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Folk theorems with Bounded Recall under(Almost) Perfect Monitoring

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  • George Mailath
  • Wojciech Olszewski

Abstract

A strategy profile in a repeated game has bounded recall L if play under the profile after two distinct histories that agree in the last L periods is equal. Mailath and Morris (2002, 2006) proved that any strict equilibrium in bounded-recall strategies of a game with full support public monitoring is robust to all perturbations of the monitoring structure towards private monitoring (the case of almost-public monitoring), while strict equilibria in unbounded-recall strategies are typically not robust. We prove that the perfect-monitoring folk theorem continues to hold when attention is restricted to strategies with bounded recall and the equilibrium is essentially required to be strict. The general result uses calendar time in an integral way in the construction of the strategy profile. If the players’ action spaces are sufficiently rich, then the strategy profile can be chosen to be independent of calendar time. Either result can then be used to prove a folk theorem for repeated games with almost-perfect almost-public monitoring.

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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 1462.

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Date of creation: Mar 2008
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Handle: RePEc:nwu:cmsems:1462

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Keywords: Repeated games; bounded recall strategies; folk theorem; imperfect monitoring;

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References

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  3. V. Bhaskar & George J. Mailath & Stephen Morris, 2004. "Purification in the Infinitely Repeated Prisoners' Dilemma," Levine's Bibliography 122247000000000028, UCLA Department of Economics.
  4. George J. Mailath & Stephen Morris, 2004. "Coordination Failure in Repeated Games with Almost-Public Monitoring," Cowles Foundation Discussion Papers 1479R, Cowles Foundation for Research in Economics, Yale University, revised Mar 2005.
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Citations

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Cited by:
  1. Mailath, George J. & Olszewski, Wojciech, 2011. "Folk theorems with bounded recall under (almost) perfect monitoring," Games and Economic Behavior, Elsevier, vol. 71(1), pages 174-192, January.
  2. Olivier Compte & Andrew Postlewaite, 2013. "Belief free equilibria," PIER Working Paper Archive 13-020, Penn Institute for Economic Research, Department of Economics, University of Pennsylvania.
  3. Łukasz Balbus & Kevin Reffett & Łukasz Woźny, 2013. "Markov Stationary Equilibria in Stochastic Supermodular Games with Imperfect Private and Public Information," Dynamic Games and Applications, Springer, vol. 3(2), pages 187-206, June.
  4. Yuichi Yamamoto, 2013. "Individual Learning and Cooperation in Noisy Repeated Games," PIER Working Paper Archive 13-038, Penn Institute for Economic Research, Department of Economics, University of Pennsylvania.
  5. Yuichi Yamamoto, 2012. "Individual Learning and Cooperation in Noisy Repeated Games," PIER Working Paper Archive 12-044, Penn Institute for Economic Research, Department of Economics, University of Pennsylvania.
  6. Aperjis, Christina & Miao, Yali & Zeckhauser, Richard J., 2011. "Variable Temptations and Black Market Reputations," Working Paper Series 11-020, Harvard University, John F. Kennedy School of Government.
  7. V. Bhaskar & George J. Mailath & Stephen Morris, 2009. "A Foundation for Markov Equilibria in Infinite Horizon Perfect Information Games," PIER Working Paper Archive 09-029, Penn Institute for Economic Research, Department of Economics, University of Pennsylvania.
  8. Barlo, Mehmet & Urgun, Can, 2011. "Stochastic discounting in repeated games: Awaiting the almost inevitable," MPRA Paper 28537, University Library of Munich, Germany.
  9. Fudenberg, Drew & Olszewski, Wojciech, 2011. "Repeated games with asynchronous monitoring of an imperfect signal," Games and Economic Behavior, Elsevier, vol. 72(1), pages 86-99, May.
  10. V. Bhaskar & George J. Mailath & Stephen Morris, 2012. "A Foundation for Markov Equilibria with Finite Social Memory," PIER Working Paper Archive 12-003, Penn Institute for Economic Research, Department of Economics, University of Pennsylvania.
  11. Sugaya, Takuo & Takahashi, Satoru, 2013. "Coordination failure in repeated games with private monitoring," Journal of Economic Theory, Elsevier, vol. 148(5), pages 1891-1928.

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