Universality Of Nash Equilibria
Algebraic Geometry
2007-05-23 v1 Commutative Algebra
Combinatorics
Abstract
Every real algebraic variety is isomorphic to the set of totally mixed Nash equilibria of some three-person game, and also to the set of totally mixed Nash equilibria of an -person game in which each player has two pure strategies. From the Nash-Tognoli Theorem it follows that every compact differentiable manifold can be encoded as the set of totally mixed Nash equilibria of some game. Moreover, there exist isolated Nash equilibria of arbitrary topological degree.
Keywords
Cite
@article{arxiv.math/0301001,
title = {Universality Of Nash Equilibria},
author = {Ruchira S. Datta},
journal= {arXiv preprint arXiv:math/0301001},
year = {2007}
}