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Universality of Nash Equilibria

Department of Mathematics, University of California, Berkeley, CA 94720-3840
datta{at}math.berkeley.edu, http://math.berkeley.edu/~datta

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.

Key Words: Totally mixed Nash equilibrium; normal form game; algebraic variety; differentiable manifold; piecewise linear manifold
History: Received: January 22, 2003; revision received: March 7, 2003;