Subsidize or charge? Optimal pricing in a two-stage sales system facing network effects and customer strategic behavior

Yu Zhang, Ruopeng Wang, Jinting Wang () and Xiangbin Yan
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Yu Zhang: University of Science and Technology Beijing
Ruopeng Wang: Beijing Institute of Petrochemical Technology
Jinting Wang: Central University of Finance and Economics
Xiangbin Yan: University of Science and Technology Beijing

Annals of Operations Research, 2025, vol. 351, issue 3, No 10, 2059-2093

Abstract: Abstract With the rapid development of e-commerce and platform economy, an increasing number of products exhibit network effects. Facing the network effects as well as system service congestion, the propensities of customers for interacting with other users are heterogeneous. In this paper, we investigate pricing in a two-stage sales model in the presence of network effects and customer heterogeneity, modeled as a single-server queueing model with congestion in each stage. In the two-stage sales system, initial sales are usually targeted at establishing the brand, while later sales are aimed at maximizing profit. In contrast to traditional sales, we find that the initial pricing decision under the influence of network effects can be optimized on either a subsidy or charging strategy. Specifically, our results indicate that the subsidy strategy is more advantageous under situations where either the second-stage price is relatively high or the strength of network effects is relatively low; otherwise, the charging strategy is better off. Further, it is revealed that strategic behavior of customers may drive prices up in the first stage, which in turn damages the firm’s revenue. Our results provide valuable insights that ignoring the impacts of network effects and strategic customer behavior may result in significant revenue loss to the firm.

Keywords: Network effects; Pricing; Queueing; Strategic customers; Two-stage sales (search for similar items in EconPapers)
Date: 2025
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DOI: 10.1007/s10479-025-06710-9

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