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.
Citation
Pando G. Georgiev. Tamaki Tanaka. Daishi Kuroiwa. Panos M. Pardalos. "Nash Equilibrium and Saddle Points for Multifunctions." Commun. Math. Anal. 10 (2) 118 - 127, 2011.
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