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Non-Zero-Sum Stochastic Games

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Handbook of Dynamic Game Theory

Abstract

This chapter describes a number of results obtained in the last 60 years on the theory of non-zero-sum discrete-time stochastic games. We provide an overview of almost all basic streams of research in this area such as the existence of stationary Nash and correlated equilibria in models on countable and general state spaces, the existence of subgame-perfect equilibria, algorithms, stopping games, and the existence of uniform equilibria. Our survey incorporates several examples of games studied in operations research and economics. In particular, separate sections are devoted to intergenerational games, dynamic Cournot competition and game models of resource extraction. The provided reference list includes not only seminal papers that commenced research in various directions but also exposes recent advances in this field.

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Acknowledgements

We thank Tamer Başar and Georges Zaccour for inviting us to write this chapter and their help. We also thank Elżbieta Ferenstein, János Flesch, Eilon Solan, Yeneng Sun, Krzysztof Szajowski and two reviewers for their comments on an earlier version of this survey.

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Authors and Affiliations

  1. Faculty of Pure and Applied Mathematics, Wrocław University of Science and Technology, Wrocław, Poland

    Anna Jaśkiewicz

  2. Faculty of Mathematics, Computer Science and Econometrics, University of Zielona Góra, Zielona Góra, Poland

    Andrzej S. Nowak

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  1. Anna Jaśkiewicz
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Correspondence to Anna Jaśkiewicz .

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Editors and Affiliations

  1. Center for Advanced Study, University of Illinois Urbana-Champaign, Urbana, Illinois, USA

    Tamer Basar

  2. GERAD, HEC Montréal, Montreal, Québec, Canada

    Georges Zaccour

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  1. Coordinated Science Laboratory and Department of Electrical and Computer Engineering, University of Illinois at Urbana-Champaign, 1308 West Main, 61801, Urbana, IL, USA

    Tamer Başar

  2. Département de sciences de la décision, GERAD, HEC Montréal, Montreal, QC, Canada

    Georges Zaccour

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Jaśkiewicz, A., Nowak, A.S. (2018). Non-Zero-Sum Stochastic Games. In: Basar, T., Zaccour, G. (eds) Handbook of Dynamic Game Theory. Springer, Cham. https://doi.org/10.1007/978-3-319-27335-8_33-3

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  1. Latest

    Non-Zero-Sum Stochastic Games
    Published:
    14 December 2017

    DOI: https://doi.org/10.1007/978-3-319-27335-8_33-3

  2. Non-Zero-Sum Stochastic Games
    Published:
    28 June 2017

    DOI: https://doi.org/10.1007/978-3-319-27335-8_33-2

  3. Original

    Non-Zero-Sum Stochastic Games
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    10 November 2016

    DOI: https://doi.org/10.1007/978-3-319-27335-8_33-1

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