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Maintaining a Reputation Against A Long-Lived Opponent

  • Marco Celentani

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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File URL: http://www.kellogg.northwestern.edu/research/math/papers/1075.pdf
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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
Contact details of provider: 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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  1. Schmidt, Klaus M, 1993. "Reputation and Equilibrium Characterization in Repeated Games with Conflicting Interests," Econometrica, Econometric Society, vol. 61(2), pages 325-51, March.
  2. David Kreps & Robert Wilson, 1999. "Reputation and Imperfect Information," Levine's Working Paper Archive 238, David K. Levine.
  3. Cripps, Martin W. & Schmidt, Klaus M. & Thomas, Jonathan P., 1996. "Reputation in perturbed repeated games," Munich Reprints in Economics 20052, University of Munich, Department of Economics.
  4. Milgrom, Paul & Roberts, John, 1982. "Predation, reputation, and entry deterrence," Journal of Economic Theory, Elsevier, vol. 27(2), pages 280-312, August.
  5. 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.
  6. Marco Celentani & Wolfgang Pesendorfer, 1992. "Reputation in Dynamic Games," Discussion Papers 1009, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
  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. Celentani, Marco, 1996. "Reputation with Observed Actions," Economic Theory, Springer, vol. 7(3), pages 407-19, April.
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