摘要：

平台经济中产品表现出来的网络效应特性已经对产品线设计和定价产生了重要影响，负网络效应对产品线定价的影响日益重要。本文从负网络效应视角，考虑不同销售阶段销量变化对顾客选择行为的影响，研究产品线的动态定价问题，基于适用性较好的MNL模型，分析产品的网络效应特性，建立产品线的动态定价模型，研究产品线的动态定价、市场份额和企业利润的最优决策。首先，理论证明了产品线的利润函数关于市场份额是凹函数；其次，获得单个产品、同质产品和异质产品的最优定价、最优市场份额和最大利润的最优解；最后，通过数值仿真，阐明了产品线定价中考虑负网络效应的重要性，验证了本文模型具有较好的鲁棒性，企业能够获得更优的市场份额和利润。研究成果可以为具有负网络效应产品的企业在产品线设计和定价方面提供理论依据和决策参考。

Abstract:

With the increasingly competitive business， in order to better meet the consumer demand of customer groups and obtain greater market share， product line design and optimization have become an urgent problem for enterprises. Successful product line design can provide rich and differentiated products， reduce development costs， expand market share， increase profits and enhance competitive advantage. In the complex and changeable market environment， the reasonable pricing of product line can effectively solve the problem of substitution between external market environment and internal product line. Due to the variability of market environment and the time-varying of customer demand， the dynamic pricing of product line is an important decision-making problem in product line optimization design. Aiming at the negative network effect in platform economy， the dynamic pricing problem of product line is studied considering the influence of sales volume change in different sales stages on customer choice behavior. The dynamic pricing of product line is studied from the perspective of negative network effects. Based on MNL model with good applicability， the dynamic pricing model of product line， which considers the network effect characteristics of products， is established to study the dynamic pricing of product line， the optimal market share and the optimal decision of the maximum profit of the enterprise.The MNL model with negative network effect is used to simulate the choice behavior of customers in dynamic product line pricing problem. In the utility function of customers， a network effect term composed of network effect coefficient and product sales volume is added. That is： v t i = y i - p t i + α i x t i ， x t i is the total sales volume of product from the first period to t period （ x t i = ∑ k = 1 t q k i ， where q k i is the sales volume of product i in k period， i.e. sales probability）； α i is the network effect parameter of the product， which indicates the degree to which the utility obtained by customers purchasing product i is affected by the total sales volume of product i .In different cases of developing single product， homogeneous product and heterogeneous product， it is proved that the return function is concave with respect to market share when considering network effect， and the analytic solutions of dynamic optimal price， optimal market share and optimal return are given respectively.Finally， through numerical simulation， the importance of considering negative network effect in product line pricing is illustrated， the robustness of the model is verified， and enterprises can obtain better market share and profit. The research results can provide theoretical basis and decision-making reference for enterprises with negative network effect products in product line design and pricing.

Key words: product line design, dynamic pricing, MNL model, network effects, robustness

两个异质产品利润的鲁棒性（II）"

α 1 ?	-4.795	-4.8	-4.805	-4.81	-4.815	-4.82
α 2 ?	-5.82	-5.815	-5.81	-5.805	-5.8	-5.795
α 1 = - 4.8 α 2 = - 5.815
π	237.98	237.86	237.76	237.65	237.56	237.46
l	0.0005	0	0.0004	0.0009	0.001	0.002
α 1 = - 4.815 α 2 = - 5.8
π	237.97	237.85	237.74	237.64	237.54	237.45
l	0.002	0.001	0.0008	0.0004	0	0.0004

地址：北京市海淀区中关村东路55号 北京8712信箱《中国管理科学》编辑部
邮编：100190
电话：010-62542629
E-mail：[email protected] 本系统由北京玛格泰克科技发展有限公司设计开发