An algorithm for a class of bilevel split equilibrium problems: application to a differentiated Nash-Cournot model with environmental constraints

Abstract

We propose a strongly convergent algorithm for solving strongly monotone variational inequality problems over the solution set of a split monotone equilibrium problem. The proposed algorithm can be considered as a combination of an extragradient method for monotone equilibrium problems and a projection procedure for variational inequalities. Under some suitable assumptions the sequence of iterates generated by the algorithm is strongly convergent to the unique solution of the problem. We then apply the algorithm to a coupled differentiated Nash-Cournot production equilibrium model with environmental constraints.