Approximation of zero-sum continuous-time Markov games under the discounted payoff criterion

Tomás Prieto-Rumeau () and José Lorenzo ()

TOP: An Official Journal of the Spanish Society of Statistics and Operations Research, 2015, vol. 23, issue 3, 799-836

Abstract: We deal with a two-person zero-sum continuous-time Markov game $$\mathcal {G}$$ G with denumerable state space, general action spaces, and unbounded payoff and transition rates. We consider noncooperative equilibria for the discounted payoff criterion. We are interested in approximating numerically the value and the optimal strategies of $$\mathcal {G}$$ G . To this end, we propose a definition of a sequence of game models $$\mathcal {G}_n$$ G n converging to $$\mathcal {G}$$ G , which ensures that the value and the optimal strategies of $$\mathcal {G}_n$$ G n converge to those of $$\mathcal {G}$$ G . For numerical purposes, we construct finite state and actions game models $$\mathcal {G}_n$$ G n that can be explicitly solved, and we study the convergence rate of the value of the games. A game model based on a population system illustrates our results. Copyright Sociedad de Estadística e Investigación Operativa 2015

Keywords: Continuous-time zero-sum Markov games; Discounted payoff criterion; Approximation of game models; 91A15; 91A25; 60J27 (search for similar items in EconPapers)
Date: 2015
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Citations: View citations in EconPapers (3)

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DOI: 10.1007/s11750-014-0354-8

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