Course: Game Theory with Ben Polak Dnatube
share this page with the world.
Lec 1 - Introduction: five first lessons
"Lec 1 - Introduction: five first lessons" Game Theory (ECON 159) 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 prisoners' dilemma. We learn that we should never choose a dominated strategy; but...
Lec 2 - Putting yourselves into other pe ...
"Lec 2 - Putting yourselves into other people's shoes" Game Theory (ECON 159) 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' shoes. We apply these first to defending the Roman Empire against...
Lec 3 - Iterative deletion and the media ...
"Lec 3 - Iterative deletion and the median-voter theorem" Game Theory (ECON 159) 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, and how we might build on it to improve it. Toward the end...
Lec 4 - Best responses in soccer and bus ...
"Lec 4 - Best responses in soccer and business partnerships" Game Theory (ECON 159) 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 this idea to analyze taking a penalty kick in soccer. Then we...
Lec 5 - Nash equilibrium: bad fashion an ...
"Lec 5 - Nash equilibrium: bad fashion and bank runs" Game Theory (ECON 159) 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 illustrate that there can be many equilibria in social settings, and...
Lec 6 - Nash equilibrium: dating and Cournot
"Lec 6 - Nash equilibrium: dating and Cournot" Game Theory (ECON 159) 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 settings, and we discuss the welfare consequences of the Cournot...
Lec 7 - Nash equilibrium: shopping, stan ...
"Lec 7 - Nash equilibrium: shopping, standing and voting on a line" Game Theory (ECON 159) 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 produce are not identical. We model the firms as stores...
Lec 8 - Nash equilibrium: location, segr ...
"Lec 8 - Nash equilibrium: location, segregation and randomization" Game Theory (ECON 159) 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 even if no one desires it. We also learn that seemingly...
Lec 9 - Mixed strategies in theory and t ...
"Lec 9 - Mixed strategies in theory and tennis" Game Theory (ECON 159) 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 a best response, then all the pure strategies in the mix must...
Lec 10 - Mixed strategies in baseball, d ...
"Lec 10 - Mixed strategies in baseball, dating and paying your taxes" Game Theory (ECON 159) 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 your mixed strategy represents my belief about...
Lec 11 - Evolutionary stability: coopera ...
"Lec 11 - Evolutionary stability: cooperation, mutation, and equilibrium" Game Theory (ECON 159) 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. The informal argument relating these ideas...
Lec 12 - Evolutionary stability: social ...
"Lec 12 - Evolutionary stability: social convention, aggression, and cycles" Game Theory (ECON 159) 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 such games can help us to predict how...
Lec 13 - Sequential games: moral hazard, ...
Game Theory (ECON 159) 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 large loan. We discuss possible remedies for this kind of problem. One remedy involves incentive design: writing contracts...
Lec 14 - Backward induction: commitment, ...
Game Theory (ECON 159) 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 advantage, and that it comes commitment and from information in the game rather than the timing per se. We notice that in...
Lec 15 - Backward induction: chess, stra ...
Game Theory (ECON 159) 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...
Lec 16 - Backward induction: reputation ...
Game Theory (ECON 159) 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 17 - Backward induction: ultimatums ...
Game Theory (ECON 159) 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...
Lec 18 - Imperfect information: informat ...
Game Theory (ECON 159) 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...
Lec 19 - Subgame perfect equilibrium: ma ...
"Lec 19 - Subgame perfect equilibrium: matchmaking and strategic investments" Game Theory (ECON 159) 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...
Lec 20 - Subgame perfect equilibrium: wa ...
"Lec 20 - Subgame perfect equilibrium: wars of attrition" Game Theory (ECON 159) 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...
Lec 21 - Repeated games: cooperation vs. ...
"Lec 21 - Repeated games: cooperation vs. the end game" Game Theory (ECON 159) 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,...
Lec 22 - Repeated games: cheating, punis ...
"Lec 22 - Repeated games: cheating, punishment, and outsourcing" Game Theory (ECON 159) 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...
Lec 23 - Asymmetric information: silence ...
"Lec 23 - Asymmetric information: silence, signaling and suffering education" Game Theory (ECON 159) 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,...
Lec 24- Asymmetric information: auctions ...
"Lec 24- Asymmetric information: auctions and the winner's curse" Game Theory (ECON 159) 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,...
Game Theory with Ben Polak
Source of these courses is Yale
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.
Yale Website: http://www.dnatube.com/school/yale
