Game Theory
配信者: Ben Polak
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説明
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 played in class and to examples drawn from economics, politics, the movies, and elsewhere. This Yale College course, taught on campus twice per week for 75 minutes, was recorded for Open Yale Courses in Fall 2007.
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1 |
1 – Introduction: Five First Lessons | We introduce Game Theory by playing a game. We organize the game into players, their strategies, and their goals or payoffs; and we learn that we should decide what our goals are before we make choices. With some plausible payoffs, our game is a prisone | 2007/9/5 | 無料 | iTunes で見る |
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2 – Putting Yourselves into Other People’s Shoes | At the start of the lecture, we introduce the “formal ingredients” of a game: the players, their strategies and their payoffs. Then we return to the main lessons from last time: not playing a dominated strategy; and putting ourselves into others’ | 2007/9/10 | 無料 | iTunes で見る |
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3 – Iterative Deletion and the Median-Voter Theorem | We apply the main idea from last time, iterative deletion of dominated strategies, to analyze an election where candidates can choose their policy positions. We then consider how good is this classic model as a description of the real political process, | 2007/9/12 | 無料 | iTunes で見る |
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4 – Best Responses in Soccer and Business Partnerships | We continue the idea (from last time) of playing a best response to what we believe others will do. More particularly, we develop the idea that you should not play a strategy that is not a best response for any belief about others’ choices. We use thi | 2007/9/17 | 無料 | iTunes で見る |
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5 – Nash Equilibrium: Bad Fashion and Bank Runs | We first define formally the new concept from last time: Nash equilibrium. Then we discuss why we might be interested in Nash equilibrium and how we might find Nash equilibrium in various games. As an example, we play a class investment game to illustra | 2007/9/19 | 無料 | iTunes で見る |
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6 – Nash Equilibrium: Dating and Cournot | We apply the notion of Nash Equilibrium, first, to some more coordination games; in particular, the Battle of the Sexes. Then we analyze the classic Cournot model of imperfect competition between firms. We consider the difficulties in colluding in such | 2007/9/24 | 無料 | iTunes で見る |
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7 – Nash Equilibrium: Shopping, Standing and Voting on a Line | We first consider the alternative “Bertrand” model of imperfect competition between two firms in which the firms set prices rather than setting quantities. Then we consider a richer model in which firms still set prices but in which the goods they p | 2007/9/26 | 無料 | iTunes で見る |
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8 – Nash Equilibrium: Location, Segregation and Randomization | We first complete our discussion of the candidate-voter model showing, in particular, that, in equilibrium, two candidates cannot be too far apart. Then we play and analyze Schelling’s location game. We discuss how segregation can occur in society eve | 2007/10/1 | 無料 | iTunes で見る |
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9 – Mixed Strategies in Theory and Tennis | We continue our discussion of mixed strategies. First we discuss the payoff to a mixed strategy, pointing out that it must be a weighed average of the payoffs to the pure strategies used in the mix. We note a consequence of this: if a mixed strategy is | 2007/10/3 | 無料 | iTunes で見る |
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10 – Mixed Strategies in Baseball, Dating and Paying Your Taxes | We develop three different interpretations of mixed strategies in various contexts: sport, anti-terrorism strategy, dating, paying taxes and auditing taxpayers. One interpretation is that people literally randomize over their choices. Another is that yo | 2007/10/8 | 無料 | iTunes で見る |
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11 – Evolutionary Stability: Cooperation, Mutation, and Equilibrium | We discuss evolution and game theory, and introduce the concept of evolutionary stability. We ask what kinds of strategies are evolutionarily stable, and how this idea from biology relates to concepts from economics like domination and Nash equilibrium. | 2007/10/10 | 無料 | iTunes で見る |
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12 – Evolutionary Stability: Social Convention, Aggression, and Cycles | We apply the idea of evolutionary stability to consider the evolution of social conventions. Then we consider games that involve aggressive (Hawk) and passive (Dove) strategies, finding that sometimes, evolutionary populations are mixed. We discuss how | 2007/10/15 | 無料 | iTunes で見る |
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13 – Sequential Games: Moral Hazard, Incentives, and Hungry Lions | We consider games in which players move sequentially rather than simultaneously, starting with a game involving a borrower and a lender. We analyze the game using “backward induction.” The game features moral hazard: the borrower will not repay a la | 2007/10/22 | 無料 | iTunes で見る |
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14 – Backward Induction: Commitment, Spies, and First-Mover Advantages | We first apply our big idea–backward induction–to analyze quantity competition between firms when play is sequential, the Stackelberg model. We do this twice: first using intuition and then using calculus. We learn that this game has a first-mover a | 2007/10/24 | 無料 | iTunes で見る |
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15 – Backward Induction: Chess, Strategies, and Credible Threats | 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 pro | 2007/10/29 | 無料 | iTunes で見る |
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16 – Backward Induction: Reputation and Duels | 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 p | 2007/10/31 | 無料 | iTunes で見る |
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17 – Backward Induction: Ultimatums and Bargaining | 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 discount | 2007/11/5 | 無料 | iTunes で見る |
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18 – Imperfect Information: Information Sets and Sub-Game Perfection | 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 can | 2007/11/7 | 無料 | iTunes で見る |
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19 – Subgame Perfect Equilibrium: Matchmaking and Strategic Investments | 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 | 2007/11/12 | 無料 | iTunes で見る |
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20 – Subgame Perfect Equilibrium: Wars of Attrition | 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 | 2007/11/14 | 無料 | iTunes で見る |
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21 – Repeated Games: Cooperation vs. the End Game | 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 tim | 2007/11/26 | 無料 | iTunes で見る |
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22 – Repeated Games: Cheating, Punishment, and Outsourcing | 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 | 2007/11/28 | 無料 | iTunes で見る |
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23 – Asymmetric Information: Silence, Signaling and Suffering Education | 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 th | 2007/12/3 | 無料 | iTunes で見る |
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24 – Asymmetric Information: Auctions and the Winner’s Curse | 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 | 2007/12/5 | 無料 | iTunes で見る |
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