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Maintaining a Reputation against a Long-Lived Opponent

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  • Celentani, Marco, et al

Abstract

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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Bibliographic Info

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. Kreps, David M. & Wilson, Robert, 1982. "Reputation and imperfect information," Journal of Economic Theory, Elsevier, vol. 27(2), pages 253-279, August.
  2. Celentani, Marco, 1996. "Reputation with Observed Actions," Economic Theory, Springer, vol. 7(3), pages 407-19, April.
  3. Celentani, Marco & Pesendorfer, Wolfgang, 1996. "Reputation in Dynamic Games," Journal of Economic Theory, Elsevier, vol. 70(1), pages 109-132, July.
  4. 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.
  5. Paul Milgrom & John Roberts, 1980. "Predation, Reputation, and Entry Deterrence," Discussion Papers 427, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
  6. Cripps, Martin W. & Schmidt, Klaus M. & Thomas, Jonathan P., 1996. "Reputation in Perturbed Repeated Games," Journal of Economic Theory, Elsevier, vol. 69(2), pages 387-410, May.
  7. Radner, Roy, 1981. "Monitoring Cooperative Agreements in a Repeated Principal-Agent Relationship," Econometrica, Econometric Society, vol. 49(5), pages 1127-48, September.
  8. Fudenberg, Drew & Tirole, Jean, 1991. "Perfect Bayesian equilibrium and sequential equilibrium," Journal of Economic Theory, Elsevier, vol. 53(2), pages 236-260, April.
  9. 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.
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Citations

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Cited by:
  1. Cripps, Martin W. & Mailath, George J. & Samuelson, Larry, 2007. "Disappearing private reputations in long-run relationships," Journal of Economic Theory, Elsevier, vol. 134(1), pages 287-316, May.
  2. Levine, David & Ely, Jeffrey & Fudenberg, Drew, 2008. "When is Reputation Bad?," Scholarly Articles 3196337, Harvard University Department of Economics.
  3. Hausken, Kjell, 2007. "Reputation, incomplete information, and differences in patience in repeated games with multiple equilibria," Economics Letters, Elsevier, vol. 97(2), pages 138-144, November.
  4. Hausken, Kjell, 2005. "The battle of the sexes when the future is important," Economics Letters, Elsevier, vol. 87(1), pages 89-93, April.
  5. Jimmy Chan, 2000. "On the Non-Existence of Reputation Effects in Two-Person Infinitely-Repeated Games," Economics Working Paper Archive 441, The Johns Hopkins University,Department of Economics.
  6. Blundell,Richard & Newey,Whitney K. & Persson,Torsten (ed.), 2006. "Advances in Economics and Econometrics," Cambridge Books, Cambridge University Press, number 9780521692083.
  7. Lu, Yang K., 2013. "Optimal policy with credibility concerns," Journal of Economic Theory, Elsevier, vol. 148(5), pages 2007-2032.
  8. Sorin, Sylvain, 1999. "Merging, Reputation, and Repeated Games with Incomplete Information," Games and Economic Behavior, Elsevier, vol. 29(1-2), pages 274-308, October.
  9. Sandroni, Alvaro, 2000. "Reciprocity and Cooperation in Repeated Coordination Games: The Principled-Player Approach," Games and Economic Behavior, Elsevier, vol. 32(2), pages 157-182, August.

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