  This paper is an exposition of algorithms for finding one or all equilibria
of a bimatrix game (a two-player game in strategic form) in the style of a
chapter in a graduate textbook. Using labeled "best-response polytopes", we
present the Lemke-Howson algorithm that finds one equilibrium. We show that the
path followed by this algorithm has a direction, and that the endpoints of the
path have opposite index, in a canonical way using determinants. For reference,
we prove that a number of notions of nondegeneracy of a bimatrix game are
equivalent. The computation of all equilibria of a general bimatrix game, via a
description of the maximal Nash subsets of the game, is canonically described
using "complementary pairs" of faces of the best-response polytopes.
