An evolutionary algorithm based on Nash Dominance for Equilibrium Problems with Equilibrium Constraints

Abstract

This paper introduces an evolutionary algorithm for the solution of a class of hierarchical (“leader–follower”) games known as Equilibrium Problems with Equilibrium Constraints (EPECs). In one manifestation of such games, players at the upper level who assume the role of leaders, are assumed to act non cooperatively to maximize individual payoffs. At the same time, each leader's payoffs are constrained not only by their competitor's actions but also by the behaviour of the followers at the lower level which manifests in the form of an equilibrium constraint. By a redefinition of the selection criteria used in evolutionary methods, the paper demonstrates that the solution for such games can be found via a simple modification to a standard evolutionary multiobjective algorithm. We give a proposed algorithm (NDEMO) and illustrate it with numerical examples drawn from both the transportation systems management literature and the electricity generation industry underlying the applicability of NDEMO in multidisciplinary contexts.