Incentives - Peer-to-Peer Computing: Applications, Architecture, Protocols, and Challenges - page 82

the system is homogeneous in that all peers have the same valuation on the
item. There is an external central authority (e.g., the original producer of the
music) that has the incentive to discourage sharing among peers in the system.
The issue is then how the central authority can introduce proper disincentives
into the system. Firstly, observe that for viability in producing the item, we
have:

v− p

k −t−c≥0

(5.1)

p n

k ≥D

(5.2)

Specifically, the above equations are to ensure that value is no smaller than
the cost.
The equilibrium (where the item is just viable to be produced) price and
profit are then given by:

p = (v−t−c)k (5.3)

π = (v−t−c)kn−D (5.4)

We can see that profit is, counterintuitively, decreasing in c. An interpreta-
tion is that c is not large enough to discourage sharing and price has to be cut
for compensation. As an analogy, consider that c represents some copy protec-
tion mechanism which merely brings inconvenience to customers but cannot
discourage sharing. To compensate for the inconvenience, the price has to be
reduced.
On the other hand, for a given value of c, suppose the price is set in such
a way that it is marginally unattractive to share. That is, we have:
p
k

+ t + c≥p (5.5)

This in turn implies that:

k
k−1 (t + c)

p = (5.6)

Now, as the maximum practical value of p is v, we have:

c = v− k−1
k

t (5.7)

Yu and Singh [Yu and Singh, 2003] also investigated the issue of proper
pricing in the presence of free-riders in a P2P system. A referral-based system
is considered in that each peer can either answer a remote query directly
(e.g., serving a requested file) or reply with a referral (e.g., pointing to a
different peer who may be able to serve the requested file). A requester (i.e.,
file consumer) needs to pay for both a referral or a direct answer. Each peer
keeps track of reserve prices of potential referrals and direct answers from any
other peer. These reserve prices are updated dynamically based on transaction