This paper aims at giving insight on the stability of collaboration choices in P2P networks. We study networks where exchanges between nodes are driven by the will of getting the best service available. This is the case for most existing P2P networks. We explore an evolution model derived from stable roommates theory that accounts for heterogeneity between nodes. We show that most P2P applications can be modeled using stable matching theory. This is the case whenever preference lists can be deduced from the exchange policy. In many cases, the preferences lists are characterized by an interesting acyclic property. This leads us to the notion of acyclic preferences. We show that P2P networks with acyclic preferences possess a unique stable state with good convergence properties.