免费增值模式下服务产品的最优定价与捆绑策略研究  

Optimal pricing and bundling strategy of service products under freemium model

作　　者：刘旭旺[1] 朱成娜 齐微[1] 雒兴刚 LIU Xuwang;ZHU Chengna;QI Wei;LUO Xinggang(Institute of Management Science and Engineering,Henan University,Kaifeng 475000,China;School of Management,Hangzhou Dianzi University,Hangzhou,Hangzhou 310018,China)

机构地区：[1]河南大学管理科学与工程研究所,开封475000 [2]杭州电子科技大学管理学院,杭州310018

出　　处：《系统工程理论与实践》2023年第6期1722-1735,共14页Systems Engineering-Theory & Practice

基　　金：国家自然科学基金(72001071);国家社会科学基金(22FGLB083);教育部人文社科基金(21YJA630061);河南省高校科技创新人才支持计划(2021-CX-004);河南省哲学社科规划项目(2022BJJ031)。

摘　　要：产品的网络效应特性是产品定价决策的重要因素,免费增值是企业利用产品网络效应的重要手段.本文考虑基础产品和服务均存在正网络效应的情况下,多种服务在分别售卖和捆绑售卖(VIP模式)下的最优定价、最优市场份额和最大收益.基于multinominal logit model (MNL)模型,构建了免费增值模式下服务产品的最优定价与策略选择优化模型,理论分析了分别售卖和捆绑售卖下的最优解和利润差异.研究表明,受正网络效应影响,在一定范围内,得到了产品服务的最优定价、最优市场份额和最大收益的理论解;最后,数值仿真表明产品进入市场初期捆绑售卖模式最优,选择异质产品分别售卖将是最优策略.研究成果可以为平台信息类产品服务的定价策略提供理论依据和决策支持.The network effect characteristic of products is an important factor in product pricing decision,and freemium is an important means for enterprises to take advantage of product network effect,which has become a widely adopted business model for digital products.The pricing strategy of products and additional services considering network effects has become the primary problem of digital product revenue management.This paper considers the optimal pricing,optimal market share and maximum revenue of various services under separate sales and bundled sales(VIP mode) under the condition that both basic products and services have positive network effects.Based on multinominal Logit model(MNL),an optimization model for pricing and policy selection of service products in the freemium model is proposed to theoretically analyze the optimal solution and profit difference between separate sales and bundled sales.The research shows that under the influence of positive network effect,in a certain range,both the market share and bundled sales are concave functions in terms of revenue,and the theoretical solutions of optimal pricing,optimal market share and maximum revenue of products and services are obtained.Finally,the numerical simulation studies the income gap between the two strategies of single sale and bundle sale when the network effect changes.The results show that the bundle sale mode is optimal at the initial stage when the product enters the market.After a period of time,with the increase of the strength of the service network effect,it will be optimal to choose the heterogeneous products to sell separately.The research results can provide theoretical basis and decision support for the pricing strategy of platform information products and services.

关 键 词：免费增值 网络效应 MNL模型 捆绑售卖 定价策略 

分 类 号：F274[经济管理—企业管理]