Equilibria in pure strategies for a two-player zero-sum average stochastic positional game

Dmitrii Lozovanu^a, Stefan Pickl<sup>b

a</sup> Institute of Mathematics and Computer Science, 5 Academiei str., Chişinău, MD-2028, Moldova
^b Institute for Theoretical Computer Science, Mathematics and Operations Research, Universität der Bundeswehr, München, 85577 Neubiberg-München, Germany

Abstract: The problem of the existence and determining equilibria in pure stationary strategies for a two-player zero-sum average stochastic positional game is considered. We show that for such a game there exists the value and players may achieve the value by applying pure stationary strategies of choosing the actions in their positions. Based on a constructive proof of these results we propose an algorithmic approach for determining the optimal pure stationary strategies of the players.

Keywords and phrases: positional game, two-player zero-sum stochastic game, average payoff, pure stationary equilibria.

MSC: 90C15, 90A20, 91A50

Received: 16.02.2022

Language: English

DOI: 10.56415/basm.y2022.i1.p75

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