Optimal Pricing in Networks with Externalities

We study the optimal pricing strategies of a monopolist selling a divisible good (service) to consumers who 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 a 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 consists of three components: (i) a nominal term that is independent of the network structure, (ii) a discount term proportional to the influence that this agent exerts over the rest of the social network (quantified by the agent's Bonacich centrality), and (iii) a markup term proportional to the influence that the network exerts on the agent. In the second part of the paper, we discuss the optimal strategy of a monopolist who 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. Third, we assume that the monopolist can offer the good in two prices, full and discounted, and we 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 who 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 who does not take into account the network effects when choosing her pricing policy to those of a monopolist who uses this information optimally

Competition and Cooperation Analysis for Data Sponsored Market: A Network Effects Model

The data sponsored scheme allows the content provider to cover parts of the cellular data costs for mobile users. Thus the content service becomes appealing to more users and potentially generates more profit gain to the content provider. In this paper, we consider a sponsored data market with a monopoly network service provider, a single content provider, and multiple users. In particular, we model the interactions of three entities as a two-stage Stackelberg game, where the service provider and content provider act as the leaders determining the pricing and sponsoring strategies, respectively, in the first stage, and the users act as the followers deciding on their data demand in the second stage. We investigate the mutual interaction of the service provider and content provider in two cases: (i) competitive case, where the content provider and service provider optimize their strategies separately and competitively, each aiming at maximizing the profit and revenue, respectively; and (ii) cooperative case, where the two providers jointly optimize their strategies, with the purpose of maximizing their aggregate profits. We analyze the sub-game perfect equilibrium in both cases. Via extensive simulations, we demonstrate that the network effects significantly improve the payoff of three entities in this market, i.e., utilities of users, the profit of content provider and the revenue of service provider. In addition, it is revealed that the cooperation between the two providers is the best choice for all three entities.Comment: 7 pages, submitted to one conferenc

A Socially-Aware Incentive Mechanism for Mobile Crowdsensing Service Market

Mobile Crowdsensing has shown a great potential to address large-scale problems by allocating sensing tasks to pervasive Mobile Users (MUs). The MUs will participate in a Crowdsensing platform if they can receive satisfactory reward. In this paper, in order to effectively and efficiently recruit sufficient MUs, i.e., participants, we investigate an optimal reward mechanism of the monopoly Crowdsensing Service Provider (CSP). We model the rewarding and participating as a two-stage game, and analyze the MUs' participation level and the CSP's optimal reward mechanism using backward induction. At the same time, the reward is designed taking the underlying social network effects amid the mobile social network into account, for motivating the participants. Namely, one MU will obtain additional benefits from information contributed or shared by local neighbours in social networks. We derive the analytical expressions for the discriminatory reward as well as uniform reward with complete information, and approximations of reward incentive with incomplete information. Performance evaluation reveals that the network effects tremendously stimulate higher mobile participation level and greater revenue of the CSP. In addition, the discriminatory reward enables the CSP to extract greater surplus from this Crowdsensing service market.Comment: 7 pages, accepted by IEEE Globecom'1