Quasi-Equilibrium Problems with Non-self Constraint Map

TL;DR

This paper introduces a new solution concept for quasi-equilibrium problems, establishes existence results, and extends these findings to related optimization and equilibrium problems, advancing theoretical understanding in this area.

Contribution

It proposes a novel solution concept for quasi-equilibrium problems and proves its existence, extending results to various related problem classes.

Findings

Existence of the new solution concept is established.

Results extend to quasi-optimization and generalized Nash equilibrium problems.

Provides a unified framework for various quasi-variational problems.

Abstract

In 2016 Aussel, Sultana and Vetrivel developed the concept of projected solution for quasi-variational inequality problems and projected Nash equilibrium. We introduce a new concept of solution for quasi-equilibrium problems and we study the existence of such solutions. Additionally, as a consequence of our results, we give existence results of projected solutions for quasi-optimization problems, quasi-variational inequalities problems and generalized Nash equilibrium problems.