A General Structure Theorem for the Nash Equilibrium Correspondence

I consider n-person normal form games where the strategy set of every player is a non-empty compact convex subset of Euclidean space, and the payoff function of player i is continuous and concave in player i''s own strategies. No further restrictions (such as multilinearity of the payoff fucntions or the requirements that the strategy sets be polyhedral) are imposed. In this setting we demonstrate that the graph of the nash equilibrium correspondence is homeomorphic to the space of games. This result generalizes a well-known structure theorem of Kohlberg and Mertens[6].