The Nash equilibria of a two-person, non-zero-sum game are the solutions of
a certain linear complementarity problem (LCP). In order to use this for
solving a game in extensive form, the game must first be converted to a
strategic description such as the normal form. The classical normal form,
however, is often exponentially large in the size of the game tree. If the
game has perfect recall, a linear-sized strategic description is the
sequence form. For the resulting small LCP, we show that an equilibrium is
found efficiently by Lemke's algorithm, a generalization of the Lemke-Howson
method.