This article is cited in 1 paper

Nash equilibria conditions for stochastic positional games

Dmitrii Lozovanu^a, Stefan Pickl<sup>b

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

Abstract: We formulate and study a class of stochastic positional games using a game-theoretical concept to finite state space Markov decision processes with an average and expected total discounted costs optimization criteria. Nash equilibria conditions for the considered class of games are proven and some approaches for determining the optimal strategies of the players are analyzed. The obtained results extend Nash equilibria conditions for deterministic positional games and can be used for studying Shapley stochastic games with average payoffs.

Keywords: Markov decision processes, stochastic positional games, Nash equilibria, Shapley stochastic games, optimal stationary strategies.

Language: English