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Communication Dans Un Congrès Année : 2015

Hypergraph conditions for the solvability of the ergodic equation for zero-sum games

Résumé

The ergodic equation is a basic tool in the study of mean-payoff stochastic games. Its solvability entails that the mean payoff is independent of the initial state. Moreover, optimal stationary strategies are readily obtained from its solution. In this paper, we give a general sufficient condition for the solvability of the ergodic equation, for a game with finite state space but arbitrary action spaces. This condition involves a pair of directed hypergraphs depending only on the ``growth at infinity'' of the Shapley operator of the game. This refines a recent result of the authors which only applied to games with bounded payments, as well as earlier nonlinear fixed point results for order preserving maps, involving graph conditions.

Dates et versions

hal-01249321 , version 1 (31-12-2015)

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Marianne Akian, Stephane Gaubert, Antoine Hochart. Hypergraph conditions for the solvability of the ergodic equation for zero-sum games. 54th IEEE Conference on Decision and Control (CDC 2015), Dec 2015, Osaka, Japan. ⟨hal-01249321⟩
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