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Uniform Equilibrium: More than Two Players

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Stochastic Games and Applications

Part of the book series: NATO Science Series ((ASIC,volume 570))

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Abstract

The basic question addressed in this chapter is: Does every multi-player stochastic game (with finite state and action spaces) admit a uniform equilibrium payoff? To this day, no counterexample has been found. A positive answer has been given for several special classes, including zero-sum stochastic games [9], two-player non-zero-sum absorbing games [28] and two-player non-zero-sum stochastic games [26]. For multi-player games, existence of stationary equilibrium profiles has been proven for irreducible games [14],[3] and of “almost” stationary equilibrium profiles for games with additive rewards and additive transitions as well as for games with perfect information [25]. In this chapter I review recent results for games with more than two players.

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Author information

Authors and Affiliations

  1. Northwestern University, Evanston, USA

    Eilon Solan

  2. Tel Aviv University, Tel Aviv, Israel

    Eilon Solan

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  1. Eilon Solan
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Editor information

Editors and Affiliations

  1. Institute of Mathematics and Center for Rationality and Interactive Decision Theory, Hebrew University of Jerusalem, Jerusalem, Israel

    Abraham Neyman

  2. Université Pierre et Marie Curie and École Polytechnique, Paris, France

    Sylvain Sorin

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Solan, E. (2003). Uniform Equilibrium: More than Two Players. In: Neyman, A., Sorin, S. (eds) Stochastic Games and Applications. NATO Science Series, vol 570. Springer, Dordrecht. https://doi.org/10.1007/978-94-010-0189-2_20

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  • DOI: https://doi.org/10.1007/978-94-010-0189-2_20

  • Publisher Name: Springer, Dordrecht

  • Print ISBN: 978-1-4020-1493-2

  • Online ISBN: 978-94-010-0189-2

  • eBook Packages: Springer Book Archive

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