• Nash equilibria via duality and homological selection

• Fulltext

https://www.ias.ac.in/article/fulltext/pmsc/124/04/0581-0602

• Keywords

Nash equilibria; Dold–Thom theorem; homological selection.

• Abstract

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.

• Author Affiliations

1. Quantitative Methods and Information Systems Area, Indian Institute of Management, Bangalore 560 076, India
2. RKM Vivekananda University, Belur Math, West Bengal 711 202, India

• Proceedings – Mathematical Sciences

Current Issue
Volume 129 | Issue 5
November 2019

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Posted on July 25, 2019