## Nash $$\epsilon$$-equilibria for stochastic games with total reward functions: an approach through Markov decision processes.(English)Zbl 1449.91018

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.

### MSC:

 91A15 Stochastic games, stochastic differential games 91A05 2-person games 90C40 Markov and semi-Markov decision processes
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### References:

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