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Journal of Dynamics and Games (JDG)
 

Average optimal strategies for zero-sum Markov games with poorly known payoff function on one side

Pages: 105 - 119, Volume 1, Issue 1, January 2014      doi:10.3934/jdg.2014.1.105

 
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Fernando Luque-Vásquez - Departamento de Matemáticas, Universidad de Sonora, Rosales s/n, Centro, C.P. 83000, Hermosillo, Sonora, Mexico (email)
J. Adolfo Minjárez-Sosa - Departamento de Matemáticas, Universidad de Sonora, Rosales s/n, Centro, C.P. 83000, Hermosillo, Sonora,, Mexico (email)

Abstract: We are concerned with two-person zero-sum Markov games with Borel spaces under a long-run average criterion. The payoff function is possibly unbounded and depends on a parameter which is unknown to one of the players. The parameter and the payoff function can be estimated by implementing statistical methods. Thus, our main objective is to combine such estimation procedure with a variant of the so-called vanishing discount approach to construct an average optimal pair of strategies for the game. Our results are applied to a class of zero-sum semi-Markov games.

Keywords:  Zero-sum Markov and semi-Markov games, average payoff criterion, incomplete information, payoff estimation.
Mathematics Subject Classification:  Primary: 91A15; Secondary: 62F10.

Received: January 2012;      Revised: June 2012;      Available Online: June 2013.

 References