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Nash Equilibrium and Saddle Points for Multifunctions

Commun. Math. Anal.
Volume 10, Number 2 (2011), 118 - 127

Nash Equilibrium and Saddle Points for Multifunctions

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Abstract

We introduce new definitions of semi-continuity for multifunctions, combining the topological and the ordered structure of a Banach space induced by a closed convex cone. We prove two types Nash equilibrium theorems for multifunctions using scalarization and the Ky Fan’s inequality. As corollaries we obtain saddle point theorems for convex-concave multifunctions, which can be considered as generalization to the vector-valued set-valued case of the Von Neumann minimax theorem.