dc.contributor.author Vigeral, Guillaume dc.date.accessioned 2012-02-03T15:14:41Z dc.date.available 2012-02-03T15:14:41Z dc.date.issued 2012 dc.identifier.uri https://basepub.dauphine.fr/handle/123456789/8028 dc.language.iso en en dc.subject dynamic programming en dc.subject Shapley operator en dc.subject nonexpansive mappings en dc.subject asymptotic properties en dc.subject zero-sum stochastic games en dc.subject.ddc 519 en dc.subject.classificationjel C73 en dc.title Iterated monotonic nonexpansive operators and asymptotic properties of zero-sum stochastic games en dc.type Document de travail / Working paper dc.description.abstracten We consider an operator $\Ps$ defined on a set of real valued functions and satisfying two properties of monotonicity and additive homogeneity. This is motivated by the case of zero sum stochastic games, for which the Shapley operator is monotone and additively homogeneous. We study the asymptotic of the trajectories defined by $v_n=\frac{\Ps^n(0)}{n}$ ($n\in N , n \rightarrow \infty$) and $v_\lambda=\lambda\Ps\left(\frac{1-\lambda}{\lambda}v_\lambda\right)$ ($\lambda \in (0,1], \lambda \rightarrow 0$). Examining the iterates of $\Ps$, we exhibit analytical conditions on the operator that imply that $v_n$ and $v_\lambda$ have at most one accumulation point for the uniform norm. In particular this establishes the uniform convergence of $v_n$ and $v_\lambda$ to the same limit for a large subclass of the class of games where only one player control the transitions. We also study the general case of two players controlling the transitions, giving a sufficient condition for convergence. en dc.publisher.name Université Paris-Dauphine en dc.publisher.city Paris en dc.identifier.citationpages 20 en dc.identifier.urlsite http://hal.archives-ouvertes.fr/hal-00662012 en dc.description.sponsorshipprivate oui en dc.subject.ddclabel Probabilités et mathématiques appliquées en
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