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REPUTATION WITH LONG RUN PLAYERS ALP E ATAKAN AND MEHMET EKMEKCI Abstract Previous work shows that reputation results may fail in repeated games with long run players with equal discount factors Attention is restricted to extensive form stage games of perfect information One and two sided reputation results are provided for repeated games with two long run players with equal discount factors where the first mover advantage is maximal If one of the players is a Stackelberg type with positive probability then that player receives the highest payoff that is part of an individually rational payoff profile in any perfect equilibria as agents become patient If both players are Stackelberg types with positive probability then perfect equilibrium payoffs converge to a unique payoff vector and the equilibrium play converges to the unique equilibrium of a continuous time war of attrition All results generalize to simultaneous move stage games if the stage game is a game of strictly conflicting interest Keywords Repeated Games Reputation Equal Discount Factor Long run Players War of Attrition JEL Classification Numbers C73 D83 1 Introduction and Related Literature This paper proves one and two sided reputation results when two players with equal discount factors play a repeated game where the first mover advantage is maximal The stage game which is repeated in each period is an extensive form game of perfect information Date First draft March 2008 This revision October 2008 We would like to thank Martin Cripps Eddie Dekel and Christoph Kuzmics for helpful discussions our co editor Larry Samuelson and three referees for detailed comments and Umberto Garfagnini for excellent research assistance 1 2 ATAKAN AND EKMEKCI A Stackelberg strategy is a player s optimal repeated game strategy if the player could publicly commit to this strategy ex ante and a Stackelberg type is a commitment type that only plays the Stackelberg strategy The first mover advantage is maximal for player 1 if



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