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

Tomás Prieto-Rumeau ^[1] ; José María Lorenzo ^[2]
1. [1] Universidad Nacional de Educación a Distancia
  
  Universidad Nacional de Educación a Distancia
  
  Madrid, España
2. [2] Universidad Complutense de Madrid
  
  Universidad Complutense de Madrid
  
  Madrid, España
Localización: Top, ISSN-e 1863-8279, ISSN 1134-5764, Vol. 23, Nº. 3, 2015, págs. 799-836
Idioma: inglés
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Resumen
- We deal with a two-person zero-sum continuous-time Markov game 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 G . To this end, we propose a definition of a sequence of game models Gn converging to G , which ensures that the value and the optimal strategies of Gn converge to those of G . For numerical purposes, we construct finite state and actions game models Gn 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.