Geodesic
Nash {\Large $\epsilon $}-equilibria for stochastic games with total reward functions: an approach through Markov decision processes
Kybernetika, Tome 55 (2019) no. 1, pp. 152-165
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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.
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.
DOI : 10.14736/kyb-2019-1-0152
Classification : 90C40, 91A15, 91A50
Keywords: stochastic games; Nash equilibrium; Markov decision processes; total rewards 
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     title = {Nash {{\Large} $\epsilon $}-equilibria for stochastic games with total reward functions: an approach through {Markov} decision processes},
     journal = {Kybernetika},
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González-Padilla, Francisco J.; Montes-de-Oca, Raúl. Nash {\Large $\epsilon $}-equilibria for stochastic games with total reward functions: an approach through Markov decision processes. Kybernetika, Tome 55 (2019) no. 1, pp. 152-165. doi: 10.14736/kyb-2019-1-0152

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