New Maximal Numbers of Equilibria in Bimatrix Games

This paper presents a new lower bound of 2:414 d = p d on the maximal number of Nash equilibria in d \Theta d bimatrix games, a central concept in game theory. The proof uses an equivalent formulation of the problem in terms of pairs of polytopes with 2d facets in d-space. It refutes a recent conjecture that 2 d \Gamma 1 is an upper bound, which was proved for d 4. The first counterexample is a 6 \Theta 6 game with 75 equilibria. The case d = 5 remains open. The result carries the lower bound closer to the previously known upper bound of 2:6 d = p d