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Correlated Equilibrium in Stochastic Games

Author

Listed:
  • Eilon Solan

    (TAU - Tel Aviv University)

  • Nicolas Vieille

    (GREGH - Groupement de Recherche et d'Etudes en Gestion à HEC - HEC Paris - Ecole des Hautes Etudes Commerciales - CNRS - Centre National de la Recherche Scientifique)

Abstract

We study the existence of uniform correlated equilibrium payoffs in stochastic games. The correlation devices that we use are either autonomous (they base their choice of signal on previous signals, but not on previous states or actions) or stationary (their choice is independent of any data and is drawn according to the same probability distribution at every stage). We prove that any n-player stochastic game admits an autonomous correlated equilibrium payoff. When the game is positive and recursive, a stationary correlated equilibrium payoff exists. Journal of Economic Literature Classification Numbers: C72, C73.

Suggested Citation

  • Eilon Solan & Nicolas Vieille, 2002. "Correlated Equilibrium in Stochastic Games," Post-Print hal-00465020, HAL.
    • Handle: RePEc:hal:journl:hal-00465020
    DOI: 10.1006/game.2001.0887
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    References listed on IDEAS

    as
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    2. Vrieze, O J & Thuijsman, F, 1989. "On Equilibria in Repeated Games with Absorbing States," International Journal of Game Theory, Springer;Game Theory Society, vol. 18(3), pages 293-310.
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    6. Eilon Solan & Nicolas Vieille, 1998. "Quitting Games," Discussion Papers 1227, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
    7. Nicolas Vieille & Dinah Rosenberg, 2000. "The Maxmin of Recursive Games with Incomplete Information on one Side," Post-Print hal-00481429, HAL.
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    13. Eilon Solan, 1999. "Three-Player Absorbing Games," Mathematics of Operations Research, INFORMS, vol. 24(3), pages 669-698, August.
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    Citations

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    Cited by:

    1. Alpern, Steve & Gal, Shmuel & Solan, Eilon, 2010. "A sequential selection game with vetoes," Games and Economic Behavior, Elsevier, vol. 68(1), pages 1-14, January.
    2. Robert Samuel Simon, 2012. "A Topological Approach to Quitting Games," Mathematics of Operations Research, INFORMS, vol. 37(1), pages 180-195, February.
    3. Elena M. Parilina & Alessandro Tampieri, 2018. "Stability and cooperative solution in stochastic games," Theory and Decision, Springer, vol. 84(4), pages 601-625, June.
    4. János Flesch & Gijs Schoenmakers & Koos Vrieze, 2009. "Stochastic games on a product state space: the periodic case," International Journal of Game Theory, Springer;Game Theory Society, vol. 38(2), pages 263-289, June.
    5. Ayala Mashiah-Yaakovi, 2015. "Correlated Equilibria in Stochastic Games with Borel Measurable Payoffs," Dynamic Games and Applications, Springer, vol. 5(1), pages 120-135, March.
    6. 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.
    7. Vieille, Nicolas, 2002. "Stochastic games: Recent results," Handbook of Game Theory with Economic Applications, in: R.J. Aumann & S. Hart (ed.), Handbook of Game Theory with Economic Applications, edition 1, volume 3, chapter 48, pages 1833-1850, Elsevier.
    8. Heng Liu, 2017. "Correlation and unmediated cheap talk in repeated games with imperfect monitoring," International Journal of Game Theory, Springer;Game Theory Society, vol. 46(4), pages 1037-1069, November.
    9. János Flesch & Gijs Schoenmakers & Koos Vrieze, 2008. "Stochastic Games on a Product State Space," Mathematics of Operations Research, INFORMS, vol. 33(2), pages 403-420, May.
    10. Abraham Neyman, 2013. "Stochastic Games with Short-Stage Duration," Dynamic Games and Applications, Springer, vol. 3(2), pages 236-278, June.
    11. Eilon Solan, 2018. "The modified stochastic game," International Journal of Game Theory, Springer;Game Theory Society, vol. 47(4), pages 1287-1327, November.
    12. Neyman, Abraham, 2017. "Continuous-time stochastic games," Games and Economic Behavior, Elsevier, vol. 104(C), pages 92-130.
    13. Heller, Yuval & Solan, Eilon & Tomala, Tristan, 2012. "Communication, correlation and cheap-talk in games with public information," Games and Economic Behavior, Elsevier, vol. 74(1), pages 222-234.
    14. Solan, Eilon, 2018. "Acceptable strategy profiles in stochastic games," Games and Economic Behavior, Elsevier, vol. 108(C), pages 523-540.
    15. Ramsey, David M. & Szajowski, Krzysztof, 2008. "Selection of a correlated equilibrium in Markov stopping games," European Journal of Operational Research, Elsevier, vol. 184(1), pages 185-206, January.
    16. Eilon Solan & Nicolas Vieille, 2010. "Computing uniformly optimal strategies in two-player stochastic games," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 42(1), pages 237-253, January.
    17. Dinah Rosenberg & Eilon Solan & Nicolas Vieille, 2002. "Stochastic Games with Imperfect Monitoring," Discussion Papers 1341, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
    18. Ramsey, David M. & Szajowski, Krzysztof, 2004. "Correlated equilibria in competitive staff selection problem," MPRA Paper 19870, University Library of Munich, Germany, revised 2006.
    19. Eilon Solan & Nicolas Vieille, 2002. "Perturbed Markov Chains," Discussion Papers 1342, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
    20. Flesch, J. & Schoenmakers, G.M. & Vrieze, K., 2008. "Stochastic games on a product state space: the periodic case," Research Memorandum 016, Maastricht University, Maastricht Research School of Economics of Technology and Organization (METEOR).
    21. Eilon Solan & Omri N. Solan, 2021. "Sunspot equilibrium in positive recursive general quitting games," International Journal of Game Theory, Springer;Game Theory Society, vol. 50(4), pages 891-909, December.
    22. Eilon Solan & Rakesh V. Vohra, 1999. "Correlated Equilibrium, Public Signaling and Absorbing Games," Discussion Papers 1272, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
    23. Michael Ludkovski, 2010. "Stochastic Switching Games and Duopolistic Competition in Emissions Markets," Papers 1001.3455, arXiv.org, revised Aug 2010.
    24. Abraham Neyman, 2002. "Stochastic games: Existence of the MinMax," Discussion Paper Series dp295, The Federmann Center for the Study of Rationality, the Hebrew University, Jerusalem.

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    More about this item

    Keywords

    stochastic games; correlated equilibrium; positive recursive games;
    All these keywords.

    JEL classification:

    • 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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