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Stationary Equilibria for Nonzero-Sum Average Payoff Ergodic Stochastic Games with General State Space

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Advances in Dynamic Games and Applications

Part of the book series: Annals of the International Society of Dynamic Games ((AISDG,volume 1))

Abstract

This paper treats of nonzero-sum average payoff stochastic games with arbitrary state spaces. Such models of games very well fit in some studies in economic theory. A natural uniform geometric ergodicity condition, often used in control theory of Markov chains, is imposed on the transition probabilities of the games. A correlation of strategies of the players, involving “public signals”, is allowed in this paper. The main result is an extension of the correlated equilibrium theorem proved recently by the author and Raghavan for dynamic games with discounting to the average payoff stochastic games. Also some special classes of games that possess Nash equilibria without public signals are discussed. This paper also provides a brief overview of the theory of nonzero-sum stochastic games which is very far from being complete.

AMS 1980 Subject Classification. Primary:90D15, Secondary: 93C30.

AMS 1980 Subject Classification, Primary:90D15, Secondary: 93C30.

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Author information

Authors and Affiliations

  1. Institute of Mathematics, Technical University of Wroclaw, Wybrzeże Wyspiańskiego 27, PL-50-370, Wroclaw, Poland

    Andrzej S. Nowak

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  1. Andrzej S. Nowak
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Editor information

Editors and Affiliations

  1. Coordinated Science Laboratory, University of Illinois, Urbana, IL, 61801, USA

    Tamer Başar

  2. Department of Management Studies, University of Geneva, CH-1211, Geneva, Switzerland

    Alain Haurie

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© 1994 Springer Science+Business Media New York

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Nowak, A.S. (1994). Stationary Equilibria for Nonzero-Sum Average Payoff Ergodic Stochastic Games with General State Space. In: Başar, T., Haurie, A. (eds) Advances in Dynamic Games and Applications. Annals of the International Society of Dynamic Games, vol 1. Birkhäuser, Boston, MA. https://doi.org/10.1007/978-1-4612-0245-5_13

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  • DOI: https://doi.org/10.1007/978-1-4612-0245-5_13

  • Publisher Name: Birkhäuser, Boston, MA

  • Print ISBN: 978-1-4612-6679-2

  • Online ISBN: 978-1-4612-0245-5

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