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Markov perfection and cooperation in repeated games

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  • Stähler, Frank

Abstract

Markov perfection has become the usual solution concept to determine the non-cooperative equilibrium in a dynamic game. However, Markov perfection is a stronger solution concept than subgame perfection: Markov perfection rules out any cooperation in a repeated prisoners' dilemma game because the history of previous cooperation does neither change the future action space nor the possible payoffs in this setting. This paper demonstrates that a dynamic modelling approach may sustain cooperation by Markov perfect strategies in situations which are usually modelled as repeated prisoners' dilemma games. The idea is that past defection from cooperation changes a compliance state variable which enters the utility function. The corresponding dynamic games are discussed for the trigger strategy and for a strategy which is weakly renegotiation-proof. Finally, the paper shows that dynamic game modelling improves the chances for strong renegotiation-proofness in the corresponding repeated game.

Suggested Citation

  • Stähler, Frank, 1996. "Markov perfection and cooperation in repeated games," Kiel Working Papers 760, Kiel Institute for the World Economy (IfW Kiel).
    • Handle: RePEc:zbw:ifwkwp:760
    as

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    References listed on IDEAS

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    1. van Damme, E.E.C., 1989. "Renegotiation-proof equilibria in repeated prisoners' dilemma," Other publications TiSEM df9180a1-537e-4331-9f2a-7, Tilburg University, School of Economics and Management.
    2. van Damme, Eric, 1989. "Renegotiation-proof equilibria in repeated prisoners' dilemma," Journal of Economic Theory, Elsevier, vol. 47(1), pages 206-217, February.
    3. 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..
    4. Farrell, Joseph & Maskin, Eric, 1989. "Renegotiation in repeated games," Games and Economic Behavior, Elsevier, vol. 1(4), pages 327-360, December.
    5. Dutta Prajit K., 1995. "Collusion, Discounting and Dynamic Games," Journal of Economic Theory, Elsevier, vol. 66(1), pages 289-306, June.
    6. Evans, Robert & Maskin, Eric, 1989. "Efficient renegotiation--proof equilibria in repeated games," Games and Economic Behavior, Elsevier, vol. 1(4), pages 361-369, December.
    7. Mohr, Ernst, 1988. "On the Incredibility of Perfect Threats in Repeated Games: Note," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 29(3), pages 551-555, August.
    8. Abreu, Dilip, 1988. "On the Theory of Infinitely Repeated Games with Discounting," Econometrica, Econometric Society, vol. 56(2), pages 383-396, March.
    9. Douglas Bernheim, B. & Ray, Debraj, 1989. "Collective dynamic consistency in repeated games," Games and Economic Behavior, Elsevier, vol. 1(4), pages 295-326, December.
    10. Becker, Gary S & Murphy, Kevin M, 1988. "A Theory of Rational Addiction," Journal of Political Economy, University of Chicago Press, vol. 96(4), pages 675-700, August.
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    More about this item

    Keywords

    Repeated games; dynamic games; Markov perfection; Folk Theorem;
    All these keywords.

    JEL classification:

    • C70 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - General
    • C72 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Noncooperative Games
    • C73 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Stochastic and Dynamic Games; Evolutionary Games

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