A Newton-like approach to solving an equilibrium problem

The paper deals with the problem of finding an equilibrium in an oligopolistic market model where several subjects supply a single homogeneous product in a non-cooperative manner. The problem is reduced to a nonlinear equation, some terms of which are determined by solving nonlinear complementarity problems. An algorithm is presented that combines the Newton method steps with dichotomy techniques. Under certain assumptions, the algorithm is shown to be convergent at a quadratic rate. Finally, the algorithm is extended to the case of nonlinear production costs, and its linear convergence is demonstrated.