We analyze a mechanism that provides strong incentives for the submission of truthful feedback in virtual communities where services are exchanged on a peer-to-peer basis. Lying peers are punished with a severity that is exponential to their frequency of lying. We had first introduced and evaluated experimentally the mechanism in [1]. In this paper, we develop a Markov-chain model of the mechanism. Based on this, we prove that, when the mechanism is employed, the system evolves to a beneficial steady-state operation even in the case of a dynamically renewed population. Furthermore, we develop a procedure for the efficient selection of the parameters of the mechanism for any peer-to-peer system; this procedure is based on ergodic arguments. Simulation experiments reveal that the procedure is indeed accurate, as well as effective regarding the incentives provided to participants for submitting truthful feedback.