Zero-Sum Markov Games with Random State-Actions-Dependent Discount Factors: Existence of Optimal Strategies

David González-Sánchez (), Fernando Luque-Vásquez () and J. Adolfo Minjárez-Sosa ()
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David González-Sánchez: CONACYT–Universidad de Sonora
Fernando Luque-Vásquez: Universidad de Sonora
J. Adolfo Minjárez-Sosa: Universidad de Sonora

Dynamic Games and Applications, 2019, vol. 9, issue 1, No 5, 103-121

Abstract: Abstract This work deals with a class of discrete-time zero-sum Markov games under a discounted optimality criterion with random state-actions-dependent discount factors of the form $$\tilde{\alpha }(x_{n},a_{n},b_{n},\xi _{n+1})$$ α ~ ( x n , a n , b n , ξ n + 1 ) , where $$x_{n}, a_{n}, b_{n}$$ x n , a n , b n , and $$\xi _{n+1}$$ ξ n + 1 are the state, the actions of players, and a random disturbance at time n, respectively, taking values in Borel spaces. Assuming possibly unbounded payoff, we prove the existence of a value of the game as well as a stationary pair of optimal strategies.

Keywords: Markov games; Discounted optimality; Nonconstant discount factor; 91A15; 91A50; 60J05 (search for similar items in EconPapers)
Date: 2019
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DOI: 10.1007/s13235-018-0248-8

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