Universality Of Nash Equilibria
Abstract
Every real algebraic variety is isomorphic to the set of totally mixed Nash equilibria of some threeperson game, and also to the set of totally mixed Nash equilibria of an $N$person game in which each player has two pure strategies. From the NashTognoli 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.
 Publication:

arXiv Mathematics eprints
 Pub Date:
 January 2003
 arXiv:
 arXiv:math/0301001
 Bibcode:
 2003math......1001D
 Keywords:

 Algebraic Geometry;
 Commutative Algebra;
 Combinatorics