Variational Analysis of Generalized Games over Banach spaces

TL;DR

This paper explores the use of variational analysis to reformulate and analyze generalized games over Banach spaces, establishing conditions for equilibrium existence via quasi-variational inequalities.

Contribution

It introduces a variational reformulation of generalized games over Banach spaces and provides new existence results for equilibria with non-ordered preferences.

Findings

Established a principal operator for the reformulation

Derived sufficient conditions for equilibrium existence

Proved existence of equilibria with non-ordered preferences

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.