The Lemke–Howson algorithm is an algorithm that computes a Nash equilibrium of a bimatrix game, named after its inventors, Carlton E. Lemke and J. T. Howson. It is said to be “the best known among the combinatorial algorithms for finding a Nash equilibrium”.
The algorithm can find at most n + m different Nash equilibria. Any choice of initially-dropped label determines the equilibrium that is eventually found by the algorithm.