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# Title: Universality Of Nash Equilibria

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 $N$-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.
 Subjects: Algebraic Geometry (math.AG); Commutative Algebra (math.AC); Combinatorics (math.CO) Cite as: arXiv:math/0301001 [math.AG] (or arXiv:math/0301001v1 [math.AG] for this version)

## Submission history

From: Ruchira S. Datta [view email]
[v1] Wed, 1 Jan 2003 06:43:58 GMT (121kb)

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