  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.
