Nash equilibria via duality and homological selection

Proceedings Mathematical Sciences

Mahan MJ¹  Samik Basu²  Arnab Basu³ 

[1] $$;RKM Vivekananda University, Belur Math, West Bengal 0, India$$;Quantitative Methods and Information Systems Area, Indian Institute of Management, Bangalore 0 0, India$$

关键词: Nash equilibria;    Dold–Thom theorem;    homological selection.;   

DOI  :  

学科分类：数学（综合）

来源: Indian Academy of Sciences

【 摘 要 】

Given a multifunction from 𝑋 to the 𝑘-fold symmetric product 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, Poincaré duality in addition to the Dold–Thom theorem.

【 授权许可】

Unknown