Convergence and optimization of agent-based coalition formation

In this paper, we analyze the model of agent-based coalition formation in markets. Our goal is to study the convergence of the coalition formation and optimize agents' strategies. We show that the model has a unique steady state (equilibrium) and prove that all solutions converge to it in the case that the maximum size of coalitions is not larger than three. The stability of the steady state in other cases is not studied while numerical simulations are given to show the convergence. The steady state, which determines both the global system gain and the average gain per agent, is expressed by the agents' strategies in the coalition formation. Through the steady state, we give the relationship between the gains and the agents' strategies, and present a series of results for the optimization of agents' strategies.