N leader--M follower coaliton games with genetic algorithms and applications

In this paper we present a computational methodology to reach a Stackelberg - Nash solution for a hierarchical 2+n person game via genetic algorithm evolution process. There are two players acting as leaders in a two level leader-follower model: the rest of players play a Nash game and react to the optimal decision taken by the two leaders who also play a Nash 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 the leader players, make their decisions simultaneously at each step of the evolutionary process, playing a so called Nash game. In this model the uniqueness of the Nash equilibrium at the lower level problem has been supposed. The algorithm convergence is illustrated by means of examples and test cases.