Geodesic
On Nash equilibria for stochastic games and determining the optimal strategies of the players
Contributions to game theory and management, Tome 8 (2015), pp. 187-198

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We consider $n$-person stochastic games in the sense of Shapley. The main results of the paper are related to the existence of Nash equilibria and determining the optimal stationary strategies of the players in the considered games. We show that a Nash equilibrium for the stochastic game with average payoff functions of the players exists if an arbitrary situation induces an ergodic Markov chain. For the stochastic game with discounted payoff functions we show that a Nash equilibrium always exists. Some approaches for determining Nash equilibria in the considered games are proposed.
Keywords: Markov decision processes, stochastic games, Nash equilibria, optimal stationary strategies. 
@article{CGTM_2015_8_a14,
     author = {Dmitrii Lozovanu and Stefan Pickl},
     title = {On {Nash} equilibria for stochastic games and determining the optimal strategies of the players},
     journal = {Contributions to game theory and management},
     pages = {187--198},
     publisher = {mathdoc},
     volume = {8},
     year = {2015},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/CGTM_2015_8_a14/}
}
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Dmitrii Lozovanu; Stefan Pickl. On Nash equilibria for stochastic games and determining the optimal strategies of the players. Contributions to game theory and management, Tome 8 (2015), pp. 187-198. http://geodesic.mathdoc.fr/item/CGTM_2015_8_a14/