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Toward a Theory of Discounted Repeated Games with Imperfect Monitoring

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    Abstract

    This paper investigates pure strategy sequential equilibria of repeated games with imperfect monitoring. The approach emphasizes the equilibrium value set and the static optimization problems embedded in external equilibria. We characterize these equilibria, and provide computational and comparative statics results. The "self-generation" and "bang-bang" propositions which were at the core of our analysis of optimal cartel equilibria [2], are generalized to asymmetric games and infinite action spaces. New results on optimal implicit reward functions include the necessity (as opposed to sufficiency) of bang-bang functions, and the nature of optimal punishment regions.

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    File URL: http://cowles.econ.yale.edu/P/cd/d07b/d0791.pdf
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    Bibliographic Info

    Paper provided by Cowles Foundation for Research in Economics, Yale University in its series Cowles Foundation Discussion Papers with number 791.

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    Length: 34 pages
    Date of creation: Apr 1986
    Date of revision:
    Publication status: Published in Econometrica (September 1990), 58(5): 1041-1063
    Handle: RePEc:cwl:cwldpp:791

    Note: CFP 762.
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    Postal: Yale University, Box 208281, New Haven, CT 06520-8281 USA
    Phone: (203) 432-3702
    Fax: (203) 432-6167
    Web page: http://cowles.econ.yale.edu/
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    Postal: Cowles Foundation, Yale University, Box 208281, New Haven, CT 06520-8281 USA

    Related research

    Keywords: Pure strategy sequential equilibria; repeated games; imperfect monitoring;

    References

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    1. Green, Edward J. & Porter, Robert H., 1982. "Noncooperative Collusion Under Imperfect Price Information," Working Papers 367, California Institute of Technology, Division of the Humanities and Social Sciences.
    2. Sanford J Grossman & Oliver D Hart, 2001. "An Analysis of the Principal-Agent Problem," Levine's Working Paper Archive 391749000000000339, David K. Levine.
    3. Paul R. Milgrom, 1981. "Good News and Bad News: Representation Theorems and Applications," Bell Journal of Economics, The RAND Corporation, vol. 12(2), pages 380-391, Autumn.
    4. Radner, Roy, 1986. "Repeated Partnership Games with Imperfect Monitoring and No Discounting," Review of Economic Studies, Wiley Blackwell, vol. 53(1), pages 43-57, January.
    5. Porter, Robert H., 1983. "Optimal cartel trigger price strategies," Journal of Economic Theory, Elsevier, vol. 29(2), pages 313-338, April.
    6. Rogerson, William P, 1985. "The First-Order Approach to Principal-Agent Problems," Econometrica, Econometric Society, vol. 53(6), pages 1357-67, November.
    7. Radner, Roy & Myerson, Roger & Maskin, Eric, 1986. "An Example of a Repeated Partnership Game with Discounting and with Uniformly Inefficient Equilibria," Review of Economic Studies, Wiley Blackwell, vol. 53(1), pages 59-69, January.
    8. 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.
    9. Mirrlees, J A, 1999. "The Theory of Moral Hazard and Unobservable Behaviour: Part I," Review of Economic Studies, Wiley Blackwell, vol. 66(1), pages 3-21, January.
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    Cited by:
    1. Kalai, Ehud & Lehrer, Ehud, 1995. "Subjective games and equilibria," Games and Economic Behavior, Elsevier, vol. 8(1), pages 123-163.
    2. Thomas, J. P., 1995. "Subgame-perfect attainment of minimax punishments in discounted two-person games," Economics Letters, Elsevier, vol. 47(1), pages 1-4, January.

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