Enumerating the Nash equilibria of rank 1-games

A bimatrix game (A, B) is called a game of rank k if the rank of the matrix A + B is at most k. We consider the problem of enumerating the Nash equilibria in (non-degenerate) games of rank 1. In particular, we show that even for games of rank 1 not all equilibria can be reached by a Lemke– Howson path and present a parametric simplex-type algorithm for enumerating all Nash equilibria of a non-degenerate game of rank 1.