On the Maximal Number of Nash Equilibria in ann × nBimatrix Game

Abstract In 7 it was shown that for each odd number y  ≤ 2 n  − 1, there is an n  ×  n bimatrix game with exactly y Nash equilibria, and it was conjectured that the number 2 n  − 1 is an upper bound for the number of Nash equilibria of an arbitrary nondegenerate n  ×  n bimatrix game. In this paper, we give an upper bound derived from the theory of convex polytopes. This bound is not necessarily tight; we show that in the case n  = 4, the Quint–Shubik bound applies in the sense that there are no more than 2 4  − 1 = 15 equilibria. Journal of Economic Literature Classification Numbers: C70, C72.