A Multiple Leader Stackelberg-Nash Model with Genetic Algorithm

We present a computational methodology to reach a Stackelberg - Nash solution for a hierarchical 2+n person game via genetic algorithm (GA). There are two players acting as leaders in a two level leader-follower model, the rest of players play a noncooperative game and react to the optimal decision taken by the two leaders who also play a noncooperative game between themselves. The idea of the Stackelberg-Nash GA is to bring together genetic algorithms and the leader-follower strategy in order to process a genetic algorithm to build the solution. The follower players, as well as the leader players, make their decisions simultaneously at each step of the evolutionary process, solving a Nash equilibrium problem. In this model the uniqueness of the Nash equilibrium of the follower players has been supposed. Applications to global emission games, together with some test cases, will be illustrated.