On a Generalization of the Lemke–Howson Algorithm to Noncooperative N -Person Games

In [1] it has been shown that the existence of equilibrium points in a bimatrix game can be proved without a fixed-point theorem. If the game is nondegenerated, the number of equilibrium points is odd and all equilibrium points are obtained by a computational procedure in finitely many steps. The purpose of this note is to show that nondegeneracy can be defined for general N-person games and that for such games also there exist an odd number of equilibrium points. The algorithm developed in [1] can be extended to nondegenerated games even for more than 2 players.