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Subgame Perfect Equilibria in Discounted Stochastic Games

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  • Mitri Kitti

    (Department of Economics, University of Turku)

Abstract

This paper considers policies and payoffs corresponding to subgame perfect equilibrium strategies in discounted stochastic games with finitely many states. It is shown that a policy is induced by an equilibrium strategy if and only if it can be supported with the threat of reverting to the induced policy that gives the least equilibrium payoff for the deviator. It follows that the correspondence of subgame perfect equilibrium payoffs is the largest fixed-point of a correspondence-valued operator defined by the players's incentive compatibility conditions. Moreover, the fixed-point iteration converges to the equilibrium payoff correspondence.

Suggested Citation

  • Mitri Kitti, 2013. "Subgame Perfect Equilibria in Discounted Stochastic Games," Discussion Papers 87, Aboa Centre for Economics.
    • Handle: RePEc:tkk:dpaper:dp87
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    References listed on IDEAS

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    1. Mertens, J.-F. & Parthasarathy, T., 1987. "Equilibria for discounted stochastic games," LIDAM Discussion Papers CORE 1987050, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
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    6. Kimmo Berg & Mitri Kitti, 2013. "Computing Equilibria in Discounted 2 × 2 Supergames," Computational Economics, Springer;Society for Computational Economics, vol. 41(1), pages 71-88, January.
    7. Richard Bellman, 1957. "On a Dynamic Programming Approach to the Caterer Problem--I," Management Science, INFORMS, vol. 3(3), pages 270-278, April.
    8. Mitri Kitti, 2011. "Conditionally Stationary Equilibria in Discounted Dynamic Games," Dynamic Games and Applications, Springer, vol. 1(4), pages 514-533, December.
    9. Eilon Solan, 1998. "Discounted Stochastic Games," Mathematics of Operations Research, INFORMS, vol. 23(4), pages 1010-1021, November.
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    11. Abreu, Dilip, 1986. "Extremal equilibria of oligopolistic supergames," Journal of Economic Theory, Elsevier, vol. 39(1), pages 191-225, June.
    12. Mitri Kitti, 2013. "Conditional Markov equilibria in discounted dynamic games," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 78(1), pages 77-100, August.
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    Cited by:

    1. Kimmo Berg, 2016. "Elementary Subpaths in Discounted Stochastic Games," Dynamic Games and Applications, Springer, vol. 6(3), pages 304-323, September.
    2. Mitri Kitti, 2014. "Equilibrium Payoffs for Pure Strategies in Repeated Games," Discussion Papers 98, Aboa Centre for Economics.

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    More about this item

    Keywords

    Subgame Perfect Equilibria in Discounted Stochastic Games;

    JEL classification:

    • C73 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Stochastic and Dynamic Games; Evolutionary Games

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