  The paper has two objectives. The first is to study rigorously the transient
behavior of some P2P networks whenever information is replicated and
disseminated according to epidemic-like dynamics. The second is to use the
insight gained from the previous analysis in order to predict how efficient are
measures taken against peer-to-peer (P2P) networks. We first introduce a
stochastic model which extends a classical epidemic model and characterize the
P2P swarm behavior in presence of free riding peers. We then study a second
model in which a peer initiates a contact with another peer chosen randomly. In
both cases the network is shown to exhibit a phase transition: a small change
in the parameters causes a large change in the behavior of the network. We
show, in particular, how the phase transition affects measures that content
provider networks may take against P2P networks that distribute non-authorized
music or books, and what is the efficiency of counter-measures.
