AN ALGORITHM BASED ON A SEQUENCE OF LINEAR COMPLEMENTARITY-PROBLEMS APPLIED TO A WALRASIAN EQUILIBRIUM-MODEL - AN EXAMPLE

The Walrasian equilibrium problem is cast as a complementarity problem, and its solution is computed by solving a sequence of linear complementarity problems (SLCP). In the context of a simple example of a Walrasian equilibrium model, we study the iterates of the SLCP algorithm. We show that a particular LCP of this process may have no, one or more complementary solutions. Other LCPs may have both homogeneous and complementary solutions. These features complicate the proof of convergence for the general case. For this particular example, however, we are able to show that C. E. Lemke's algorithm computes a solution to an LCP if one exists, and that the iterative process converges globally.