Existence results for generalized nash equilibrium problems under continuity-like properties of sublevel sets*

Abstract

A generalized Nash equilibrium problem corresponds to a noncooperative interaction between a finite set of players in which the cost function and the feasible set of each player depend on the decisions of the others. The classical existence result for generalized equilibria due to Arrow and Debreu requires continuity of the cost functions. In this work, we provide an existence of solutions transferring this hypothesis to a continuity-like condition over the sublevel sets of the aforementioned functions. Comparison with Reny's approach for discontinuous games is also considered.