1. Introduction: five first lessons

Summary

Professor Ben Polak introduces game theory as a way to study strategic situations—situations where what happens to you depends not only on your own choices, but also on what other people choose. He contrasts these with simplified cases such as perfect competition and monopoly, where individual firms have less need to anticipate competitors’ actions. Strategic reasoning can apply in economics, politics, law, biology, and sports.

Game 1: The grade-choice game

Students privately chose Alpha or Beta, then were randomly paired. Grades depended on both choices:

Partner chooses Alpha Partner chooses Beta You choose Alpha Both get B− You get A; partner gets C You choose Beta You get C; partner gets A Both get B+

Polak emphasizes that choices and outcomes alone do not fully define a game: players’ objectives, or payoffs, matter too. Game theory does not prescribe what people ought to value; it can help analyze choices once their goals are specified.

Five central lessons

1. Do not play a strictly dominated strategy. A strategy is strictly dominated when another strategy gives you a higher payoff no matter what the other player does. Under the initial, self-interested payoffs, Alpha dominates Beta: Alpha gives the player a better grade whether the partner chooses Alpha or Beta.

2. Rational choices can lead to bad or inefficient outcomes. If both players care only about their own grades, each has an incentive to choose Alpha. They then both receive B−, even though both would receive B+ if they both chose Beta. This is the structure of a Prisoner’s Dilemma: individually rational choices can produce a worse result for everyone than cooperation would.

3. Payoffs matter: identify your goals before choosing. Polak changes the assumed payoffs while keeping the grade outcomes the same. In the second version, players care about fairness or feel guilt and indignation when grades are unequal. Neither Alpha nor Beta then dominates: Alpha is better when the other player chooses Alpha, while Beta is better when the other player chooses Beta. The result is a coordination problem, with different incentives and possible outcomes. The practical lesson is to clarify what you are trying to achieve before analyzing a situation.

4. Put yourself in other people’s shoes. A player’s best choice may depend on what the other player values and is likely to do. In examples where one player is self-interested and the other has fairness-based payoffs, the self-interested player still has Alpha as a dominant strategy. The fairness-minded player can reason that the self-interested player will choose Alpha, then choose a best response. Strategic thinking therefore involves anticipating others’ incentives, not just considering your own.

5. The class’s results are presented humorously as “Yale students are evil.” Polak reports that 238 students chose Alpha and 36 chose Beta—roughly 15% chose Beta. He jokes that this shows Yale students are “evil,” while noting that people might choose Beta for reasons such as concern for others or expectations of repeated play.

Prisoner’s Dilemma, cooperation, and enforcement

Polak uses several examples to illustrate the dilemma:

• Roommates: Each person may prefer that the other clean, but if the other does not, neither wants to do the work. The room can end up dirty even though both would prefer a clean room.
• Competing firms: Each may have an incentive to undercut the other, reducing profits for both.
• Prisoners and legal disputes: Each side may benefit from betraying or outspending the other, even when mutual cooperation would be better.

Communication alone may not solve the problem: people can agree to cooperate but still have an incentive to break the agreement. A contract is “communication with teeth” because enforcement can change incentives. Legal contracts are not always available—for example, price-fixing agreements between firms are illegal. Repeated dealings may encourage cooperation between roommates or other recurring partners. In settings without reliable legal enforcement, the threat of retaliation or other forms of nonlegal enforcement may support agreements.

Game 2: Guessing a number

The class is also given a second game: each student chooses an integer from 1 to 100. The target is two-thirds of the class average, and the winner is the person whose number is closest to that target. The prize is $5 minus one cent for each unit of difference. The class submits its choices, but the subtitles do not give the result.

Course and recording arrangements

Polak briefly covers course logistics: the stated grade breakdown is 30% problem sets, 30% midterm, and 40% final. He recommends Dutta’s Strategy and Games and Joel Watson’s Strategies as supplementary texts rather than books he will follow closely, and also recommends Thinking Strategically.

The class is being filmed for Yale’s open-education project. Students are asked to sign release forms, and microphones are used for classroom discussion.

Speakers and sources featured

• Professor Ben Polak — lecturer and principal speaker.
• Students — several speak during the discussion. Named students include Courtney, Clara Elise, Travis, and Henry. Mary and Erica are named in a hypothetical example about an agreement between classmates. Other student contributions are unnamed or inaudible.
• Jude — cameraman, identified by Polak and entrusted with the prize money for Game 2.
• Wes — audio technician, introduced by Polak.
• Teaching assistants — operate microphones, collect forms, and help with class logistics. Kaj is asked to count the forms.

Sources and references mentioned by Polak include Dutta’s Strategy and Games, Joel Watson’s Strategies, Thinking Strategically, Strunk and White, and Joe Jackson, whose lyric is paraphrased as “you can’t get what you want till you know what you want.” He also mentions the television shows Law & Order and The Sopranos. Polak refers to the X-Men and The Matrix as humorous examples while discussing the idea that one person’s reasoning cannot magically control another person’s choices.