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Perfect Public Equilibrium When Players Are Patient

  • Takahashi, Satoru
  • Levine, David
  • Fudenberg, Drew

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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File URL: http://dash.harvard.edu/bitstream/handle/1/3196336/perfect_public.pdf
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Paper provided by Harvard University Department of Economics in its series Scholarly Articles with number 3196336.

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Date of creation: 2007
Date of revision:
Publication status: Published in Games and Economic Behavior
Handle: RePEc:hrv:faseco:3196336
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Web page: http://www.economics.harvard.edu/

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  1. Susan Athey & Kyle Bagwell, 1999. "Optimal Collusion with Private Information," Working papers 99-17, Massachusetts Institute of Technology (MIT), Department of Economics.
  2. Farrell, Joseph & Maskin, Eric, 1989. "Renegotiation in repeated games," Games and Economic Behavior, Elsevier, vol. 1(4), pages 327-360, December.
  3. D. Fudenberg & D. M. Kreps & E. Maskin, 1998. "Repeated Games with Long-run and Short-run Players," Levine's Working Paper Archive 608, David K. Levine.
  4. Michihiro Kandori & Hitoshi Matsushima, 1998. "Private Observation, Communication and Collusion," Econometrica, Econometric Society, vol. 66(3), pages 627-652, May.
  5. 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.
  6. Fudenberg, D. & Levine, D.K., 1991. "Efficiency and Obsevability with Long-Run and Short-Run Players," Working papers 591, Massachusetts Institute of Technology (MIT), Department of Economics.
  7. 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.
  8. 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.
  9. Abreu, Dilip, 1986. "Extremal equilibria of oligopolistic supergames," Journal of Economic Theory, Elsevier, vol. 39(1), pages 191-225, 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 & Pearce, David & Stacchetti, Ennio, 1986. "Optimal cartel equilibria with imperfect monitoring," Journal of Economic Theory, Elsevier, vol. 39(1), pages 251-269, June.
  12. Jeffrey Ely & Drew Fudenberg & David K Levine, 2005. "When is Reputation Bad," Levine's Working Paper Archive 618897000000000016, David K. Levine.
  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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