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Lecture 24 Game Theory c 2009 Je rey A Miron Outline 1 Introduction 2 The Payo Matrix of a Game 3 Nash Equilibrium 4 Mixed Strategies 5 The Prisoner s Dilemma 6 Repeated Games 7 Sequential Games 8 A Game of Entry Deterrence 1 Introduction In the previous lecture we discussed oligopoly behavior in particular the fact that cartel members have an incentive to cheat This creates a demand for strategies the cartel members could pursue that might discourage cheating and increase pro ts on average This is but one example of a more general phenomenon strategic interaction occurs in many aspects of life By strategic interaction we mean situations in which my desired choice of behavior depends on what I think you will do and your desired choice depends on what you think I will do This kind of situation is addressed by the branch of economics known as game theory Note the key di erence between the strategic setting and most of those we have considered so far Both a pure competitor and a monopolist take market conditions as given they can then decide what actions are in their own best interest without 1 worrying about how some other economic actor will respond In all the models of consumer behavior that we have considered consumers took prices as given In many instances however what matters is how I think others will respond to my actions how they think I will respond to their actions how I think they will think that I will respond and so on We now examine game theory as a method of modeling these kinds of environments We are interested in applications of game theory to the theory of the rm especially in the case of oligopoly but also in the insights and techniques that come from game theory more generally 2 The Payo Matrix of a Game Game theory in principle can be applied in settings with many participants e g an industry with many competitors but we limit our analysis to two person games for simplicity This allows us to portray the key aspects of the game in a payo matrix

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