Variational Analysis of Generalized Games over Banach spaces
Optimization and Control
2024-07-29 v1 Functional Analysis
Abstract
We study generalized games defined over Banach spaces using variational analysis. To reformulate generalized games as quasi-variational inequality problems, we will first form a suitable principal operator and study some significant properties of this operator. Then, we deduce the sufficient conditions under which an equilibrium for the generalized game can be obtained by solving a quasi-variational inequality. Based on this variational reformulation, we derive the existence of equilibrium for generalized games with non-ordered (that is, associated weak preference relations need not be complete and transitive) and mid-point continuous preference maps.
Keywords
Cite
@article{arxiv.2407.18539,
title = {Variational Analysis of Generalized Games over Banach spaces},
author = {Asrifa Sultana and Shivani Valecha},
journal= {arXiv preprint arXiv:2407.18539},
year = {2024}
}