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Reputation in the Long-Run with Imperfect Monitoring

  • Alp Atakan
  • Mehmet Ekmekci

We study an infinitely repeated game where two players with equal discount factors play a simultaneous-move stage game. Player one monitors the stagegame actions of player two imperfectly, while player two monitors the pure stagegame actions of player one perfectly. Player one’s type is private information and he may be a “commitment type,” drawn from a countable set of commitment types, who is locked into playing a particular strategy. Under a full-support assumption on the monitoring structure, we prove a reputation result for games with locally nonconflicting interests or games with strictly conflicting interests: if there is positive probability that player one is a particular type whose commitment payoff is equal to player one’s highest payoff, consistent with the players’ individual rationality, then a patient player one secures this type’s commitment payoff in any Bayes-Nash equilibrium of the repeated game. In contrast, if the type’s commitment payoff is strictly less than player one’s highest payoff consistent with the players’ individual rationality, then the worst perfect Bayesian equilibrium payoff for a patient player one is equal to his minimax payoff.

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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 1506.

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Date of creation: 01 Aug 2009
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Handle: RePEc:nwu:cmsems:1506
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  1. Olivier Gossner, 2011. "Simple Bounds on the Value of a Reputation," Econometrica, Econometric Society, vol. 79(5), pages 1627-1641, 09.
  2. Drew Fudenberg & David K. Levine & Eric Maskin, 1994. "The Folk Theorem with Imperfect Public Information," Levine's Working Paper Archive 2058, David K. Levine.
  3. Marco Celentani, 1993. "Maintaining a Reputation Against A Long-Lived Opponent," Discussion Papers 1075R, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
  4. Alp E. Atakan & Mehmet Ekmekci, 2012. "Reputation in Long-Run Relationships," Review of Economic Studies, Oxford University Press, vol. 79(2), pages 451-480.
  5. Cripps,Martin & Scmidt,Klaus & Thomas,Jonathan, 1993. "Reputation in pertubed repeated games," Discussion Paper Serie A 410, University of Bonn, Germany.
  6. 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.
  7. Robert Evans & Jonathan P. Thomas, 1997. "Reputation and Experimentation in Repeated Games with Two Long-Run Players," Econometrica, Econometric Society, vol. 65(5), pages 1153-1174, September.
  8. Fudenberg, Drew & Levine, David K, 1992. "Maintaining a Reputation When Strategies Are Imperfectly Observed," Review of Economic Studies, Wiley Blackwell, vol. 59(3), pages 561-79, July.
  9. Fudenberg, Drew & Levine, David K, 1989. "Reputation and Equilibrium Selection in Games with a Patient Player," Econometrica, Econometric Society, vol. 57(4), pages 759-78, July.
  10. Schmidt, Klaus M, 1993. "Reputation and Equilibrium Characterization in Repeated Games with Conflicting Interests," Econometrica, Econometric Society, vol. 61(2), pages 325-51, March.
  11. 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.
  12. Cripps, Martin W. & Dekel, Eddie & Pesendorfer, Wolfgang, 2005. "Reputation with equal discounting in repeated games with strictly conflicting interests," Journal of Economic Theory, Elsevier, vol. 121(2), pages 259-272, April.
  13. Aoyagi, Masaki, 1996. "Reputation and Dynamic Stackelberg Leadership in Infinitely Repeated Games," Journal of Economic Theory, Elsevier, vol. 71(2), pages 378-393, November.
  14. Mailath, George J. & Samuelson, Larry, 2006. "Repeated Games and Reputations: Long-Run Relationships," OUP Catalogue, Oxford University Press, number 9780195300796, March.
  15. Cripps, Martin W. & Thomas, Jonathan P., 1997. "Reputation and Perfection in Repeated Common Interest Games," Games and Economic Behavior, Elsevier, vol. 18(2), pages 141-158, February.
  16. Davidson, James, 1994. "Stochastic Limit Theory: An Introduction for Econometricians," OUP Catalogue, Oxford University Press, number 9780198774037, March.
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