A minmax theorem for concave-convex mappings with no regularity assumptions.
Vianney, Perchet; Vigeral, Guillaume (2015), A minmax theorem for concave-convex mappings with no regularity assumptions., Journal of Convex Analysis, 22, 2, p. 537-540
TypeArticle accepté pour publication ou publié
External document linkhttps://hal.archives-ouvertes.fr/hal-00927071
Journal nameJournal of Convex Analysis
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Abstract (EN)We prove that zero-sum games with a concave-convex payoff mapping defined on a product of convex sets have a value as soon as the payoff function is bounded and one of the set is bounded and finite dimensional. In particular, no additional regularity assumption is required, such as lower or upper semicontinuity of the function or compactness of the sets. We provide several examples that show that our assumptions are minimal.
Subjects / Keywordsconcave-convex mappings; zero-sum games
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