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Stochastic games: Recent results

In: Handbook of Game Theory with Economic Applications

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  • Vieille, Nicolas

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

  • 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.
    • Handle: RePEc:eee:gamchp:3-48
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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. Burhaneddin Sandıkçı & Lisa M. Maillart & Andrew J. Schaefer & Oguzhan Alagoz & Mark S. Roberts, 2008. "Estimating the Patient's Price of Privacy in Liver Transplantation," Operations Research, INFORMS, vol. 56(6), pages 1393-1410, December.
    3. 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.
    4. Andrzej Nowak & Eilon Solan & Sylvain Sorin, 2013. "Preface: Special Issue on Stochastic Games," Dynamic Games and Applications, Springer, vol. 3(2), pages 125-127, June.
    5. Boyarchenko, Svetlana & Levendorskiĭ, Sergei, 2014. "Preemption games under Lévy uncertainty," Games and Economic Behavior, Elsevier, vol. 88(C), pages 354-380.

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    JEL classification:

    • C - Mathematical and Quantitative Methods

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