A generalized complementary pivoting algorithm

The first algorithm to use a complementary pivoting procedure was that devised by Lemke and Howson to find a Nash equilibrium point of a bimatrix game [ 15 ]. This algorithm introduced a novel proof of convergence not relying on standard monotonicity arguments. Lemke [ 12] generalized his complementary pivot algorithm to solve certain classes of linear complementarity problem (LCP), which Dantzig and Cottle had shown to be the "fundamental" problem of linear programming, convex quadratic programming, and bimatrix games [6]. More general conditions under which Lemke's algorithm will "process" such an LCP (by "process" we mean find a solution or show none exists) were found by Eaves [7]. The LCP was further extended in the generalized linear complementarity problem (GLCP) of Cottle and Dantzig [5]. However, Lemke [ 14] showed that the GLCP is in fact a special case of the LCP, and does not provide an essentially different use of complementary pivoting. Using the same basic idea, Scarf, with Hansen, introduced a combina-