Optimal online pricing with network externalities

Ahmad Khajehnejad, Mohammad Ghodsi, afshin nikzad

Abstract:

We study the optimal pricing strategy for profit maximization in presence of network
externalities where a decision to buy a product depends on the price offered to the buyer
and also on the set of her friends who have already bought that product. We model the
network influences by a weighted graph where the utility of each buyer is the sum of
her initial value on the product, and the linearly additive influence from her friends. We
assume that the buyers arrive online and the seller should offer a price to each buyer when
she enters the market. We also take into account the manufacturing cost. In this paper, we
first assume that the monopolist defines a unique price for the product and commits to it
for all buyers. In this case, we present an FPTAS algorithm that approximates the optimal
price with a high probability. We also prove that finding the optimum price is NP-hard.
Second, we consider a market with positive network externalities and assume that the
monopolist could offer a private price to each customer. We prove that this problem is also
hard to approximate for linear influences. On the positive side, we present a polynomial
time algorithm for the problem when influences are symmetric. At last, we show that the
seller has more ability to extract influences with price discrimination.