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Operator approach to values of stochastic games with varying stage duration

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SySGV.Op2015RR.pdf (316.4Kb)
Date
2016
Dewey
Probabilités et mathématiques appliquées
Sujet
Stochastic games; Stage duration; Shapley operator; Non expansive map; Evolution equation
Journal issue
International Journal of Game Theory
Volume
45
Number
1-2
Publication date
03-2016
Article pages
389–410
Publisher
Pergamon
DOI
http://dx.doi.org/10.1007/s00182-015-0512-8
URI
https://basepub.dauphine.fr/handle/123456789/17290
Collections
  • CEREMADE : Publications
Metadata
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Author
Sorin, Sylvain
22 Institut de Mathématiques de Jussieu [IMJ]
Vigeral, Guillaume
60 CEntre de REcherches en MAthématiques de la DEcision [CEREMADE]
Type
Article accepté pour publication ou publié
Abstract (EN)
We study the links between the values of stochastic games with varying stage duration h, the corresponding Shapley operators T and Th and the solution of f˙t=(T−Id)ft. Considering general non expansive maps we establish two kinds of results, under both the discounted or the finite length framework, that apply to the class of “exact” stochastic games. First, for a fixed length or discount factor, the value converges as the stage duration go to 0. Second, the asymptotic behavior of the value as the length goes to infinity, or as the discount factor goes to 0, does not depend on the stage duration. In addition, these properties imply the existence of the value of the finite length or discounted continuous time game (associated to a continuous time jointly controlled Markov process), as the limit of the value of any time discretization with vanishing mesh.

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