Geodesic
Empirical approximation in Markov games under unbounded payoff: discounted and average criteria
Kybernetika, Tome 53 (2017) no. 4, pp. 694-716.

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This work deals with a class of discrete-time zero-sum Markov games whose state process $\left\{ x_{t}\right\} $ evolves according to the equation $ x_{t+1}=F(x_{t},a_{t},b_{t},\xi _{t}),$ where $a_{t}$ and $b_{t}$ represent the actions of player 1 and 2, respectively, and $\left\{ \xi _{t}\right\} $ is a sequence of independent and identically distributed random variables with unknown distribution $\theta$. Assuming possibly unbounded payoff, and using the empirical distribution to estimate $\theta$, we introduce approximation schemes for the value of the game as well as for optimal strategies considering both, discounted and average criteria.
DOI : 10.14736/kyb-2017-4-0694
Classification : 62G07, 91A15
Keywords: Markov games; empirical estimation; discounted and average criteria 
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     title = {Empirical approximation in {Markov} games under unbounded payoff: discounted and average criteria},
     journal = {Kybernetika},
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Luque-Vásquez, Fernando; Minjárez-Sosa, J. Adolfo. Empirical approximation in Markov games under unbounded payoff: discounted and average criteria. Kybernetika, Tome 53 (2017) no. 4, pp. 694-716. doi : 10.14736/kyb-2017-4-0694. http://geodesic.mathdoc.fr/articles/10.14736/kyb-2017-4-0694/

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