Class_10(2) - GameTheory Lecture 10 Today Repeated games...

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Econ 171 – Introduction to  Game Theory Lecture 10
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Today Repeated games & reputation Finite and 'stage' games 2-stage game Infinite games
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Repeated games As in the bargaining model, certain static games may be played multiple times. Provide a richer game environment by allowing cooperation, reputation, retribution, patience. Actions in a single static game may be unreasonable, not telling us much about behaviors. Use repeated games to explain strategies and behavior previously consider non-optimal in a single simultaneous games. Opportunity to analyzing more sophisticated or realistic interactions.
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Repeated games By assumption, single period static games are played in a vacuum. Decisions in future game play depend on a history of interactions. i.e. Repeated games are not only about what has happened in the past, but also what will happen as a result of the interactions. Nash equilibrium in stage games may be inefficient. In repeated games, cooperation/higher outcomes are possible because one can build a reputation and condition on the reputation of others.
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Repeated games In a repeated game, each period the players play a “stage game” which means they play a single static game. They choose their actions simultaneously and independently, then move to the next period. T periods; players have perfect recall and perfect information . Important: while we know the period we are in and the results of the previous stages, individual stages are not played sequentially . Game payoffs are the sums of the players’ outcomes in each stage game.
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Finite repeated games Game trees and strategy spaces can be intractably large in finite games. For example, in a simple 2-stage repeated Prisoners’ Dilemma the strategies are: 1 st stage: {C,D} & {c,d} 2 nd stage: { (C’D’,C’D’’,C’D’’’,C’D’’’’),
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