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Folk theorems with Bounded Recall under(Almost) Perfect Monitoring

Listed author(s):
  • George Mailath
  • Wojciech Olszewski

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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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
Handle: RePEc:nwu:cmsems:1462
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  1. Sabourian, Hamid, 1998. "Repeated games with M-period bounded memory (pure strategies)," Journal of Mathematical Economics, Elsevier, vol. 30(1), pages 1-35, August.
  2. George Mailath & Wojciech Olszewski, 2008. "Folk theorems with Bounded Recall under(Almost) Perfect Monitoring," Discussion Papers 1462, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
  3. Ely, Jeffrey C. & Valimaki, Juuso, 2002. "A Robust Folk Theorem for the Prisoner's Dilemma," Journal of Economic Theory, Elsevier, vol. 102(1), pages 84-105, January.
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  8. George J Mailath & Stephen Morris, 1999. "Repeated Games with Almost Public Monitoring," Levine's Working Paper Archive 2107, David K. Levine.
  9. repec:dau:papers:123456789/6381 is not listed on IDEAS
  10. V. Bhaskar, 1998. "Informational Constraints and the Overlapping Generations Model: Folk and Anti-Folk Theorems," Review of Economic Studies, Oxford University Press, vol. 65(1), pages 135-149.
  11. Fudenberg, Drew & Maskin, Eric, 1986. "The Folk Theorem in Repeated Games with Discounting or with Incomplete Information," Econometrica, Econometric Society, vol. 54(3), pages 533-554, May.
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  13. Barlo, Mehmet & Carmona, Guilherme, 2004. "Time Dependent Bounded Recall Strategies Are Enough to Play the Discounted Repeated Prisoners Dilemma," FEUNL Working Paper Series wp449, Universidade Nova de Lisboa, Faculdade de Economia.
  14. V. Bhaskar & George J. Mailath & Stephen Morris, 2008. "Purification in the Infinitely-Repeated Prisoners' Dilemma," Review of Economic Dynamics, Elsevier for the Society for Economic Dynamics, vol. 11(3), pages 515-528, July.
  15. George J. Mailath & Stephen Morris, 2004. "Coordination Failure in Repeated Games with Almost-Public Monitoring," PIER Working Paper Archive 04-033, Penn Institute for Economic Research, Department of Economics, University of Pennsylvania.
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  18. Johannes Horner & Wojciech Olszewski, 2005. "The Folk Theorem for Games with Private, Almost-Perfect Monitoring," NajEcon Working Paper Reviews 172782000000000006, www.najecon.org.
  19. Abreu, Dilip & Pearce, David & Stacchetti, Ennio, 1986. "Optimal cartel equilibria with imperfect monitoring," Journal of Economic Theory, Elsevier, vol. 39(1), pages 251-269, June.
  20. Itzhak Gilboa & David Schmeidler, 1989. "Infinite Histories and Steady Orbits in Repeated Games," Discussion Papers 846, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
  21. Mailath, George J. & Samuelson, Larry, 2006. "Repeated Games and Reputations: Long-Run Relationships," OUP Catalogue, Oxford University Press, number 9780195300796, December.
  22. Michihiro Kandori & Hitoshi Matsushima, 1998. "Private Observation, Communication and Collusion," Econometrica, Econometric Society, vol. 66(3), pages 627-652, May.
  23. Jeffrey C. Ely & Johannes Hörner & Wojciech Olszewski, 2005. "Belief-Free Equilibria in Repeated Games," Econometrica, Econometric Society, vol. 73(2), pages 377-415, 03.
  24. Piccione, Michele, 2002. "The Repeated Prisoner's Dilemma with Imperfect Private Monitoring," Journal of Economic Theory, Elsevier, vol. 102(1), pages 70-83, January.
  25. Johannes Hörner & Wojciech Olszewski, 2009. "How Robust is the Folk Theorem?," The Quarterly Journal of Economics, Oxford University Press, vol. 124(4), pages 1773-1814.
  26. Lehrer Ehud, 1994. "Finitely Many Players with Bounded Recall in Infinitely Repeated Games," Games and Economic Behavior, Elsevier, vol. 7(3), pages 390-405, November.
  27. Gilad Bavly & Abraham Neyman, 2003. "Online Concealed Correlation by Boundedly Rational Players," Discussion Paper Series dp336, The Federmann Center for the Study of Rationality, the Hebrew University, Jerusalem.
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