Ergodicity Condition for Zero-Sum Games

Marianne Akian 1, 2 Stephane Gaubert 1, 2 Antoine Hochart 2, 1
2 MAXPLUS - Max-plus algebras and mathematics of decision
CMAP - Centre de Mathématiques Appliquées - Ecole Polytechnique, Inria Saclay - Ile de France
Abstract : For zero-sum repeated stochastic games, basic questions are whether the mean payoff per time unit is independent of the initial state, and whether this property is robust to perturbations of rewards. In the case of finite action spaces, we show that the answer to both questions is positive if and only if an ergodicity condition involving fixed points of the recession function of the Shapley operator or reachability in directed hypergraphs is satisfied.
Type de document :
Communication dans un congrès
SIAM Conference on Control and its Applications (SIAM CT'15), Jul 2015, Paris, France. 〈http://www.siam.org/meetings/ct15/〉
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https://hal.inria.fr/hal-01252413
Contributeur : Marianne Akian <>
Soumis le : jeudi 7 janvier 2016 - 15:23:20
Dernière modification le : mercredi 14 novembre 2018 - 15:20:12

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  • HAL Id : hal-01252413, version 1

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Marianne Akian, Stephane Gaubert, Antoine Hochart. Ergodicity Condition for Zero-Sum Games. SIAM Conference on Control and its Applications (SIAM CT'15), Jul 2015, Paris, France. 〈http://www.siam.org/meetings/ct15/〉. 〈hal-01252413〉

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