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Maintaining a Reputation Against A Long-Lived Opponent

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  • Marco Celentani

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

Paper provided by Northwestern University, Center for Mathematical Studies in Economics and Management Science in its series Discussion Papers with number 1075R.

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Date of creation: Dec 1993
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Handle: RePEc:nwu:cmsems:1075r

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Postal: Center for Mathematical Studies in Economics and Management Science, Northwestern University, 580 Jacobs Center, 2001 Sheridan Road, Evanston, IL 60208-2014
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Web page: http://www.kellogg.northwestern.edu/research/math/
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Keywords: Repeated games; commitment; reputation; patience.;

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References

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  1. Schmidt, Klaus M., 1993. "Reputation and Equilibrium Characterization in Repeated Games with Conflicting Interests," Munich Reprints in Economics 3395, University of Munich, Department of Economics.
  2. 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.
  3. Celentani, Marco, 1996. "Reputation with Observed Actions," Economic Theory, Springer, vol. 7(3), pages 407-19, April.
  4. Cripps,Martin & Scmidt,Klaus & Thomas,Jonathan, 1993. "Reputation in pertubed repeated games," Discussion Paper Serie A 410, University of Bonn, Germany.
  5. Marco Celentani & Wolfgang Pesendorfer, 1992. "Reputation in Dynamic Games," Discussion Papers 1009, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
  6. Kreps, David M. & Wilson, Robert, 1982. "Reputation and imperfect information," Journal of Economic Theory, Elsevier, vol. 27(2), pages 253-279, August.
  7. Paul Milgrom & John Roberts, 1980. "Predation, Reputation, and Entry Deterrence," Discussion Papers 427, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
  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. Radner, Roy, 1981. "Monitoring Cooperative Agreements in a Repeated Principal-Agent Relationship," Econometrica, Econometric Society, vol. 49(5), pages 1127-48, September.
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Citations

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Cited by:
  1. Lu, Yang K., 2013. "Optimal policy with credibility concerns," Journal of Economic Theory, Elsevier, vol. 148(5), pages 2007-2032.
  2. Ely, Jeffrey & Fudenberg, Drew & Levine, David K., 2008. "When is reputation bad?," Games and Economic Behavior, Elsevier, vol. 63(2), pages 498-526, July.
  3. Martin Cripps & George J. Mailath & Larry Samuelson, 2004. "Disappearing Private Reputations in Long-Run Relationships," Levine's Bibliography 122247000000000086, UCLA Department of Economics.
  4. Sorin, Sylvain, 1999. "Merging, Reputation, and Repeated Games with Incomplete Information," Games and Economic Behavior, Elsevier, vol. 29(1-2), pages 274-308, October.
  5. 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.
  6. Blundell,Richard & Newey,Whitney K. & Persson,Torsten (ed.), 2006. "Advances in Economics and Econometrics," Cambridge Books, Cambridge University Press, number 9780521692083.
  7. 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.
  8. Hausken, Kjell, 2005. "The battle of the sexes when the future is important," Economics Letters, Elsevier, vol. 87(1), pages 89-93, April.
  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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