We consider the problem of approximating the values and the equilibria in two-person zero-sum discounted semi-Markov games with infinite horizon and compact action spaces, when several uncertainties are present about the parameters of the model. Specifically: 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 (SIAM J. Control and Optimization, 1996) on generic zero-sum games. We provide conditions under which these results can be applied. We also discuss the application of such approximations for finite-horizon games, in relation with the Approximate Rolling Horizon procedure proposed in Della Vecchia et al. (INRIA RR 8019, 2012).
Structural approximations in discounted semi-Markov games