Differential evolution to find Stackelberg-Nash equilibrium in bilevel problems with multiple followers

This paper considers bilevel programming problems with one leader and multiple followers when there is information shared among the followers. In this model, the objective function and the set of constraints of each follower include the leader's variables and the variables of the other followers. We propose a differential evolution method to solve the so called Stackelberg-Nash problem, in which the leader announces a decision first and then, in response to this decision, the followers make their decisions simultaneously solving a Nash equilibrium problem. The algorithm performance is illustrated by means of several test problems.