Optimal Iterative Pricing with Positive Network Externalities

In this paper, we study optimal pricing for revenue maxi- mization 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 buyer's decision to buy an item de- pends on the price of the item as well as the set of other buyers that own the item. The revenue maximization prob- lem in the context of social networks has been initiated by Hartline, Mirrokni, and Sundararajan (6), following the pre- vious line of research on optimal viral marketing strategies in social networks (7, 9). In contrast to the previous work by Hartline et. al. (6), we study revenue maximization without price discrimination. In particular, we study iterative pricing models in which a seller iteratively posts a price for a digital good (visible to all buyers), and all interested buyers can buy the item at this price. We consider the Bayesian setting in which we have some prior (probability distribution) on the valuations of buyers. We study two iterative pricing models that al- low difierent rates of re-pricing: In the case that we are allowed to re-price the item very frequently, we show that the revenue maximization problem is inapproximable even for simple deterministic valuation functions, and in light of this hardness result, we present constant and logarithmic approximation algorithms for a special case of the problem with identical individual distributions. On the other hand, in the second model in which we are only allowed to re-price the item at a limited rate, we give an FPTAS for the optimal pricing strategy in the general case.