考虑参考价格效应的最优灰色市场结构与定价决策

doi:10.16381/j.cnki.issn1003-207x.2022.1419

摘要/Abstract

摘要：

基于分销商灰市和第三方灰市两种结构，分别探究了参考价格效应对供应链各成员定价决策及利润的影响，并分析了不同成员偏好的最优灰市结构。研究结果表明：分销商灰市下，参考价格效应对制造商来说是把“双刃剑”，在市场发展初期，参考价格效应有助于制造商快速占领市场，提升市场占有率；而市场进入成熟期后，参考价格效应将导致灰市扩张，损害制造商利润并对品牌信誉产生负面影响。第三方灰市下，由于第三方投机者独立于系统之外，制造商应对灰市发展更为困难，参考价格效应对灰市运作的影响也更为模糊。对比两种灰市结构，发现无参考价格效应时，分销商灰市更不利于制造商进行全渠道扩张，从而对制造商利润产生较大的负面影响；一个反直觉的发现是，分销商自行参与灰市获取的利润并非一定高于第三方灰市的情形；满足特定条件时，第三方灰市成为分销商灰市的帕累托改进。引入算例，发现参考价格效应的存在将导致不同灰市结构下成员利润的对比更为复杂；任何灰市结构下，参考价格效应都将导致社会福利下降；无论是否有参考价格效应，第三方灰市下的社会福利总是高于分销商灰市的情形。

关键词: 灰色市场, 参考价格效应, 定价决策, 供应链

Abstract:

In reality， both third parties and distributors have incentives to engage in gray market speculation， driven by the arbitrage opportunities created by price differentials between different markets. At the same time， the coexistence of multiple channels in the gray market environment makes consumers' purchasing behavior more complex， they can easily get the price information from different channels by using search engines. Thus， consumers are more cautious when purchasing gray-market products and are more sensitive to the price， and they tend to take the price of licensed products in the high-priced market as an important reference point， which results in the reference price effect.The impact of reference price effect on pricing decisions and profits of supply chain members is investigated under the distributor gray market and the third-party gray market， respectively. The optimal gray market structure with different member preferences is also analyzed. Research shows that in the distributor gray market， the reference price effect is a “double-edged sword” for the manufacturer. In the early stage of market development， the reference price effect may help him quickly occupy the market and increase market share. However， after the market enters a mature stage， the reference price effect will lead to gray market expansion， damage his profit， and have a negative impact on his brand reputation. In the third-party gray market， the manufacturer faces more difficulties in dealing with the development of the gray market， due to the independence of the third-party speculator from the system. The impact of reference price effect on the operation of the gray market is also more ambiguous. Comparing two types of gray market structures， it is found that without reference price effect， the distributor gray market is more unfavorable for the manufacturer's market expansion through all channels， thus having a significant negative impact on his profit. A counterintuitive finding is that the distributor's participation in the gray market does not necessarily result in higher profit than the third-party gray market. The third-party gray market may become a Pareto improvement of the distributor gray market when specific conditions are met. Finally， by introducing a numerical example， it is found that the reference price effect will make the comparison of members' profits more complex under different gray market structures. The reference price effect will lead to a decrease in social welfare under any gray market structure. Regardless of whether there is a reference price effect， the social welfare under the third-party gray market is always higher than that under the distributor gray market.The findings of this paper provide decision-making references for manufacturers to reasonably respond to the development of gray market under different gray market structures and reference price effects. At the same time， it also provides theoretical references for exploring the preferences of system members for different gray market structures and seeking the optimal structure.

Key words: gray market, reference price effect, pricing, supply chain

中图分类号:

F272

冯颖,陈苏雨,魏敏, 等. 考虑参考价格效应的最优灰色市场结构与定价决策[J]. 中国管理科学, 2026, 34(2): 239-249.

Ying Feng,Suyu Chen,Min Wei, et al. Optimal Gray Market Structure and Pricing Decisions Considering Reference Price effect[J]. Chinese Journal of Management Science, 2026, 34(2): 239-249.

图/表 12

图1

图2

表1

符号说明"

符号	说明
$u i$	消费者购买市场 $i$ 中产品获得的效用
$θ$	消费者对灰市产品的偏好系数
$b$	参考价格效应的强度
$w, w j$	制造商在低价市场分销给分销商的单位产品批发价格及 $j$ 模型下的均衡解
$p i, p i j$	市场 $i$ 单位产品的零售价格及其在 $j$ 模型下的均衡解
$D i, D i'$	无参考价格效应和有参考价格效应情形下市场 $i$ 的需求
$D i j$	市场 $i$ 在 $j$ 模型下的均衡需求
$π k, π k j$	系统成员 $k$ 的利润及其在 $j$ 的均衡利润
$i ∈ h, l, j$	下角标 $i$ 表示市场类型，包括高价市场 $h$ 、低价市场 $l$ 色市场 $g$
$j ∈ R P I, C R P, T P I, C T P$	上角标 $j$ 表示博弈模型，包括分销商灰市下无参考价格效应RPI和有参考价格效应CRP，第三方灰市下无参考价格效应TPI和有参考价格效应CTP
$k ∈ m, r, s$	下角标 $k$ 表示成员类型，包括制造商 $m$ 、分销商 $r$ 和第三方投机者 $s$

