Generalized iterations of non expansive maps, evolution equations and values of zero-sum stochastic games with varying stage duration
Sorin, Sylvain; Vigeral, Guillaume (2015), Generalized iterations of non expansive maps, evolution equations and values of zero-sum stochastic games with varying stage duration. https://basepub.dauphine.fr/handle/123456789/14700
TypeDocument de travail / Working paper
External document linkhttp://arxiv.org/pdf/1502.04000.pdf
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Abstract (EN)We study the links between the values of stochastic games wit h varying stage du- ration h , the corresponding Shapley operators T and T h and the solution of ̇ f t = ( T − Id ) f t . For a large class of stochastic games we establish two kinds o f results, under both the discounted or the finite duration framework. On the one hand, for a fixed ho rizon or discount factor, the value converges as the stage duration go to 0. On the other han d, the asymptotic behavior of the normalized value as the horizon goes to infinity, or as the discount factor goes to 0, does not depend on the stage duration.
Subjects / Keywordsnon expansive map; Shapley operators; stochastic games
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