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Deterministic Markov Nash equilibria for potential discrete-time stochastic games
Kybernetika, Tome 58 (2022) no. 2, pp. 163-179
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In this paper, we study the problem of finding deterministic (also known as feedback or closed-loop) Markov Nash equilibria for a class of discrete-time stochastic games. In order to establish our results, we develop a potential game approach based on the dynamic programming technique. The identified potential stochastic games have Borel state and action spaces and possibly unbounded nondifferentiable cost-per-stage functions. In particular, the team (or coordination) stochastic games and the stochastic games with an action independent transition law are covered.
In this paper, we study the problem of finding deterministic (also known as feedback or closed-loop) Markov Nash equilibria for a class of discrete-time stochastic games. In order to establish our results, we develop a potential game approach based on the dynamic programming technique. The identified potential stochastic games have Borel state and action spaces and possibly unbounded nondifferentiable cost-per-stage functions. In particular, the team (or coordination) stochastic games and the stochastic games with an action independent transition law are covered.
DOI : 10.14736/kyb-2022-2-0163
Classification : 91A10, 91A14, 91A25, 91A50, 93E20
Keywords: stochastic games; optimal control; potential approach; dynamic programming 
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Fonseca-Morales, Alejandra. Deterministic Markov Nash equilibria for potential discrete-time stochastic games. Kybernetika, Tome 58 (2022) no. 2, pp. 163-179. doi: 10.14736/kyb-2022-2-0163

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