A Newton-like approach to solvingan equilibrium problem

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