2011 | OriginalPaper | Chapter
Optimal Pricing in Social Networks with Incomplete Information
Authors : Wei Chen, Pinyan Lu, Xiaorui Sun, Bo Tang, Yajun Wang, Zeyuan Allen Zhu
Published in: Internet and Network Economics
Publisher: Springer Berlin Heidelberg
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In revenue maximization of selling a digital product in a social network, the utility of an agent is often considered to have two parts: a private valuation, and linearly additive influences from other agents. We study the incomplete information case where agents know a common distribution about others’ private valuations, and make decisions simultaneously. The “rational behavior” of agents in this case is captured by the well-known Bayesian Nash equilibrium.
Two challenging questions arise: how to
compute
an equilibrium and how to
optimize
a pricing strategy accordingly to maximize the revenue assuming agents follow the equilibrium? In this paper, we mainly focus on the natural model where the private valuation of each agent is sampled from a uniform distribution, which turns out to be already challenging.
Our main result is a polynomial-time algorithm that can
exactly
compute the equilibrium and the optimal price, when pairwise influences are non-negative. If negative influences are allowed, computing any equilibrium even approximately is PPAD-hard. Our algorithm can also be used to design an FPTAS for optimizing discriminative price profile.