Existence of equilibrium for generalized games in choice form and applications

TL;DR

This paper establishes simple conditions for the existence of equilibrium in generalized choice form games and applies these results to solve various vector quasi-equilibrium problems, highlighting their broader utility.

Contribution

It provides new, straightforward conditions ensuring equilibrium existence in generalized games and demonstrates their application to vector quasi-equilibrium systems.

Findings

Existence conditions for equilibrium in generalized games

Application to vector quasi-equilibrium problems

Broader implications for optimization research

Abstract

This paper has two central aims: first, to provide simple conditions under which the generalized games in choice form and, consequently, the abstract economies, admit equilibrium; second, to study the solvability of several types of systems of vector quasi-equilibrium problems as an application. Our work outlines that there still is much to be gained from using the results concerning the existence of equilibrium of games as tools of research for other optimization problems.