IDEAS home Printed from https://ideas.repec.org/p/tkk/dpaper/dp87.html
   My bibliography  Save this paper

Subgame Perfect Equilibria in Discounted Stochastic Games

Author

Listed:
  • 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
    as

    Download full text from publisher

    File URL: http://ace-economics.fi/kuvat/dp87.pdf
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    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).
    2. Cronshaw, Mark B, 1997. "Algorithms for Finding Repeated Game Equilibria," Computational Economics, Springer;Society for Computational Economics, vol. 10(2), pages 139-168, May.
    3. 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.
    4. Abreu, Dilip, 1988. "On the Theory of Infinitely Repeated Games with Discounting," Econometrica, Econometric Society, vol. 56(2), pages 383-396, March.
    5. Kenneth L. Judd & Sevin Yeltekin & James Conklin, 2003. "Computing Supergame Equilibria," Econometrica, Econometric Society, vol. 71(4), pages 1239-1254, July.
    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.
    10. 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.
    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.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    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.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. 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.
    2. Kimmo Berg, 2016. "Elementary Subpaths in Discounted Stochastic Games," Dynamic Games and Applications, Springer, vol. 6(3), pages 304-323, September.
    3. Kimmo Berg & Mitri Kitti, 2014. "Equilibrium Paths in Discounted Supergames," Discussion Papers 96, Aboa Centre for Economics.
    4. Kimmo Berg & Markus Kärki, 2018. "Critical Discount Factor Values in Discounted Supergames," Games, MDPI, vol. 9(3), pages 1-17, July.
    5. 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.
    6. Kimmo Berg, 2017. "Extremal Pure Strategies and Monotonicity in Repeated Games," Computational Economics, Springer;Society for Computational Economics, vol. 49(3), pages 387-404, March.
    7. Kimmo Berg & Gijs Schoenmakers, 2017. "Construction of Subgame-Perfect Mixed-Strategy Equilibria in Repeated Games," Games, MDPI, vol. 8(4), pages 1-14, November.
    8. Mitri Kitti, 2014. "Equilibrium Payoffs for Pure Strategies in Repeated Games," Discussion Papers 98, Aboa Centre for Economics.
    9. Rasch, Alexander & Wambach, Achim, 2009. "Internal decision-making rules and collusion," Journal of Economic Behavior & Organization, Elsevier, vol. 72(2), pages 703-715, November.
    10. Susanne Goldlücke & Sebastian Kranz, 2018. "Discounted stochastic games with voluntary transfers," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 66(1), pages 235-263, July.
    11. Labrecciosa Paola & Colombo Luca, 2010. "Technology Uncertainty and Market Collusion," The B.E. Journal of Economic Analysis & Policy, De Gruyter, vol. 10(1), pages 1-17, March.
    12. Cheng, Long & McDonald, Stuart & Ye, Guangliang, 2023. "Cartelization under present bias and imperfect public signals," Mathematical Social Sciences, Elsevier, vol. 123(C), pages 77-86.
    13. Döpper, Hendrik & Rasch, Alexander, 2024. "Combinable products, price discrimination, and collusion," International Journal of Industrial Organization, Elsevier, vol. 94(C).
    14. Gary Gorton & Ping He, 2023. "Optimal monetary policy in a collateralized economy," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 75(1), pages 55-89, January.
    15. Barelli, Paulo & Duggan, John, 2014. "A note on semi-Markov perfect equilibria in discounted stochastic games," Journal of Economic Theory, Elsevier, vol. 151(C), pages 596-604.
    16. Basuchoudhary, Atin & Conlon, John R., 2013. "Silence is golden: communication, silence, and cartel stability," MPRA Paper 44246, University Library of Munich, Germany.
    17. Colombo, Luca & Labrecciosa, Paola, 2006. "Optimal punishments with detection lags," Economics Letters, Elsevier, vol. 92(2), pages 198-201, August.
    18. Abito, Jose Miguel, 2015. "How much can we identify from repeated games?," MPRA Paper 66378, University Library of Munich, Germany.
    19. Cesi Berardino & Iozzi Alberto & Valentini Edilio, 2012. "Regulating Unverifiable Quality by Fixed-Price Contracts," The B.E. Journal of Economic Analysis & Policy, De Gruyter, vol. 12(1), pages 1-39, September.

    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

    NEP fields

    This paper has been announced in the following NEP Reports:

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:tkk:dpaper:dp87. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Susmita Baulia (email available below). General contact details of provider: https://edirc.repec.org/data/tukkkfi.html .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.