Projected solution for Generalized Nash Games with Non-ordered Preferences
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.
Cite
@article{arxiv.2305.07275,
title = {Projected solution for Generalized Nash Games with Non-ordered Preferences},
author = {Asrifa Sultana and Shivani Valecha},
journal= {arXiv preprint arXiv:2305.07275},
year = {2023}
}