Optimal Pricing in Social Networks with Incomplete Information

  • Wei Chen
  • Pinyan Lu
  • Xiaorui Sun
  • Bo Tang
  • Yajun Wang
  • Zeyuan Allen Zhu
Part of the Lecture Notes in Computer Science book series (LNCS, volume 7090)


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.


Nash Equilibrium Probability Vector Optimal Price Uniform Price Congestion Game 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


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Copyright information

© Springer-Verlag Berlin Heidelberg 2011

Authors and Affiliations

  • Wei Chen
    • 1
  • Pinyan Lu
    • 1
  • Xiaorui Sun
    • 3
  • Bo Tang
    • 2
  • Yajun Wang
    • 1
  • Zeyuan Allen Zhu
    • 4
  1. 1.Microsoft Research AsiaUSA
  2. 2.Shanghai Jiaotong UniversityChina
  3. 3.Columbia UniversityUSA

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