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Nonzero-Sum Stochastic Games

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Stochastic and Differential Games

Part of the book series: Annals of the International Society of Dynamic Games ((AISDG,volume 4))

Abstract

This chapter discusses stochastic games. We focus on nonzero-sum games and provide a detailed survey of selected recent results. In Section 1, we consider stochastic Markov games. A correlation of strategies of the players, involving “public signals,” is described, and a correlated equilibrium theorem proved recently by Nowak and Raghavan for discounted stochastic games with general state space is presented. We also resport an extension of this result to a class of undiscounted stochastic games, satisfying some uniform ergodicity condition. Stopping games are related to stochastic Markov games. In Section 2, we describe a version of Dynkin’s game related to observation of a Markov process with random assignment mechanism of states to the players. Some recent constributions of the second author in this area are reported. The chapter also provides a brief overview of the theory of nonzero-sum stochastic games and stopping games.

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Authors and Affiliations

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

    Andrzej S. Nowak & Krzysztof Szajowski

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  1. Andrzej S. Nowak
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  2. Krzysztof Szajowski
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Editors and Affiliations

  1. Dipartimento di Matematica Pura e Applicata, Università degli Studi di Padova, 35131, Padova, Italy

    Martino Bardi

  2. Department of Mathematics, University of Illinois, Chicago, IL, USA

    T. E. S. Raghavan

  3. Indian Statistical Institute, New Delhi, India

    T. Parthasarathy

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Nowak, A.S., Szajowski, K. (1999). Nonzero-Sum Stochastic Games. In: Bardi, M., Raghavan, T.E.S., Parthasarathy, T. (eds) Stochastic and Differential Games. Annals of the International Society of Dynamic Games, vol 4. Birkhäuser, Boston, MA. https://doi.org/10.1007/978-1-4612-1592-9_7

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