Lecture_24_Game_Theory

Lecture_24_Game_Theory - Lecture 24: Game Theory c...

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Unformatted text preview: Lecture 24: Game Theory c & 2008 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 prots 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 environ- ments. 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. Consider a speci&c example with two players named A and B. Each player can choose between two strategies. Player A writes one of two words on a piece of paper, Top or Bottom . Simultaneously, Player B writes Left or Right. Each player does this independently, i.e., without knowledge of the others actions. After the players do this, the pieces of paper are examined, and each player gets the payo/ depicted in the table. 2 Player A Player B Top Bottom Left Right 1, 2 0, 1 2, 1 1, The payo/ to A is the &rst entry in each pair; the payo/ to B is the second entry. Person A has two stratgies: top or bottom. These could represent economic choices like raise price or lower price, or they could represent other things like declare war or make peace; go to the movies or not, etc. The strategies do not have to be strategic per se; they are just choices the players might make....
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Lecture_24_Game_Theory - Lecture 24: Game Theory c...

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