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Tauberian theorems for general iterations of operators: Applications to zero-sum stochastic games

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1609.02175(1).pdf (211.4Kb)
Date
2018
Link to item file
https://hal.archives-ouvertes.fr/hal-01936551
Dewey
Analyse
Sujet
Tauberian theorem; Nonexpansive operators; Stochastic games; Asymptotic value; Weighted payoffs
Journal issue
Games and Economic Behavior
Volume
108
Number
March 2018
Publication date
2018
Article pages
486 - 503
Publisher
Elsevier
DOI
http://dx.doi.org/10.1016/j.geb.2018.01.009
URI
https://basepub.dauphine.fr/handle/123456789/18677
Collections
  • CEREMADE : Publications
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Author
Ziliotto, Bruno
60 CEntre de REcherches en MAthématiques de la DEcision [CEREMADE]
Type
Article accepté pour publication ou publié
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.

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