English

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 XX to the kk-fold symmetric product Symk(X)Sym_k(X), 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.)

R2 v1 2026-06-21T19:30:15.402Z