Nash Equilibrium and Minimax Theorems via Variational Tools of Convex Analysis
Optimization and Control
2024-08-27 v1
Abstract
In this paper, we first provide a simple variational proof of the existence of Nash equilibrium in Hilbert spaces by using optimality conditions in convex minimization and Schauder's fixed-point theorem. Then applications of convex analysis and generalized differentiation are given to the existence of Nash equilibrium and extended versions of von Neumann's minimax theorem in locally convex topological vector spaces. Our analysis in this part combines generalized differential tools of convex analysis with elements of fixed point theory revolving around Kakutani's fixed-point theorem and related issues.
Keywords
Cite
@article{arxiv.2408.14433,
title = {Nash Equilibrium and Minimax Theorems via Variational Tools of Convex Analysis},
author = {Nguyen Xuan Duy Bao and Boris Mordukhovich and Nguyen Mau Nam},
journal= {arXiv preprint arXiv:2408.14433},
year = {2024}
}