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Perfect Public Equilibrium When Players Are Patient

Author

Listed:
  • Takahashi, Satoru
  • Levine, David
  • Fudenberg, Drew
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.

Suggested Citation

  • Takahashi, Satoru & Levine, David & Fudenberg, Drew, 2007. "Perfect Public Equilibrium When Players Are Patient," Scholarly Articles 3196336, Harvard University Department of Economics.
    • Handle: RePEc:hrv:faseco:3196336
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    References listed on IDEAS

    as
    1. 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.
    2. Drew Fudenberg & David Levine & Eric Maskin, 2008. "The Folk Theorem With Imperfect Public Information," World Scientific Book Chapters, in: Drew Fudenberg & David K Levine (ed.), A Long-Run Collaboration On Long-Run Games, chapter 12, pages 231-273, World Scientific Publishing Co. Pte. Ltd..
    3. Jeffrey Ely & Drew Fudenberg & David K. Levine, 2008. "When is reputation bad?," World Scientific Book Chapters, in: Drew Fudenberg & David K Levine (ed.), A Long-Run Collaboration On Long-Run Games, chapter 10, pages 177-205, World Scientific Publishing Co. Pte. Ltd..
    4. Athey, Susan & Bagwell, Kyle, 2001. "Optimal Collusion with Private Information," RAND Journal of Economics, The RAND Corporation, vol. 32(3), pages 428-465, Autumn.
    5. Drew Fudenberg & David K. Levine, 2008. "Efficiency and Observability with Long-Run and Short-Run Players," World Scientific Book Chapters, in: Drew Fudenberg & David K Levine (ed.), A Long-Run Collaboration On Long-Run Games, chapter 13, pages 275-307, World Scientific Publishing Co. Pte. Ltd..
    6. Farrell, Joseph & Maskin, Eric, 1989. "Renegotiation in repeated games," Games and Economic Behavior, Elsevier, vol. 1(4), pages 327-360, December.
    7. Wen, Quan, 1994. "The "Folk Theorem" for Repeated Games with Complete Information," Econometrica, Econometric Society, vol. 62(4), pages 949-954, July.
    8. Drew Fudenberg & David M. Kreps & Eric S. Maskin, 1990. "Repeated Games with Long-run and Short-run Players," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 57(4), pages 555-573.
    9. Abreu, Dilip & Pearce, David & Stacchetti, Ennio, 1990. "Toward a Theory of Discounted Repeated Games with Imperfect Monitoring," Econometrica, Econometric Society, vol. 58(5), pages 1041-1063, September.
    10. Drew Fudenberg & Eric Maskin, 2008. "The Folk Theorem In Repeated Games With Discounting Or With Incomplete Information," World Scientific Book Chapters, in: Drew Fudenberg & David K Levine (ed.), A Long-Run Collaboration On Long-Run Games, chapter 11, pages 209-230, World Scientific Publishing Co. Pte. Ltd..
    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. Abreu, Dilip & Dutta, Prajit K & Smith, Lones, 1994. "The Folk Theorem for Repeated Games: A NEU Condition," Econometrica, Econometric Society, vol. 62(4), pages 939-948, July.
    13. Abreu, Dilip, 1986. "Extremal equilibria of oligopolistic supergames," Journal of Economic Theory, Elsevier, vol. 39(1), pages 191-225, June.
    14. Tomala, Tristan, 2009. "Perfect communication equilibria in repeated games with imperfect monitoring," Games and Economic Behavior, Elsevier, vol. 67(2), pages 682-694, November.
    15. Michihiro Kandori & Hitoshi Matsushima, 1998. "Private Observation, Communication and Collusion," Econometrica, Econometric Society, vol. 66(3), pages 627-652, May.
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    JEL classification:

    • I10 - Health, Education, and Welfare - - Health - - - General

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