Operator approach to values of stochastic games with varying stage duration
Sorin, Sylvain; Vigeral, Guillaume (2016), Operator approach to values of stochastic games with varying stage duration, International Journal of Game Theory, 45, 1-2, p. 389–410. 10.1007/s00182-015-0512-8
TypeArticle accepté pour publication ou publié
Journal nameInternational Journal of Game Theory
MetadataShow full item record
Institut de Mathématiques de Jussieu [IMJ]
CEntre de REcherches en MAthématiques de la DEcision [CEREMADE]
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.
Subjects / KeywordsStochastic games; Stage duration; Shapley operator; Non expansive map; Evolution equation
Showing items related by title and author.
Generalized iterations of non expansive maps, evolution equations and values of zero-sum stochastic games with varying stage duration Sorin, Sylvain; Vigeral, Guillaume (2015) Document de travail / Working paper