Emergence of coalitions in mean field stochastic systems

In this paper we define and investigate coalition formation for the large population dynamic LQG tracking game that was studied in [1], [2]. First, we present a mean field stochastic control algorithm which, when applied by all agents in the system, gives rise to system behaviour where (i) all agents systems are L² stable, and (ii) the set of controls yields an ε-Nash equilibrium. Then, as the population size tends to infinity, we show that the system with a coalition state converges to a major-minor agent system studied in [3], where in the limit the coalition state acts as a single major agent. We investigate the existence properties of the coalition state, and further discuss the stability of the coalitions in the overall dynamic system with respect to the fraction of the agents in the coalition.