About the links between equilibrium problems and variational inequalities (Q2418715)

The present chapter deals with the relationship between equilibrium problems and variational inequalities. A state of the art of relationships between these two problems is given nicely. The variational inequality problem and equilibrium problem generated by an optimization problem are considered first, then the existence of solutions of the equilibrium problem through the variational inequality problem is derived. Some examples of equilibrium problems are given. The Nash equilibrium problem is also studied as a particular case of the equilibrium problem. A short section on quasi-equilibrium problems and quasi-variational inequalities is also given in which some observations about the relation between the quasi-equilibrium problem and the quasi-variational inequality problem are presented. For the entire collection see [Zbl 1411.90006].