Nash Equilibria via Duality and Homological Selection
Algebraic Topology
2016-12-30 v3 Computer Science and Game Theory
Geometric Topology
Optimization and Control
Abstract
Given a multifunction from to the fold symmetric product , we use the Dold-Thom Theorem to establish a homological selection Theorem. This is used to establish existence of Nash equilibria. Cost functions in problems concerning the existence of Nash Equilibria are traditionally multilinear in the mixed strategies. The main aim of this paper is to relax the hypothesis of multilinearity. We use basic intersection theory, Poincar\'e Duality in addition to the Dold-Thom Theorem.
Keywords
Cite
@article{arxiv.1111.0754,
title = {Nash Equilibria via Duality and Homological Selection},
author = {Arnab Basu and Samik Basu and Mahan Mj},
journal= {arXiv preprint arXiv:1111.0754},
year = {2016}
}
Comments
20 pages, 4 figures. Final version to appear in Proceedings of the Indian Academy of Sciences (Math. Sci.)