Optimal Pricing in Networks with Externalities (1101.5617v1)

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. 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.

• The paper reveals that pricing strategies based on Bonacich centrality optimize profit by tailoring prices to consumers' network positions.
• It introduces a polynomial-time algorithm for uniform pricing and examines NP-hardness in the two-tier discount pricing scenario.
• The findings highlight significant profit gains from exploiting network externalities, inspiring future research in dynamic and competitive market settings.

Optimal Pricing in Networks with Externalities: A Summary

The paper "Optimal Pricing in Networks with Externalities" by Ozan Candogan, Kostas Bimpikis, and Asuman Ozdaglar addresses the problem of determining optimal pricing strategies for a monopolist selling a divisible good in a social network with positive local network effects. In such a network, a consumer's usage influences the usage levels of their neighbors, resulting in externalities that the monopolist can exploit for pricing decisions.

Key Contributions

1. Individualized Pricing Based on Network Position:
   • The paper provides an explicit characterization of the optimal price for each consumer as a function of their network position. It establishes that it is optimal for the monopolist to set prices proportional to each agent's Bonacich centrality, a measure of network influence.
2. Uniform Pricing Algorithm:
   • When individualized pricing is not feasible, the paper details a polynomial-time algorithm to determine a single uniform price for all agents. The algorithm identifies subsets of consumers and computes the optimal price assuming only those subsets purchase the good.
3. Pricing with Two-Tier Options:
   • The research examines a scenario where the monopolist can offer two prices: full and discounted. It highlights that determining the optimal set of agents for the discounted price is NP-hard, but the authors provide an approximation algorithm that guarantees capturing at least 88% of the optimal profit.
4. Value of Network Information:
   • By comparing profits of a monopolist who ignores network effects versus one who uses network-informed pricing, the paper showcases the significant profit margins gained from understanding the network's structure.

Theoretical and Practical Implications

The theoretical implications underpin the economic rationale for using Bonacich centrality in pricing strategies — a novel cross-disciplinary application of sociological network metrics. Practically, the findings suggest that firms can leverage social network data to enhance pricing strategies and boost profitability. The proposed algorithms ensure computational feasibility, even in large-scale networks typical of modern digital platforms.

Numerical Insights and Future Directions

The paper provides quantitative results demonstrating how accounting for network externalities can lead to significant increases in profit compared to traditional pricing strategies. While the paper focuses on static and monopolistic settings, future research could explore dynamic pricing models and competitive environments to extend the applicability of these findings to broader market scenarios.

Concluding Thoughts

This work significantly enriches the understanding of optimal pricing within networks affected by local externalities. By characterizing pricing structures in terms of network centrality, the paper offers both firm-level insights for strategic pricing and foundational results that may inspire further research in network economics and related fields. The insights gained could be particularly beneficial as businesses increasingly seek to capitalize on the rich data available in social networks.