Structural approximations in discounted semi-Markov games

Abstract

We consider the problem of approximating the values and the equilibria in two-person zero-sum discounted semi-Markov games with in nite horizon and compact action spaces, when several uncertainties are present about the parameters of the model. Speci cally: on the one hand, we study approximations made on the transition probabilities, the discount factor and the reward functions when the state space is a borelian set. On the other hand, we study approximations on the state space for denumerable ones. Our results are based on those of Tidball and Altman on generic zero-sum games [9]. We provide conditions under which these results can be applied. We also discuss the application of such approximations for nite-horizon games, in relation with the Approximate Rolling Horizon procedure proposed in [3].