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Yale Open Courses ECON 159: Game Theory


About the Course This course is an introduction to game theory and strategic thinking. Ideas such as dominance, backward induction, Nash equilibrium, evolutionary stability, commitment, credibility, asymmetric information, adverse selection, and signaling are discussed and applied to games playedRead more

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Lecture 24 - Asymmetric Information: Auctions and the Winner's Curse

Jun 8 • 01:02:28
We discuss auctions. We first distinguish two extremes: common values and private values. We hold a common value auction in class and discover the winner’s curse, the winner tends to overpay. We discuss why this occurs and how to avoid it: you should bid as if you knew that your bid would win; that is, as if you knew your initial estimate of the common value was the highes...

Lecture 23 - Asymmetric Information: Silence, Signaling and Suffering Education

Jun 8 • 01:10:36
We look at two settings with asymmetric information; one side of a game knows something that the other side does not. We should always interpret attempts to communicate or signal such information taking into account the incentives of the person doing the signaling. In the first setting, information is verifiable. Here, the failure explicitly to reveal information can be in...

Lecture 22 - Repeated Games: Cheating, Punishment, and Outsourcing

Jun 8 • 01:15:46
In business or personal relationships, promises and threats of good and bad behavior tomorrow may provide good incentives for good behavior today, but, to work, these promises and threats must be credible. In particular, they must come from equilibrium behavior tomorrow, and hence form part of a subgame perfect equilibrium today. We find that the grim strategy forms such a...

Lecture 21 - Repeated Games: Cooperation vs. the End Game

Jun 8 • 01:15:18
We discuss repeated games, aiming to unpack the intuition that the promise of rewards and the threat of punishment in the future of a relationship can provide incentives for good behavior today. In class, we play prisoners’ dilemma twice and three times, but this fails to sustain cooperation. The problem is that, in the last stage, since there is then is future, there is n...

Lecture 20 - Subgame Perfect Equilibrium: Wars of Attrition

Jun 8 • 01:15:36
We first play and then analyze wars of attrition; the games that afflict trench warfare, strikes, and businesses in some competitive settings. We find long and damaging fights can occur in class in these games even when the prizes are small in relation to the accumulated costs. These could be caused by irrationality or by players’ having other goals like pride or reputatio...

Lecture 19 - Subgame Perfect Equilibrium: Matchmaking and Strategic Investments

Jun 8 • 01:17:08
We analyze three games using our new solution concept, subgame perfect equilibrium (SPE). The first game involves players’ trusting that others will not make mistakes. It has three Nash equilibria but only one is consistent with backward induction. We show the other two Nash equilibria are not subgame perfect: each fails to induce Nash in a subgame. The second game involve...

Lecture 18 - Imperfect Information: Information Sets and Sub-Game Perfection

Jun 8 • 01:15:57
We consider games that have both simultaneous and sequential components, combining ideas from before and after the midterm. We represent what a player does not know within a game using an information set: a collection of nodes among which the player cannot distinguish. This lets us define games of imperfect information; and also lets us formally define subgames. We then ex...

Lecture 17 - Backward Induction: Ultimatums and Bargaining

Jun 8 • 01:10:44
We develop a simple model of bargaining, starting from an ultimatum game (one person makes the other a take it or leave it offer), and building up to alternating offer bargaining (where players can make counter-offers). On the way, we introduce discounting: a dollar tomorrow is worth less than a dollar today. We learn that, if players are equally patient, if offers can be ...

Lecture 16 - Backward Induction: Reputation and Duels

Jun 8 • 01:15:40
In the first half of the lecture, we consider the chain-store paradox. We discuss how to build the idea of reputation into game theory; in particular, in setting like this where a threat or promise would otherwise not be credible. The key idea is that players may not be completely certain about other players’ payoffs or even their rationality. In the second half of the lec...

Lecture 15 - Backward Induction: Chess, Strategies, and Credible Threats

Jun 6 • 01:12:38
We first discuss Zermelo’s theorem: that games like tic-tac-toe or chess have a solution. That is, either there is a way for player 1 to force a win, or there is a way for player 1 to force a tie, or there is a way for player 2 to force a win. The proof is by induction. Then we formally define and informally discuss both perfect information and strategies in such games. Th...

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