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Perfect Public Equilibrium When Players are Patient

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Author Info

  • Drew Fudenberg
  • David K Levine
  • Satoru Takahashi

Abstract

We provide a characterization of the limit set of perfect public equilibrium payoffs of repeated games with imperfect public monitoring as the discount factor goes to one. Our result covers general stage games including those that fail a “full-dimensionality†condition that had been imposed in past work. It also provides a characterization of the limit set when the strategies are restricted in a way that endogenously makes the full-dimensionality condition fail, as in the strongly symmetric equilibrium studied by Abreu [Abreu, D., 1986. Extremal equilibria of oligopolistic supergames. J. Econ. Theory 39, 191–228] and Abreu et al. [Abreu, D., Pearce, D., Stacchetti, E., 1986. Optimal cartel equilibria with imperfect monitoring. J. Econ. Theory 39, 251–269]. Finally, we use our characterization to give a sufficient condition for the exact achievability of first-best outcomes. Equilibria of this type, for which all continuation payoffs lie on the Pareto frontier, have a strong renegotiation-proofness property: regardless of the history, players can never unanimously prefer another equilibrium.

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Bibliographic Info

Paper provided by David K. Levine in its series Levine's Working Paper Archive with number 618897000000000865.

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Date of creation: 26 Sep 2004
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Handle: RePEc:cla:levarc:618897000000000865

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Web page: http://www.dklevine.com/

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References

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  1. D. Fudenberg & D. K. Levine, 1994. "Efficiency and Observability with Long-Run and Short-Run Players," Levine's Working Paper Archive 627, David K. Levine.
  2. Joseph Farrell and Eric Maskin., 1987. "Renegotiation in Repeated Games," Economics Working Papers 8759, University of California at Berkeley.
  3. Fudenberg, Drew & Kreps, David M & Maskin, Eric S, 1990. "Repeated Games with Long-run and Short-run Players," Review of Economic Studies, Wiley Blackwell, vol. 57(4), pages 555-73, October.
  4. Abreu, Dilip & Dutta, Prajit K & Smith, Lones, 1994. "The Folk Theorem for Repeated Games: A NEU Condition," Econometrica, Econometric Society, vol. 62(4), pages 939-48, July.
  5. Fudenberg, D. & Maskin, E., 1990. "Nash and perfect equilibria of discounted repeated games," Journal of Economic Theory, Elsevier, vol. 51(1), pages 194-206, June.
  6. Michihiro Kandori & Hitoshi Matsushima, 1998. "Private Observation, Communication and Collusion," Econometrica, Econometric Society, vol. 66(3), pages 627-652, May.
  7. Levine, David & Ely, Jeffrey & Fudenberg, Drew, 2008. "When is Reputation Bad?," Scholarly Articles 3196337, Harvard University Department of Economics.
  8. Susan Athey & Kyle Bagwell, 1999. "Optimal Collusion with Private Information," Working papers 99-17, Massachusetts Institute of Technology (MIT), Department of Economics.
  9. 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.
  10. Wen, Quan, 1994. "The "Folk Theorem" for Repeated Games with Complete Information," Econometrica, Econometric Society, vol. 62(4), pages 949-54, July.
  11. Abreu, Dilip, 1986. "Extremal equilibria of oligopolistic supergames," Journal of Economic Theory, Elsevier, vol. 39(1), pages 191-225, June.
  12. Abreu, Dilip & Pearce, David & Stacchetti, Ennio, 1990. "Toward a Theory of Discounted Repeated Games with Imperfect Monitoring," Econometrica, Econometric Society, vol. 58(5), pages 1041-63, September.
  13. 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. Yamamoto, Yuichi, 2009. "A limit characterization of belief-free equilibrium payoffs in repeated games," Journal of Economic Theory, Elsevier, vol. 144(2), pages 802-824, March.
  2. Fudenberg, Drew & Yamamoto, Yuichi, 2011. "Learning from private information in noisy repeated games," Journal of Economic Theory, Elsevier, vol. 146(5), pages 1733-1769, September.
  3. Markus Kinateder, 2008. "Repeated Games Played in a Network," Working Papers 2008.22, Fondazione Eni Enrico Mattei.
  4. Johannes Horner & Satoru Takahashi & Nicolas Vieille, 2012. "On the Limit Equilibrium Payoff Set in Repeated and Stochastic Games," Levine's Working Paper Archive 786969000000000412, David K. Levine.
  5. repec:hal:journl:halshs-00524134 is not listed on IDEAS
  6. Contou-Carrère, Pauline & Tomala, Tristan, 2011. "Finitely repeated games with semi-standard monitoring," Journal of Mathematical Economics, Elsevier, vol. 47(1), pages 14-21, January.
  7. Chen, Bo, 2008. "On effective minimax payoffs and unequal discounting," Economics Letters, Elsevier, vol. 100(1), pages 105-107, July.
  8. Mihaela van der Schaar & Yuanzhang Xiao & William Zame, 2013. "Designing Efficient Resource Sharing For Impatient Players Using Limited Monitoring," EIEF Working Papers Series 1320, Einaudi Institute for Economics and Finance (EIEF), revised Aug 2013.
  9. Fudenberg, Drew & Levine, David, 2007. "Continuous Time Limits of Repeated Games with Imperfect Public Monitoring," Scholarly Articles 3196334, Harvard University Department of Economics.
  10. Kinateder, Markus, 2009. "Delayed Perfect Monitoring in Repeated Games," MPRA Paper 20443, University Library of Munich, Germany.
  11. Jérôme Renault & Tristan Tomala, 2011. "General Properties of Long-Run Supergames," Dynamic Games and Applications, Springer, vol. 1(2), pages 319-350, June.
  12. Kobayashi, Hajime & Ohta, Katsunori, 2012. "Optimal collusion under imperfect monitoring in multimarket contact," Games and Economic Behavior, Elsevier, vol. 76(2), pages 636-647.
  13. 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.
  14. Eduardo Monteiro & Humberto Moreira, 2006. "Effciency In Two Player Repeated Games Of Imperfect Monitoring," Anais do XXXIV Encontro Nacional de Economia [Proceedings of the 34th Brazilian Economics Meeting] 113, ANPEC - Associação Nacional dos Centros de Pósgraduação em Economia [Brazilian Association of Graduate Programs in Economics].
  15. Richard McLean & Ichiro Obara & Andrew Postlewaite, 2005. "Informational Smallness and Privae Momnitoring in Repeated Games, Second Version," PIER Working Paper Archive 11-029, Penn Institute for Economic Research, Department of Economics, University of Pennsylvania, revised 10 Feb 2011.
  16. Du, Chuang, 2012. "Solving payoff sets of perfect public equilibria: an example," MPRA Paper 38622, University Library of Munich, Germany.
  17. Tomala, Tristan, 2009. "Perfect communication equilibria in repeated games with imperfect monitoring," Games and Economic Behavior, Elsevier, vol. 67(2), pages 682-694, November.
  18. Yuichi Yamamoto, 2010. "The use of public randomization in discounted repeated games," International Journal of Game Theory, Springer, vol. 39(3), pages 431-443, July.
  19. Chen, Bo & Takahashi, Satoru, 2012. "A folk theorem for repeated games with unequal discounting," Games and Economic Behavior, Elsevier, vol. 76(2), pages 571-581.

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