Distributed team formation in multi-agent systems: stability and approximation

We consider a scenario in which leaders are required to recruit teams of followers. Each leader cannot recruit all followers, but interaction is constrained according to a bipartite network. The objective for each leader is to reach a state of local stability in which it controls a team whose size is equal to a given constraint. We focus on distributed strategies, in which agents have only local information of the network topology and propose a distributed algorithm in which leaders and followers act according to simple local rules. The performance of the algorithm is analyzed with respect to the convergence to a stable solution. Our results are as follows. For any network, the proposed algorithm is shown to converge to an approximate stable solution in polynomial time, namely the leaders quickly form teams in which the total number of additional followers required to satisfy all team size constraints is an arbitrarily small fraction of the entire population. In contrast, for general graphs there can be an exponential time gap between convergence to an approximate solution and to a stable solution.