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Folk Theorems with Bounded Recall under (Almost) Perfect Monitoring

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  • George J. Mailath

    ()
    (Department of Economics, University of Pennsylvania)

  • Wojciech Olszewski

    ()
    (Department of Economics, Northwestern University)

Abstract

A strategy profile in a repeated game has L bounded recall 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 Penn Institute for Economic Research, Department of Economics, University of Pennsylvania in its series PIER Working Paper Archive with number 08-019.

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Length: 29 pages
Date of creation: 30 May 2008
Date of revision:
Handle: RePEc:pen:papers:08-019

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

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References

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  1. Fudenberg, Drew & Maskin, Eric, 1986. "The Folk Theorem in Repeated Games with Discounting or with Incomplete Information," Econometrica, Econometric Society, vol. 54(3), pages 533-54, May.
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Citations

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Cited by:
  1. 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.
  2. Aperjis, Christina & Miao, Yali & Zeckhauser, Richard Jay, 2011. "Variable Temptations and Black Mark Reputations," Scholarly Articles 5027138, Harvard Kennedy School of Government.
  3. 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.
  4. V. Bhaskar & George J. Mailath & Stephen Morris, 2012. "A Foundation for Markov Equilibria in Infinite Horizon Perfect Information Games," PIER Working Paper Archive 12-043, Penn Institute for Economic Research, Department of Economics, University of Pennsylvania.
  5. Sugaya, Takuo & Takahashi, Satoru, 2013. "Coordination failure in repeated games with private monitoring," Journal of Economic Theory, Elsevier, vol. 148(5), pages 1891-1928.
  6. 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.
  7. 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.
  8. Barlo, Mehmet & Urgun, Can, 2011. "Stochastic discounting in repeated games: Awaiting the almost inevitable," MPRA Paper 28537, University Library of Munich, Germany.
  9. 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.
  10. 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.
  11. 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.

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