Year: 2023
Type: preprint
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.
Source: arXiv (Cornell University)
Authors: Sultana, Asrifa, Valecha, Shivani
Institution: Indian Institute of Technology Bhilai
Language: English
Subfield: Computational Theory and Mathematics
Field: Computer Science
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W4376632563