A splitting proximal point method for Nash-Cournot equilibrium models involving nonconvex cost functions

TL;DR

This paper introduces a local numerical method based on a splitting proximal point approach to find stationary points in nonconvex Nash-Cournot equilibrium models, with proven convergence and complexity estimates.

Contribution

It develops a novel local algorithm for nonconvex Nash-Cournot problems and provides convergence analysis and numerical validation.

Findings

Algorithm converges to stationary points under certain conditions

Numerical examples demonstrate the convergence behavior

Complexity estimates support practical applicability

Abstract

Unlike convex case, a local equilibrium point of a nonconvex Nash-Cournot oligopolistic equilibrium problem may not be a global one. Finding such a local equilibrium point or even a stationary point of this problem is not an easy task. This paper deals with a numerical method for Nash-Cournot equilibrium models involving nonconvex cost functions. We develop a local method to compute a stationary point of this class of problems. The convergence of the algorithm is proved and its complexity is estimated under certain assumptions. Numerical examples are implemented to illustrate the convergence behavior of the proposed algorithm.