Location of nash equilibria: A riemannian geometrical approach

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20 Citations (Scopus)

Abstract

Existence and location of Nash equilibrium points are studied for a large class of a finite family of payoff functions whose domains are not necessarily convex in the usual sense. The geometric idea is to embed these non-convex domains into suitable Riemannian manifolds regaining certain geodesic convexity properties of them. By using recent non-smooth analysis on Riemannian manifolds and a variational inequality for acyclic sets, an efficient location result of Nash equilibrium points is given. Some examples show the applicability of our results.

Original languageEnglish
Pages (from-to)1803-1810
Number of pages8
JournalProceedings of the American Mathematical Society
Volume138
Issue number5
DOIs
Publication statusPublished - May 1 2010

Keywords

  • Nash equilibrium point
  • Nonsmooth analysis
  • Riemannian manifold

ASJC Scopus subject areas

  • Mathematics(all)
  • Applied Mathematics

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