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Users of the BitTorrent file-sharing protocol and its variants are incentivized to contribute their upload capacity in a bilateral manner: Downloading is possible in return for uploading to the same user. An alternative is to use multilateral exchange to match user demand for content to available supply at other users in the system. We provide a formal comparison of peer-to-peer system designs based on bilateral exchange with those that enable multilateral exchange via a price-based market mechanism to match supply and demand. First, we compare the two types of exchange in terms of the equilibria that arise. A multilateral equilibrium allocation is Pareto-efficient, while we demonstrate that bilateral equilibrium allocations are not Pareto-efficient in general. We show that Pareto efficiency represents the “gap” between bilateral and multilateral equilibria: A bilateral equilibrium allocation corresponds to a multilateral equilibrium allocation if and only if it is Pareto-efficient. Our proof exploits the fact that Pareto efficiency implies reversibility of an appropriately constructed Markov chain. Second, we compare the two types of exchange through the expected percentage of users that can trade in a large system, assuming a fixed file popularity distribution. Our theoretical results as well as analysis of a BitTorrent dataset provide quantitative insight into regimes where bilateral exchange may perform quite well even though it does not always give rise to Pareto-efficient equilibrium allocations.
Date of Publication: Oct. 2011