Structural approximations in discounted semi-Markov games
نویسندگان
چکیده
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]. Key-words: Game theory, Semi-Markov games, Zero-sum games ∗ CONICET UNR, Pellegrini 250, Rosario, Argentina, [email protected]. † CONICET UNR, Pellegrini 250, Rosario, Argentina, [email protected] . ‡ INRIA and LIRMM, CNRS/Université Montpellier 2, 161 Rue Ada, 34392 Montpellier, France, [email protected]. ha l-0 07 64 21 7, v er si on 1 12 D ec 2 01 2 Approximations structurelles dans les jeux semi-Markoviens actualisés Résumé : Nous considérons le problème de l'approximation des valeurs et des équilibres d'un jeu semi-Markovien actualisé, en horizon in ni avec des ensembles d'actions compacts, en présence d'incertitude sur plusieurs paramètres du modèle. Spéci quement: d'une part nous étudions les approximations sur les probabilités de transition, sur le facteur d'actualisation et sur les coûts, quand l'espace d'états est un ensemble Borélien. D'autre part, nous étudions les approximations de l'ensemble d'états quand celui-ci est dénombrable. Nos résultats sont basés sur ceux de Tidball et Altman [9]. Nous donnons des conditions sous lesquelles ces résultats peuvent être appliqués. Nous discutons aussi de l'application de telles approximations à des jeux en horizon ni, en relation avec la procédure de l'horizon roulant approchée, proposée dans [3]. Mots-clés : Théorie des jeux, jeux semi-Markoviens, jeux à somme nulle ha l-0 07 64 21 7, v er si on 1 12 D ec 2 01 2 Structural approximations in discounted semi-Markov games 3
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