Optimal Pricing in Networks with Externalities

Abstract

We study the optimal pricing strategies of a monopolist selling a divisible good (service) to consumers that are embedded in a social network. A key feature of our model is that consumers experience a (positive) local network effect. In particular, each consumer's usage level depends directly on the usage of her neighbors in the social network structure. Thus, the monopolist's optimal pricing strategy may involve offering discounts to certain agents, who have a central position in the underlying network. Our results can be summarized as follows. First, we consider a setting where the monopolist can offer individualized prices and derive an explicit characterization of the optimal price for each consumer as a function of her network position. In particular, we show that it is optimal for the monopolist to charge each agent a price that is proportional to her Bonacich centrality in the social network. In the second part of the paper, we discuss the optimal strategy of a monopolist that can only choose a single uniform price for the good and derive an algorithm polynomial in the number of agents to compute such a price. Thirdly, we assume that the monopolist can offer the good in two prices, full and discounted, and study the problem of determining which set of consumers should be given the discount. We show that the problem is NP-hard, however we provide an explicit characterization of the set of agents that should be offered the discounted price. Next, we describe an approximation algorithm for finding the optimal set of agents. We show that if the profit is nonnegative under any feasible price allocation, the algorithm guarantees at least 88 % of the optimal profit. Finally, we highlight the value of network information by comparing the profits of a monopolist that does not take into account the network effects when choosing her pricing policy to those of a monopolist that uses this information optimally.

Dynamic Pricing in the Presence of Social Learning and Strategic Consumers

“…consider a firm selling two substitutable products to a stream of consumers who arrive sequentially and whose purchasing decisions can be influenced by earlier purchases. Candogan et al (2012) and Hu and Wang (2013) study optimal pricing strategies in social networks with positive externalities. Tereyagoglu and Veeraraghavan (2012) consider a setting in which consumers may use their purchases to display their social status.…”

Price Competition in Product Variety Networks

“…From the technical viewpoint, our approach is related to literature on games on networks (Jackson and Zenou, 2015) where the network is explicitly modeled as a graph and the payoff functions There is also a growing literature that models price competition between firms with an explicit network. Two important papers in this literature are that of Bloch and Quérou (2013) and Candogan et al (2012). 6 Bloch and Quérou (2013) study optimal monopoly pricing in the presence of network externalities across consumers.…”

“…The setting proposed by these authors involves a homogeneous good produced by a monopolist, and many consumers whose probability to purchase the good. Candogan et al (2012) develop a similar approach, but with a divisible good. 7 In contrast to these papers, we account for product differentiation and consider a price-setting game among several firms.…”

The fashion game: Network extension of Matching Pennies

“…Computational complexities and approximation algorithms for marketing problems among rebels are discussed in [8]. For more research on social network pricing and marketing problems from the perspective of algorithmic game theory, we refer the reader to [2,6,7,10,15].…”