Modelling Real P2P Networks: The Effect of Altruism

We develop a model of the interaction of rational peers in an incentive-free peer-to-peer (P2P) network and use game theoretic analysis to derive results about peer and network behavior. We calculate and discuss Nash equilibria and predict peer behavior in terms of individual contribution. At the heart of our model is altruism, an intrinsic parameter reflecting peers inherent willingness to contribute. Two different approaches for modelling altruistic behavior and its attendant benefit are introduced and discussed. We consider the cases of P2P networks of peers that (i) have homogeneous altruism levels or (ii) have heterogeneous altruism levels, but with known probability distributions. We find that, under the effects of altruism, a substantial fraction of peers will contribute when altruism levels are within certain intervals, even though no incentive mechanism is used. Our results corroborate empirical evidence of large P2P networks surviving or even flourishing without or with barely functioning incentive mechanisms.

1 Introduction

Peer-to-Peer networks have created a new paradigm for distributed applications, have received a lot of attention from the academic community and are used for a variety of diverse applications, from distributed backup and computation to anonymous web publishing. The most common application of P2P networks today remains file sharing (e.g., KaZaA¹

http://www.kazaa.com

, or eMule²

http://www.emule-project.net

). It has been shown empirically, e.g., [1], that in such P2P networks a large fraction of peers is free-riding, i.e., does not contribute content to the network. In practice P2P networks remain quite popular despite the free-riders, as a small fraction of users is contributing content (often in large quantities). Theoretically, the problem of contribution to P2P networks fits in the general framework of private provision of a public good [3].³

For some important differences of P2P network contribution from the typical public goods context, see for example [13].

So, if we assume that peers are rational utility maximizers whose utility depends only on their own consumption (i.e., downloads), we can show that the average contribution and the percentage of contributing peers would drop to zero [16].