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Article Dans Une Revue Journal of Convex Analysis Année : 2018

Minimax representation of nonexpansive functions and application to zero-sum recursive games

Résumé

We show that a real-valued function on a topological vector space is positively homogeneous of degree one and nonexpansive with respect to a weak Minkowski norm if and only if it can be written as a minimax of linear forms that are nonexpansive with respect to the same norm. We derive a representation of monotone, additively and positively homogeneous functions on L∞ spaces and on Rn, which extend results of Kolokoltsov, Rubinov, Singer, and others. We apply this representation to nonconvex risk measures and to zero-sum games. We derive in particular results of representation and polyhedral approximation for the class of Shapley operators arising from games without instantaneous payments (Everett's recursive games).

Dates et versions

hal-01425551 , version 1 (03-01-2017)

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Marianne Akian, Stéphane Gaubert, Antoine Hochart. Minimax representation of nonexpansive functions and application to zero-sum recursive games. Journal of Convex Analysis, 2018, 25 (1). ⟨hal-01425551⟩
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