Generalized Nash equilibrium problems for lowersemi-continuous strategy maps

摘要

We consider a class of generalized Ky Fan inequalities (quasi-variational inequal-ities) in which the involved multi-valued mapping is lower semi-continuous. We present arelaxed version of the generalized Nash equilibrium problem involving strategy maps, whichare only lower semi-continuous. This relaxed version may have no exact Nash equilibrium,but we prove that it has an e-Nash equilibrium for every e > 0. Easy examples of suchproblems show no existence of exact solutions, but existence of e-solutions for every e > 0.We give positive answers to two questions (in the compact case) raised in a recent paper ofCubiotti and Yao.