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Title: Nash {\Large $\epsilon $}-equilibria for stochastic games with total reward functions: an approach through Markov decision processes (English)
Author: González-Padilla, Francisco J.
Author: Montes-de-Oca, Raúl
Language: English
Journal: Kybernetika
ISSN: 0023-5954 (print)
ISSN: 1805-949X (online)
Volume: 55
Issue: 1
Year: 2019
Pages: 152-165
Summary lang: English
Category: math
Summary: 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. (English)
Keyword: stochastic games
Keyword: Nash equilibrium
Keyword: Markov decision processes
Keyword: total rewards
MSC: 90C40
MSC: 91A15
MSC: 91A50
idZBL: Zbl 07088883
idMR: MR3935419
DOI: 10.14736/kyb-2019-1-0152
Date available: 2019-05-07T11:15:02Z
Last updated: 2020-02-27
Stable URL:
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