Projected solution for Generalized Nash Games with Non-ordered Preferences

TL;DR

This paper introduces a new approach to finding solutions in generalized Nash equilibrium problems with non-ordered preferences, extending existing methods to handle incomplete and non-transitive preferences without compactness assumptions.

Contribution

It develops the concept of projected solutions for GNEPs with non-ordered preferences and provides conditions for their existence, broadening the applicability of equilibrium analysis.

Findings

Established necessary and sufficient conditions for projected solutions.

Derived the occurrence of solutions via variational reformulation.

Proved existence of solutions without compactness assumptions.

Abstract

Any individual's preference represents his choice in the set of available options. It is said to be complete if the person can compare any pair of available options. We aim to initiate the notion of projected solutions for the generalized Nash equilibrium problem with non-ordered (not necessarily complete and transitive) preferences and non-self constraint map. We provide the necessary and sufficient conditions under which projected solutions of a quasi-variational inequality and the considered GNEP coincide. Based on this variational reformulation, we derive the occurrence of projected solutions for the considered GNEP. Alternatively, by using a fixed point result, we ensure the existence of projected solutions for the considered GNEP without requiring the compactness of choice sets.