Generic 4 x 4 two person games have at most 15 Nash equilibria

The maximal generic number of Nash equilibria for two person games in which the two agents each have four pure strategies is shown to be 15. In contra st to Keiding (1997), Games Econ. Behav. 21, 148-160, who arrives at this r esult by referring to the enumeration of Grunbaum and Sreedharan (1967), J. Combin. Theory 2, 437-465, our argument is based on a collection of lemmas that constrain the set of equilibria. Several of these pertain to any comm on number d of pure strategies for the two agents. Classification Number: C 72. (C) 1999 Academic Press.