Tauberian theorems for general iterations of operators: Applications to zero-sum stochastic games
Ziliotto, Bruno (2018), Tauberian theorems for general iterations of operators: Applications to zero-sum stochastic games, Games and Economic Behavior, 108, March 2018, p. 486 - 503. 10.1016/j.geb.2018.01.009
TypeArticle accepté pour publication ou publié
External document linkhttps://hal.archives-ouvertes.fr/hal-01936551
Journal nameGames and Economic Behavior
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CEntre de REcherches en MAthématiques de la DEcision [CEREMADE]
Abstract (EN)This paper proves several Tauberian theorems for general iterations of operators, and provides two applications to zero-sum stochastic games where the total payoff is a weighted sum of the stage payoffs. The first application is to provide conditions under which the existence of the asymptotic value implies the convergence of the values of the weighted game, as players get more and more patient. The second application concerns stochastic games with finite state space and action sets. This paper builds a simple class of asymptotically optimal strategies in the weighted game, that at each stage play optimally in a discounted game with a discount factor corresponding to the relative weight of the current stage.
Subjects / KeywordsTauberian theorem; Nonexpansive operators; Stochastic games; Asymptotic value; Weighted payoffs
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