Communications in Mathematical Analysis
- Commun. Math. Anal.
- Volume 10, Number 2 (2011), 118-127.
Nash Equilibrium and Saddle Points for Multifunctions
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.
Commun. Math. Anal., Volume 10, Number 2 (2011), 118-127.
First available in Project Euclid: 13 February 2012
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Georgiev, Pando G.; Tanaka, Tamaki; Kuroiwa, Daishi; Pardalos, Panos M. Nash Equilibrium and Saddle Points for Multifunctions. Commun. Math. Anal. 10 (2011), no. 2, 118--127. https://projecteuclid.org/euclid.cma/1329151188