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

IF 4.5 3区 管理学 Q1 OPERATIONS RESEARCH & MANAGEMENT SCIENCE
Yu Zhang, Ruopeng Wang, Jinting Wang, Xiangbin Yan
{"title":"Subsidize or charge? Optimal pricing in a two-stage sales system facing network effects and customer strategic behavior","authors":"Yu Zhang,&nbsp;Ruopeng Wang,&nbsp;Jinting Wang,&nbsp;Xiangbin Yan","doi":"10.1007/s10479-025-06710-9","DOIUrl":null,"url":null,"abstract":"<div><p>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.</p></div>","PeriodicalId":8215,"journal":{"name":"Annals of Operations Research","volume":"351 3","pages":"2059 - 2093"},"PeriodicalIF":4.5000,"publicationDate":"2025-07-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Annals of Operations Research","FirstCategoryId":"91","ListUrlMain":"https://link.springer.com/article/10.1007/s10479-025-06710-9","RegionNum":3,"RegionCategory":"管理学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"OPERATIONS RESEARCH & MANAGEMENT SCIENCE","Score":null,"Total":0}
引用次数: 0

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.

补贴还是收费?面向网络效应和顾客战略行为的两阶段销售系统的最优定价
随着电子商务和平台经济的快速发展,越来越多的产品呈现出网络效应。面对网络效应和系统服务拥塞,用户与其他用户交互的倾向是异构的。本文研究了存在网络效应和客户异质性的两阶段销售模型中的定价问题,该模型被建模为每个阶段都存在拥塞的单服务器排队模型。在两阶段销售体系中,初期销售通常以建立品牌为目标,后期销售以利润最大化为目标。对比传统销售,我们发现在网络效应影响下的初始定价决策可以在补贴或收费策略上进行优化。具体而言,我们的研究结果表明,在第二阶段价格较高或网络效应强度较低的情况下,补贴策略更有利;否则,收费策略会更好。在第一阶段,顾客的战略行为可能会推动价格上涨,进而损害企业的收益。我们的研究结果提供了有价值的见解,忽略网络效应和战略客户行为的影响可能会导致公司的重大收入损失。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
求助全文
约1分钟内获得全文 求助全文
来源期刊
Annals of Operations Research
Annals of Operations Research 管理科学-运筹学与管理科学
CiteScore
7.90
自引率
16.70%
发文量
596
审稿时长
8.4 months
期刊介绍: The Annals of Operations Research publishes peer-reviewed original articles dealing with key aspects of operations research, including theory, practice, and computation. The journal publishes full-length research articles, short notes, expositions and surveys, reports on computational studies, and case studies that present new and innovative practical applications. In addition to regular issues, the journal publishes periodic special volumes that focus on defined fields of operations research, ranging from the highly theoretical to the algorithmic and the applied. These volumes have one or more Guest Editors who are responsible for collecting the papers and overseeing the refereeing process.
×
引用
GB/T 7714-2015
复制
MLA
复制
APA
复制
导出至
BibTeX EndNote RefMan NoteFirst NoteExpress
×
提示
您的信息不完整,为了账户安全,请先补充。
现在去补充
×
提示
您因"违规操作"
具体请查看互助需知
我知道了
×
提示
确定
请完成安全验证×
copy
已复制链接
快去分享给好友吧!
我知道了
右上角分享
点击右上角分享
0
联系我们:info@booksci.cn Book学术提供免费学术资源搜索服务,方便国内外学者检索中英文文献。致力于提供最便捷和优质的服务体验。 Copyright © 2023 布克学术 All rights reserved.
京ICP备2023020795号-1
ghs 京公网安备 11010802042870号
Book学术文献互助
Book学术文献互助群
群 号:604180095
Book学术官方微信