Solving a Class of Equilibrium Problems With Equilibrium Constraints*

An equilibrium problem with equilibrium constraints (EPEC) can be looked on as a generalized Nash equilibrium problem (GNEP) and the mathematical programs with equilibrium constraints (MPEC) whose constraints contain a parametric variational inequality or complementarity system. In this paper, we particularly consider a class of EPEC and solve its normalized stationary points where the multipliers of the leaders on the shared constraints are proportionable. We reformulate this kind of EPEC to a standard MPEC. In addition, we demonstrate the proposed approach on an EPEC model in similar products market.

Upper Semicontinuity of Solution Mappings to Parametric Generalized Vector Quasiequilibrium Problems

We establish the upper semicontinuity of solution mappings for a class of parametric generalized vector quasiequilibrium problems. As applications, we obtain the upper semicontinuity of solution mappings to several problems, such as parametric optimization problem, parametric saddle point problem, parametric Nash equilibria problem, parametric variational inequality, and parametric equilibrium problem.