考虑负网络效应的产品线动态定价研究

doi:10.16381/j.cnki.issn1003-207x.2021.0090

Abstract

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

CLC Number:

F274

Xu-wang LIU, Cheng-na ZHU, Xing-gang LUO, Wei Qi. Dynamic Pricing of Product Line Considering Negative Network Effect[J]. Chinese Journal of Management Science, 2023, 31(9): 127-136.

Figures/Tables 12

$α$	0	-2.25	-2.4	-2.5	-2.6	-2.75	-2.9	-3
$π$	29.2	98.3	64	52.8	49	45	39.2	36.9

$α 1$	0	-4.7	-4.75	-4.8	-4.85	-4.9	-4.95	-5
$α 2$	0	-5.7	-5.75	-5.8	-5.85	-5.9	-5.95	-6
$π$	0.73	380.14	296.96	244.02	207.35	180.45	159.87	1461

$α 1$	0	-5	-4.95	-4.9	-4.85	-4.8	-4.75	-4.7
$α 2$	0	-5.7	-5.75	-5.8	-5.85	-5.9	-5.95	-6
$π$	0.73	207.16	206.72	206.78	207.35	208.44	210.07	212.25

$α 1$	0	-5.2	-5.3	-5.4	-5.5	-5.6	-5.7	-5.8
$α 2$	0	-5.2	-5.3	-5.4	-5.5	-5.6	-5.7	-5.8
$π$	0.73	452.21	271.48	194.27	151.83	124.96	106.36	119.31

$α ̂$	-2.9	-3	-1	-2	-3	-4
$α = - 3$
$π ̂$	37838	32.2952	31.1661	30.2931	29.6044	29.0525
$l$	0.05	0	0.03	0.06	0.08	0.1
$α = - 3.3$
$π ̂$	31.2543	29.8762	28.8327	28.0250	27.3877	26.8773
$l$	0.14	0.09	0.05	0.02	0	0.02

$α 1 ̃$	-4.795	-4.8	-4.805	-4.81	-4.815	-4.82
$α 2 ̃$	-5.795	-5.8	-5.805	-5.81	-5.815	-5.82
$α 1 = - 4.8$ $α 2 = - 5.8$
$π$	237.75	244.02	229.80	226.03	222.39	218.87
$l$	0.026	0	0.058	0.074	0.088	0.103
$α 1 = - 4.815$ $α 2 = - 5.815$
$π$	247.71	244.03	239.42	235.49	231.69	228.04
$l$	0.069	0.053	0.033	0.016	0	0.016

$α 1 ̃$	-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

$α 1 ̃$	-5.195	-5.2	-5.205	-5.21	-5.215	-5.22
$α 2 ̃$	-5.195	-5.2	-5.205	-5.21	-5.215	-5.22
$α 1 = - 5.2$ $α 2 = - 5.2$
$π$	472.12	456.21	441.38	427.53	414.55	402.37
$l$	0.034	0	0.032	0.062	0.091	0.118
$α 1 = - 5.215$ $α 2 = - 5.215$
$π$	471.03	455.17	440.38	426.56	4162	401.46
$l$	0.138	0.100	0.064	0.031	0	0.029

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Dynamic Pricing of Product Line Considering Negative Network Effect

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