表1

表2

RPI和CRP情形下各成员的利润函数"

利润函数	无参考价格效应（RPI）	有参考价格效应（CRP）
制造商 $π m$	$p h D h + w D l + D g$	$p h D h' + w D l' + D g'$
分销商 $π r$	$p l - w D l + p g - w D g$	$p l - w D l' + p g - w D g'$

表2

表3

RPI和CRP情形下的内点均衡结果"

均衡结果	无参考价格效应（RPI）	有参考价格效应（CRP）
$w j$	$θ v h v l 4 - θ 2 2 v l + θ v h 2 - θ$	$2 θ v h v l θ 4 - θ + b 1 + 2 θ v l 8 θ 1 + b - b 2 1 - θ + 4 θ 2 v h 2 + b - θ$
$p h j$	$v h v l 2 + θ + 2 θ v h 1 - θ 2 2 v l + θ v h 2 - θ$	$θ v h 4 θ v h 1 - θ + v l b 5 + θ + 2 2 + θ v l 8 θ 1 + b - b 2 1 - θ + 4 θ 2 v h 2 + b - θ$
$p l j$	$v l 4 v l + θ v h 8 - 3 θ 4 2 v l + θ v h 2 - θ$	$v l 2 + θ v h v l θ 4 - θ + b 1 + 2 θ v l 8 θ 1 + b - b 2 1 - θ + 4 θ 2 v h 2 + b - θ$
$p g j$	$θ v h 3 v l + θ v h 1 - θ 2 2 v l + θ v h 2 - θ$	$θ v h 4 θ v h 1 + θ θ + b + v l 12 θ + b 2 7 + 5 θ + b 6 + 19 θ - θ 2 2 1 + b v l 8 θ 1 + b - b 2 1 - θ + 4 θ 2 v h 2 + b - θ$
$D h j$	$12$	$4 v h θ 2 2 + b - θ + v l b 2 2 + θ + θ 8 + 4 b + b θ 2 v l 8 θ 1 + b - b 2 1 - θ + 8 θ 2 v h 2 + b - θ$
$D l j$	$4 v l - θ 2 v h 4 2 v l + θ v h 2 - θ$	$12 - θ v h θ 4 - θ + b 1 + 2 θ v l 8 θ 1 + b - b 2 1 - θ + 4 θ 2 v h 2 + b - θ$
$D g j$	$θ v h - v l 2 2 v l + θ v h 2 - θ$	$4 θ v h θ + b - v l 2 2 θ - b + 3 b θ - b 2 v l 8 θ 1 + b - b 2 1 - θ + 8 θ 2 v h 2 + b - θ$
$D j$	$34$	$θ v h 6 θ 2 - θ + 2 b 1 + 2 θ + v l b 2 + 9 θ + θ 2 + 12 θ 2 v l 8 θ 1 + b - b 2 1 - θ + 8 θ 2 v h 2 + b - θ$

表3

表4

TPI和CTP情形下各成员的利润函数"

利润函数	无参考价格效应（TPI）	有参考价格效应（CTP）
制造商 $π m$	$p h D h + w D l + D g$	$p h D h' + w D l' + D g'$
分销商 $π r$	$p l - w D l + D g$	$p l - w D l' + D g'$
投机者 $π s$	$p g - p l D g$	$p g - p l D g'$

表4

表5

TPI和CTP情形下的内点均衡结果"

均衡解	无参考价格效应（TPI）	有参考价格效应（CTP）
$w j$	$θ v h v l 3 - θ 2 v l + θ v h 2 - θ$	$2 θ v h v l 2 A + B E - B b θ 1 - θ A + B C$
$p h j$	$v h v l 1 + θ + 2 θ v h 1 - θ 2 v l + θ v h 2 - θ$	$2 θ v h 4 A + v l 4 1 - θ + b 5 + 3 θ C$
$p l j$	$θ v h v l 2 v l 2 - θ + θ v h 1 - θ 8 - 3 θ 2 v l + θ v h 2 - θ v l + 2 θ v h 1 - θ$	$2 θ v h v l A + B 3 E - 2 θ 1 + b - 2 B θ θ + b A + B C$
$p g T P I$	$θ v h 4 θ 2 v h 2 1 - θ 2 + v l 2 5 - θ + θ v h 1 - θ 12 - θ 4 v l + θ v h 2 - θ v l + 2 θ v h 1 - θ$
$p g C T P$	$θ v h 4 A 2 θ + b + v l A 11 + 60 θ - 5 θ 2 + 4 b 2 6 + 5 θ + v l B 4 θ 5 - θ + b 7 + 30 θ - 5 θ 2 + 8 b 2 1 + θ 1 + b A + B C$

表5

图3

图4

图5

图6

图7

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