1Bilateral and Multilateral Exchanges
for Peer-Assisted Content Distribution
Christina Aperjis, Ramesh Johari, and Michael J. Freedman
Abstract—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 mul-
tilateral 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.
Index Terms—Peer-to-peer systems, Markov chains, Economics
I. INTRODUCTION
Early peer-to-peer systems did not provide any incentives
for participation, leading to extensive free riding: many peers
were using the resources of other peers without contributing
their own [2, 16]. The peer-to-peer community responded with
mechanisms to prevent free riding by incentivizing sharing on
a bilateral exchange basis, as used by BitTorrent [10] and its
variants [28, 34].
According to the BitTorrent protocol, each user splits his
available upload rate among users from which he gets the
highest download rates. As a result, an increase in the upload
rate to one user may increase the download rate from that
particular user; however, it does not increase the download
rate from other users. Thus, two users are incentivized to
exchange only if each has content the other wants. This results
in a significant drawback of bilateral exchange: it breaks down
between users that do not have reciprocally desired files.
The difficulties of bilateral exchange (or barter) in an
economy have been long known, the most important being
the improbability of coincidence between persons wanting and
possessing [19]. As discussed in [19], “there may be many
people wanting, and many possessing those things wanted;
but to allow of an act of barter, there must be a double
coincidence, which will rarely happen.” In modern economies,
the aforementioned difficulty is eliminated by the use of
money. Money can enable multilateral exchange by serving as
a medium of exchange and a common measure of value. Even
though modern societies take the use of money for granted,
the same is not the case in peer-to-peer systems.
Peer-to-peer systems could potentially also use market-
based multilateral exchange to match user demand for content
to available supply at other users in the system. This can
be done by using virtual currency and assigning a budget
to each user that decreases when downloading and increases
when uploading. Monetary incentives with a virtual currency
have been previously proposed to encourage contribution in
peer-to-peer systems [15, 33, 31, 6, 5]; however, such designs
are usually more complex than bilateral protocols and are
not widespread. Thus, there is a significant tradeoff: bilateral
exchange without money is simple, while multilateral exchange
allows more users to trade. In this paper, we provide a formal
comparison of two peer-to-peer system designs: bilateral barter
systems such as BitTorrent, and a market-based exchange of
content enabled by a price mechanism to match supply and
demand. Our main goal is to identify precisely what benefits
a currency-based system might offer, and whether these ben-
efits are sufficient to actually warrant all the complexity of
implementation presented by such systems.
We start in Section II with a fundamental abstraction of
content exchange in systems like BitTorrent: exchange ratios.
The exchange ratio from one user to another gives the down-
load rate received per unit upload rate. Exchange ratios are a
useful formal tool because they allow us to define and study
the equilibria of bilateral exchange. In the model of bilateral
exchange we consider, each user optimizes with respect to
exchange ratios. In Section III, we define bilateral equilibrium
as a rate vector and a vector of exchange ratios, where all
users have simultaneously optimized given exchange ratios.
We also define multilateral equilibrium, where users optimize
with respect to prices; our definition of multilateral equilibrium
is the same as competitive equilibrium in economics [22]. In
a multilateral equilibrium, the presence of money enables a
potentially wider set of exchanges than is possible in bilateral
equilibrium.
In Section IV, we compare bilateral and multilateral peer-
to-peer systems through the allocations that arise at equilibria.
A multilateral equilibrium allocation is always Pareto efficient,
while bilateral equilibria may be inefficient. Our main result
in this section is that a bilateral equilibrium allocation is
Pareto efficient if and only if it is a multilateral equilibrium
allocation—in other words, efficient bilateral equilibria must
effectively yield “supporting prices” as in a multilateral equi-
librium. This result provides formal justification of the effi-
ciency benefits of multilateral equilibria. The proof exploits an
interesting connection between equilibria and Markov chains: