Lecture7 (1).pdf - EC3312 Game Theory and Applications to...

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EC3312 Game Theory and Applications to Economics Luo Xiao, Lecturer Department of Economics, National University of Singapore 16 March 2008 A/P Luo Xiao EC3312 - Lecture 7 16 March 2008 1 / 13
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Repeated Games A repeated game is a dynamic game in which the same static game (i.e. stage game) is played at every stage After every stage, players observe the actions chosen by all players The repeated game has either a °nite or an in°nite number of repetitions A/P Luo Xiao EC3312 - Lecture 7 16 March 2008 2 / 13
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Repeated Games Many economic and social phenomena can be modelled and analyzed using the model of repeated game. The examples include wars and human con±icts (e.g. India²Pakistan, Israel²Arab, North²South Korea, and China-Taiwan); see Robert Aumann³s Nobel lecture: War and Peace. The model of repeated game is designed to examine the logic of longterm interaction. It captures the idea that a player will take into account the e/ect of his current behavior on the other players³future behavior, and aims to explain phenomena like cooperation, revenge, and threats. Folk Theorem: The cooperative outcomes of stage game G can be supported by the subgame-perfect equilibrium outcomes of its repeated game G . A/P Luo Xiao EC3312 - Lecture 7 16 March 2008 3 / 13
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Finitely Repeated Games We assume that the payo/ in the °nitely repeated game is simply the sum of the payo/s attained in all the stage games Example: The following prisoners³dilemma game is repeated twice don³t confess confess don³t confess 4,4 0,5 confess 5,0 1,1 The unique subgame-perfect outcome : (confess, confess) in the °rst stage, followed by (confess, confess) in the second stage Proposition: If the stage game has a unique Nash equilibrium, then
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