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Subgame Perfect Equilibria in Discounted Stochastic Games

Author

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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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    File URL: http://ace-economics.fi/kuvat/dp87.pdf
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    References listed on IDEAS

    as
    1. Cronshaw, Mark B, 1997. "Algorithms for Finding Repeated Game Equilibria," Computational Economics, Springer;Society for Computational Economics, vol. 10(2), pages 139-168, May.
    2. Ashok P. Maitra & William D. Sudderth, 2007. "Subgame-Perfect Equilibria for Stochastic Games," Mathematics of Operations Research, INFORMS, vol. 32(3), pages 711-722, August.
    3. Mitri Kitti, 2011. "Conditionally Stationary Equilibria in Discounted Dynamic Games," Dynamic Games and Applications, Springer, vol. 1(4), pages 514-533, December.
    4. Abreu, Dilip, 1988. "On the Theory of Infinitely Repeated Games with Discounting," Econometrica, Econometric Society, vol. 56(2), pages 383-396, March.
    5. Eilon Solan, 1998. "Discounted Stochastic Games," Mathematics of Operations Research, INFORMS, vol. 23(4), pages 1010-1021, November.
    6. 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.
    7. Kenneth L. Judd & Sevin Yeltekin & James Conklin, 2003. "Computing Supergame Equilibria," Econometrica, Econometric Society, vol. 71(4), pages 1239-1254, July.
    8. Abreu, Dilip, 1986. "Extremal equilibria of oligopolistic supergames," Journal of Economic Theory, Elsevier, vol. 39(1), pages 191-225, June.
    9. 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.
    10. repec:spr:compst:v:78:y:2013:i:1:p:77-100 is not listed on IDEAS
    11. Richard Bellman, 1957. "On a Dynamic Programming Approach to the Caterer Problem--I," Management Science, INFORMS, vol. 3(3), pages 270-278, April.
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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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