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Maintaining a Reputation against a Long-Lived Opponent

We analyze in a game between a patient player 1 and a non-myopic but less patient opponent, player 2. We assume that Player 1's type is private information and that players do not directly observe each other's action but rather see an imperfect signal of it. We show that in any Nash equilibrium of the game player 1 will get almost the largest payoff consistent with player 2 choosing a best response in a finite truncation of the game. If the discount factor of player 2 is sufficiently large, then player 1 will get approximately the maximum payoff consistent with player 2 getting at least his pure strategy minmax payoff.

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Article provided by Econometric Society in its journal Econometrica.

Volume (Year): 64 (1996)
Issue (Month): 3 (May)
Pages: 691-704

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Handle: RePEc:ecm:emetrp:v:64:y:1996:i:3:p:691-704
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  1. Cripps,Martin & Scmidt,Klaus & Thomas,Jonathan, 1993. "Reputation in pertubed repeated games," Discussion Paper Serie A 410, University of Bonn, Germany.
  2. Celentani, Marco & Pesendorfer, Wolfgang, 1996. "Reputation in Dynamic Games," Journal of Economic Theory, Elsevier, vol. 70(1), pages 109-132, July.
  3. Schmidt, K.M., 1992. "Reputation and Equilibrium Characterization in Repeated Games with Conflicting Interests," Working papers 92-7, Massachusetts Institute of Technology (MIT), Department of Economics.
  4. Paul Milgrom & John Roberts, 1980. "Predation, Reputation, and Entry Deterrence," Discussion Papers 427, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
  5. Marco Celentani, 1996. "Reputation with observed actions (*)," Economic Theory, Springer, vol. 7(3), pages 407-419.
  6. Kreps, David M. & Wilson, Robert, 1982. "Reputation and imperfect information," Journal of Economic Theory, Elsevier, vol. 27(2), pages 253-279, August.
  7. Radner, Roy, 1981. "Monitoring Cooperative Agreements in a Repeated Principal-Agent Relationship," Econometrica, Econometric Society, vol. 49(5), pages 1127-48, September.
  8. Cripps, Martin W & Thomas, Jonathan P, 1995. "Reputation and Commitment in Two-Person Repeated Games without Discounting," Econometrica, Econometric Society, vol. 63(6), pages 1401-19, November.
  9. Fudenberg, Drew & Tirole, Jean, 1991. "Perfect Bayesian equilibrium and sequential equilibrium," Journal of Economic Theory, Elsevier, vol. 53(2), pages 236-260, April.
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