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

Abstract

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

CLC Number:

F272

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.

Figures/Tables 12

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 $s$

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 $π r$	$p l - w D l + p g - w D g$	$p l - w D l' + p g - w D g'$

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

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 $π s$	$p g - p l D g$	$p g - p l D g'$

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

References 22

[1]	Shao J， Krishnan H， McCormick S T. Gray markets and supply chain incentives［J］. Production and Operations Management， 2016，25（11）：1807-1819.
[2]	Li H， Shao J， Zhu S X. Parallel importation in a supply chain： The impact of gray market structure［J］. Transactions Research Part E： Logistics and Transportation Review， 2018，114：220-241.
[3]	Matsui K. Gray-market trade with product information service in global supply chains［J］. International Journal of Production Economics， 2014，147：351-361.
[4]	Ahmadi R， Iravani F， Mamani H. Coping with gray markets： The impact of market conditions and product characteristics［J］. Production and Operations Management， 2015，24 （5）：762-777.
[5]	Yun S. Parallel imports， their deterrence and accommodation with service differentiation［J］.The International Trade Journal， 2017，31（3）：217-231.
[6]	Autrey R L， Bova F， Soberman D A. When gray is good： Gray markets and market-creating investments［J］. Production and Operations Management， 2015，24（4）：547-559.
[7]	詹天宇，肖婷婷. 灰色市场条件下的供应链广告策略研究［J］. 管理评论， 2023，35（1）：159-173+198.
	Zhan T Y， Xiao T T. Advertising strategy of supply chains with gray markets［J］. Management Review， 2023，35（1）： 159-173+198.
[8]	Zhang Q， Jiang X Q， Zheng Y N. Blockchain adoption and gray markets in a global supply chain［J］. Omega， 2023，115：102785.
[9]	Srivastava A， Mateen A. Supply chain contracts in the presence of gray markets［J］. Decision Sciences，2020， 51（1）： 110-147.
[10]	Xiao Y， Palekar U， Liu Y C. Shades of gray-the impact of gray markets on authorized distribution channels［J］. Quantitative Marketing and Economics， 2011， 9（2）： 155-178.
[11]	王琇媚，李军. 制造商广告激励策略对灰色市场的影响研究［J］. 运筹与管理， 2022，31（11）： 213-218.
	Wang X M， Li J. Manufacturers’ advertising incentive strategies in the gray market［J］. Operations Research and Management Science，2022，31（11）： 213-218.
[12]	谢博，王先甲. 考虑售后服务的灰色市场环境下供应链运营策略［J］.工业工程与管理，2023，28（1）： 144-158.
	Xie B， Wang X J. Supply chain operational strategy in gray market environment considering after-sales service［J］. Industrial Engineering and Management， 2023，28（1）： 144-158.
[13]	洪定军，马永开，倪得兵. 灰色市场环境下供应链协调的补偿策略研究［J］. 系统工程学报，2018，33（1）：103-115.
	Hong D J， Ma Y K， Ni D B. Compensation strategy for supply chain coordination in gray markets［J］. Journal of Systems Engineering， 2018，33（1）：103-115.
[14]	洪定军，付红，万娜娜，等. 灰色市场与制造商渠道结构选择［J］. 工业工程与管理，2021，26（1）：61-67.
	Hong D J， Fu H， Wan N N， et al. Gray markets and manufacturer’s channel structure selection［J］. Industrial Engineering and Management， 2021，26（1）：61-67.
[15]	do Nascimento A J Jr， Klotzle M C， Brandão L E T， et al. Prospect theory and narrow framing bias： Evidence from emerging markets［J］. The Quarterly Review of Economics and Finance， 2021， 80： 90-101.
[16]	Cao Y， Duan Y R. Joint production and pricing inventory system under stochastic reference price effect［J］. Computers & Industrial Engineering，2020，143： 106411.
[17]	Chen X， Hu P， Hu Z Y. Efficient algorithms for the dynamic pricing problem with reference price effect［J］. Management Science， 2016， 63（12）： 4389-4408.
[18]	Lu L H， Gou Q L， Tang W S， et al. Joint pricing and advertising strategy with reference price effect［J］. International Journal of Production Research， 2016， 54（17）： 5250-5270.
[19]	林志炳.基于制造商建议零售价的供应链定价策略［J］.中国管理科学， 2016， 24（11）： 153-161．
	Lin Z B. Pricing strategy of supply chain based on manufacturer's suggested retail price［J］. Chinese Journal of Management Science， 2016， 24（11）：153-161.
[20]	Zhou J D. Reference dependence and market competition［J］. Journal of Economics &Management Strategy， 2011， 20（4）： 1073-1097.
[21]	冯颖，魏敏，何文豪，等.质量信息不对称下考虑参考价格效应的灰市供应链定价决策［J］.中国管理科学，2024，32（6）： 207-218.
	Feng Y， Wei M， He W H， et al. Price decision-making in a gray market supply chain considering reference price effect under quality information asymmetric［J］.Chinese Journal of Management Science， 2024，32（6）： 207-218.
[22]	Panda S， Modak N M， Cárdenas-Barrón L E. Coordinating a socially responsible closed-Loop supply chain with product recycling［J］. International Journal of Production Economics， 2017， 188： 11-21.

Optimal Gray Market Structure and Pricing Decisions Considering Reference Price effect

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