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Stochastic Games: recent results

Author

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  • 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

This chapter presents developments in the theory of stochastic games that have taken place in recent years. It complements the contribution by Mertens. Major emphasis is put on stochastic games with finite state and action sets. In the zero-sum case, a classical result of Mertens and Neyman states that given [epsilon] > 0, each player has a strategy that is [epsilon]-optimal for all discount factors close to zero. Extensions to non-zero-sum games are dealt with here. In particular, the proof of existence of uniform equilibrium payoffs for two-player games is discussed, as well as the results available for more-than-two-player games. Important open problems related to N-player games are introduced by means of a class of simple stochastic games, called quitting, or stopping, games. Finally, recent results on zero-sum games with imperfect monitoring and on zero-sum games with incomplete information are surveyed.

Suggested Citation

  • Nicolas Vieille, 2001. "Stochastic Games: recent results," Working Papers hal-00596229, HAL.
  • Handle: RePEc:hal:wpaper:hal-00596229
    Note: View the original document on HAL open archive server: https://hal-hec.archives-ouvertes.fr/hal-00596229
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    References listed on IDEAS

    as
    1. Robert J. Aumann, 1995. "Repeated Games with Incomplete Information," MIT Press Books, The MIT Press, edition 1, volume 1, number 0262011476.
    2. Frank Thuijsman & Thirukkannamangai E. S. Raghavan, 1997. "Perfect Information Stochastic Games and Related Classes," International Journal of Game Theory, Springer;Game Theory Society, vol. 26(3), pages 403-408.
    3. Sorin, Sylvain, 1992. "Repeated games with complete information," Handbook of Game Theory with Economic Applications, in: R.J. Aumann & S. Hart (ed.), Handbook of Game Theory with Economic Applications, edition 1, volume 1, chapter 4, pages 71-107, Elsevier.
    4. Solan, Eilon & Vieille, Nicolas, 2002. "Correlated Equilibrium in Stochastic Games," Games and Economic Behavior, Elsevier, vol. 38(2), pages 362-399, February.
    5. Aumann, Robert J. & Heifetz, Aviad, 2002. "Incomplete information," 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 43, pages 1665-1686, Elsevier.
    6. Mertens, Jean-Francois, 2002. "Stochastic games," 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 47, pages 1809-1832, Elsevier.
    7. Eilon Solan & Nicolas Vieille, 2001. "Quitting Games," Mathematics of Operations Research, INFORMS, vol. 26(2), pages 265-285, May.
    8. repec:dau:papers:123456789/6231 is not listed on IDEAS
    9. Nicolas Vieille & Dinah Rosenberg, 2000. "The Maxmin of Recursive Games with Incomplete Information on one Side," Post-Print hal-00481429, HAL.
    10. Mertens,Jean-François & Sorin,Sylvain & Zamir,Shmuel, 2015. "Repeated Games," Cambridge Books, Cambridge University Press, number 9781107030206, February.
      • Mertens,Jean-François & Sorin,Sylvain & Zamir,Shmuel, 2015. "Repeated Games," Cambridge Books, Cambridge University Press, number 9781107662636, February.
    11. Eilon Solan, 1999. "Three-Player Absorbing Games," Mathematics of Operations Research, INFORMS, vol. 24(3), pages 669-698, August.
    12. Zamir, Shmuel, 1992. "Repeated games of incomplete information: Zero-sum," Handbook of Game Theory with Economic Applications, in: R.J. Aumann & S. Hart (ed.), Handbook of Game Theory with Economic Applications, edition 1, volume 1, chapter 5, pages 109-154, Elsevier.
    13. Donald A. Walker (ed.), 2000. "Equilibrium," Books, Edward Elgar Publishing, volume 0, number 1585.
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    Cited by:

    1. Laraki, Rida & Sorin, Sylvain, 2015. "Advances in Zero-Sum Dynamic Games," Handbook of Game Theory with Economic Applications,, Elsevier.
    2. Walker, Mark & Wooders, John & Amir, Rabah, 2011. "Equilibrium play in matches: Binary Markov games," Games and Economic Behavior, Elsevier, vol. 71(2), pages 487-502, March.

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    More about this item

    Keywords

    Stochastic Games; zero-sum games; uniform equilibrium payoffs;
    All these keywords.

    JEL classification:

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

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