Variational Analysis of Generalized Games over Banach spaces

Abstract

We study generalized games defined over Banach spaces using variational analysis. To reformulate generalized games as quasi-variational inequality problems, we will first form a suitable principal operator and study some significant properties of this operator. Then, we deduce the sufficient conditions under which an equilibrium for the generalized game can be obtained by solving a quasi-variational inequality. Based on this variational reformulation, we derive the existence of equilibrium for generalized games with non-ordered (that is, associated weak preference relations need not be complete and transitive) and mid-point continuous preference maps.