Efficiency and Stability in a Process of Teams Formation

We analyze a team formation process that generalizes matching models and network formation models, allowing for overlapping teams of heterogeneous size. We define a weak concept of stability, called myopic team-wise stability, which extends to our setup the concept of pair-wise stability used in network formation models. Then we refine it in two ways: (i) through stochastic stability, where agents are still myopic and errors occurring with vanishing probability can dissolve or create teams, and (ii) through coalitional stability, where agents are perfectly rational and able to coordinate. We find that the first concept has in many cases a much stronger predictive power than the second one. In particular, under some stark assumptions, coalitional stability in no way refines myopic team-wise stability. By contrast, stochastically stable states are, under a very general assumption, feasible states that maximize the overall number of activities performed by teams. Finally, we apply our main result to the marriage problem, and we use the marriage theorem to obtain a characterization of stochastically stable matchings. JEL classification code: C72, C73, D85, H41.