | D By adding a player to the game |
Correct. This new player represents the net combined profits or losses of the other players. |
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Classify each statement below as describing a prisoner’s dilemma or a zero-sum game. |
Connecting Content. Prisoner’s dilemma games are discussed at the beginning of the lecture. Zero-sum games are discussed throughout the rest of the lecture. |
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| a The two sides in the game are better off cooperating. |
Prisoner’s Dilemma. This is one of the key features of a prisoner’s dilemma. |
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| b One side cannot gain without the other side losing. |
Zero-Sum Game. This is a key feature of zero-sum games. |
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| c Cooperation requires high levels of trust. |
Prisoner’s Dilemma. This is one of the requirements of avoiding the “confession trap” of a prisoner’s dilemma. |
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| d It can be dangerous to society as a whole. |
Zero-Sum Game. This is mentioned near the end of a lecture as a potential consequence of zero-sum games. |