Internet and Network Economics

Volume 6484 of the series Lecture Notes in Computer Science pp 415-423

Optimal Iterative Pricing over Social Networks (Extended Abstract)

  • Hessameddin AkhlaghpourAffiliated withComputer Engineering Department, Sharif University of Technology
  • , Mohammad GhodsiAffiliated withComputer Engineering Department, Sharif University of TechnologyInstitute for Research in Fundamental Sciences (IPM)
  • , Nima HaghpanahAffiliated withEECS Department, Northwestern University
  • , Vahab S. MirrokniAffiliated withGoogle Research NYC
  • , Hamid MahiniAffiliated withComputer Engineering Department, Sharif University of Technology
  • , Afshin NikzadAffiliated withTepper School of Business, Carnegie Mellon University

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We study the optimal pricing for revenue maximization over social networks in the presence of positive network externalities. In our model, the value of a digital good for a buyer is a function of the set of buyers who have already bought the item. In this setting, a decision to buy an item depends on its price and also on the set of other buyers that have already owned that item. The revenue maximization problem in the context of social networks has been studied by Hartline, Mirrokni, and Sundararajan [4], following the previous line of research on optimal viral marketing over social networks [5,6,7].

We consider the Bayesian setting in which there are some prior knowledge of the probability distribution on the valuations of buyers. In particular, we study two iterative pricing models in which a seller iteratively posts a new price for a digital good (visible to all buyers). In one model, re-pricing of the items are only allowed at a limited rate. For this case, we give a FPTAS for the optimal pricing strategy in the general case. In the second model, we allow very frequent re-pricing of the items. We show that the revenue maximization problem in this case is inapproximable even for simple deterministic valuation functions. In the light of this hardness result, we present constant and logarithmic approximation algorithms when the individual distributions are identical.