Paolo Pin, Università degli Studi di Siena

"Eciency and Stability in a Process of Teams Formation"

Abstract

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 rst 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 matching