Equilibrium problems with complementarity constraints: case study with applications to oligopolistic markets

Abstract

The article concerns a rather new class of hierarchical games called equilibrium problems with equilibrium constraints (EPECs), or more precisely, in our setting, equilibrium problems with complementarity constraints (EPCCs). Among others, via EPECs and EPCCs, one can model a hierarchical oligopolistic market with more than one “Leader”. In the article, we investigate the case when the Leaders cooperate, and we assume that the behaviour of the “Followers” is described by a mixed complementarity problem. Using advanced tools of modern variational analysis and generalized differentiation, we derive new necessary optimality conditions and propose a numerical method to solve the class of EPCCs under consideration. The results obtained are applied to an oligopolistic market model which primarily motivates this research.