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Kybernetika 55 no. 1, 152-165, 2019

Nash ε-equilibria for stochastic games with total reward functions: an approach through Markov decision processes

Francisco J. González-Padilla and Raúl Montes-de-OcaDOI: 10.14736/kyb-2019-1-0152

Abstract:

The main objective of this paper is to find structural conditions under which a stochastic game between two players with total reward functions has an $\epsilon$-equilibrium. To reach this goal, the results of Markov decision processes are used to find $\epsilon$-optimal strategies for each player and then the correspondence of a better answer as well as a more general version of Kakutani's Fixed Point Theorem to obtain the $\epsilon$-equilibrium mentioned. Moreover, two examples to illustrate the theory developed are presented.

Keywords:

Nash equilibrium, Markov decision processes, stochastic games, total rewards

Classification:

91A15, 91A50, 90C40

paper.pdf

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