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http://dx.doi.org/10.4134/JKMS.2008.45.5.1297

BEST PROXIMITY PAIRS AND NASH EQUILIBRIUM PAIRS  

Kim, Won-Kyu (Department of Mathematics Education Chungbuk National University)
Kum, Sang-Ho (Department of Mathematics Education Chungbuk National University)
Publication Information
Journal of the Korean Mathematical Society / v.45, no.5, 2008 , pp. 1297-1310 More about this Journal
Abstract
Main purpose of this paper is to combine the optimal form of Fan's best approximation theorem and Nash's equilibrium existence theorem into a single existence theorem simultaneously. For this, we first prove a general best proximity pair theorem which includes a number of known best proximity theorems. Next, we will introduce a new equilibrium concept for a generalized Nash game with normal form, and as applications, we will prove new existence theorems of Nash equilibrium pairs for generalized Nash games with normal form.
Keywords
best proximity pairs; Nash equilibrium pair;
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