Coerciveness condition for quasi-equilibrium problems

TL;DR

This paper establishes existence results for quasi-equilibrium problems on unbounded sets using a coerciveness condition, extending the theory to broader classes of equilibrium problems.

Contribution

It introduces a coerciveness condition tailored for quasi-equilibrium problems, generalizing existing results for quasi-variational inequalities.

Findings

Existence of solutions under coerciveness conditions

Extension to unbounded constraint sets

Relation to existing literature on equilibrium problems

Abstract

A quasi-equilibrium problem is an equilibrium problem where the constraint set does depend on the reference point. It generalizes important problems such as quasi-variational inequalities and generalized Nash equilibrium problems. We study the existence of equilibria on unbounded sets under a coerciveness condition adapted from one specific for quasi-variational inequalities recently proposed by Aussel and Sultana. We discuss the relation of our results with others that are present in the literature.