Abstract

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 mapping 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

Author information

Contact details are reproduced from the original publication and may be historical.

Guillaume Vigeral

Université Paris-Dauphine, CEREMADE, Place Mar. Lattre de Tassigny, 75775 Paris Cedex 16, France

vigeral@ceremade.dauphine.fr

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Suggested citation

V. Perchet, G. Vigeral. “A Minmax Theorem for Concave-convex Mappings with no Regularity Assumptions.” Journal of Convex Analysis 22 (2015), No. 2, 537–540. https://doi.org/10.68381/jca22025

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Published by Heldermann Verlag, 2015. Rights now held by Banach Press LLC.