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An Approach for Determining Stationary Equilibria in a Single-Controller Average Stochastic Game

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Frontiers of Dynamic Games

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Abstract

In this paper the problem of the existence and determining stationary Nash equilibria in a single-controller average stochastic game is considered. The set of states and the set of actions in the game are assumed to be finite. We show that all stationary equilibria for such a game can be obtained from an auxiliary noncooperative static game in normal form where the payoffs are quasi-monotonic (quasi-convex and quasi-concave) with respect to the corresponding strategies of the players and graph-continuous in the sense of Dasgupta and Maskin. Based on this we present a proof of the existence of stationary equilibria in a single-controller average stochastic game and propose an approach for determining the optimal stationary strategies of the players.

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Acknowledgements

The authors are grateful to the referee for the valuable suggestions and remarks contributing to improve the presentation of the paper.

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Authors and Affiliations

  1. Institute of Mathematics and Computer Science, Chisinau, Moldova

    Dmitrii Lozovanu

  2. Universität der Bundeswehr München, München, Germany

    Stefan Pickl

Authors
  1. Dmitrii Lozovanu
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  2. Stefan Pickl
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Correspondence to Dmitrii Lozovanu .

Editor information

Editors and Affiliations

  1. St. Petersburg State University, St. Petersburg, Russia

    Leon A. Petrosyan

  2. Institute of Applied Mathematical Research, Russian Academy of Sciences, Petrozavodsk, Russia

    Vladimir V. Mazalov

  3. Graduate School of Management, St. Petersburg State University, St. Petersburg, Russia

    Nikolay A. Zenkevich

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Lozovanu, D., Pickl, S. (2021). An Approach for Determining Stationary Equilibria in a Single-Controller Average Stochastic Game. In: Petrosyan, L.A., Mazalov, V.V., Zenkevich, N.A. (eds) Frontiers of Dynamic Games. Trends in Mathematics. Birkhäuser, Cham. https://doi.org/10.1007/978-3-030-93616-7_13

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