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Pure and Mixed Stationary Nash Equilibria for Average Stochastic Positional Games

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Frontiers of Dynamic Games

Part of the book series: Static & Dynamic Game Theory: Foundations & Applications ((SDGTFA))

Abstract

In this paper we study the problem of the existence of Nash equilibria in pure and mixed stationary strategies for average stochastic positional games. We prove the existence of Nash equilibria in pure stationary strategies for an arbitrary two-player zero-sum average stochastic positional game and for an m-player average stochastic positional game in the case when the probability transition matrices induced by any profile of stationary strategies of the players are unichain. For the general case of an m-player average stochastic positional game we show that a Nash equilibrium in pure stationary strategies may not exist, however a Nash equilibrium always exists in mixed stationary strategies. Based on the proof of these results we present conditions for determining the optimal strategies of the players in the considered average stochastic positional games.

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Acknowledgements

The author is grateful to the referee for useful 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 of Moldova Academy of Sciences, Chisinau, Moldova

    Dmitrii Lozovanu

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  1. Dmitrii Lozovanu
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Correspondence to Dmitrii Lozovanu .

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Editors and Affiliations

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

    Leon A. Petrosyan

  2. Institute of Applied Mathematical Research, Karelia Research Center of RAS, 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. (2019). Pure and Mixed Stationary Nash Equilibria for Average Stochastic Positional Games. In: Petrosyan, L., Mazalov, V., Zenkevich, N. (eds) Frontiers of Dynamic Games. Static & Dynamic Game Theory: Foundations & Applications. Birkhäuser, Cham. https://doi.org/10.1007/978-3-030-23699-1_8

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