碳配额交易政策下考虑消费者偏好和成员行为的供应链微分博弈研究

doi:10.16381/j.cnki.issn1003-207x.2021.2262

摘要/Abstract

摘要：

随着消费者绿色偏好的不断提高，其在购买产品时会更加关注企业的环境绩效。作为企业环境绩效的重要表征，绿色商誉是随时间变化的无形资产。给定碳配额及其交易价格，本文构建了需求依赖于绿色商誉的微分博弈模型，从实际碳排放的短期和长期效应出发，求解并分析了消费者绿色偏好对三种决策模式策略和收益的影响，并对关键参数进行敏感性分析，最后对零售商远视和短视行为的策略和收益进行了比较和分析。通过理论分析和数值算例发现：碳配额交易价格和消费者绿色偏好系数与制造商广告策略负相关，与零售商的定价策略正相关；当消费者绿色偏好系数为零时，零售商的行为选择不会对广告和定价策略产生影响；集中决策模式下绿色商誉和利润最高，零售商远视的绿色商誉小于零售商短视情形；制造商更倾向于短视零售商，因为制造商可以挤压其利润空间，巩固领导地位和增加利润份额。

关键词: 碳配额交易, 微分博弈, 消费者绿色偏好, 绿色商誉, 短视行为

Abstract:

As environmental conditions deteriorate and climate change accelerates， consumers’ green preference continue to increase in order to reduce their carbon footprint. They will pay more attention to the firm’s environmental performance when purchasing products. Consumers who has green preference are willing to buy environmentally friendly products even if they cost a bit more. Meantime， several legislations， such as emission standard， carbon tax， carbon subsidy， and cap-and-trade system have been issued to reduce the emissions of carbon dioxide and other greenhouse gases by the regulators to deal with pollution reduction problems. The pollutant emissions are accumulated with the increase of production， which is not welcome by the environment and has a negative impact on firm’s reputation. Given the manufacturer’s actual emission of production， a reference level is introduced for emissions， which represents the number of emissions permits allocated to the firm by the regulator， and the market price of the carbon quota. Then the impact on the manufacturer’s profit of carbon quota is calculated with respect to actual emissions.As an important characteristic of firm’s environmental performance， green goodwill is an intangible asset that changes over time. In the dynamic equation of green goodwill， we use a parameter to scale the manufacturer’s environmental performance， i.e.， the gap between the actual emission and emission standard $σ (e ˉ - e)$ ， which is interpreted as the consumers’ green preference. When the actual emission is smaller than the standard， i.e.， $e ˉ - e > 0$ ， the environmental performance will have a positive impact on the green goodwill and demand. On the contrary， the impact is negative. The manufacturer’s advertising strategy also has a positive impact on the green goodwill. When the impact of environmental performance is negative， the positive effects of advertising strategy can offset the negative effects.From the short-term and long-term effects of actual carbon emissions， a differential game model is established that demands rely on green goodwill， it is found the advertising and pricing strategies of manufacturer and retailer in different decision-making models， respectively. The impact of key parameters on the strategies and profits is analyzed. Furthermore， the impact of retailer’s myopic behavior on the equilibrium strategies and outcomes is assessed. The retailer is myopic when she ignores the effect of today’s decision on future outcomes. In this setting， the strategies and profits are found and compared when retailer is myopic or far-sight. From the theoretical analysis and numerical simulations， it is found that the carbon quota price and consumers’ green preference coefficient are negatively related to the manufacturer’s advertising strategy and positively to the retailer’s pricing strategy. When the consumers’ green preference coefficient is zero， the retailer’s myopic behavior will have no influence on the advertising and pricing strategies. The environmental performance also has no impact on the decision of consumers. Green goodwill and profits are highest in the centralized decision-making model， and the manufacturer’s green goodwill in myopic scenario is higher than a far-sight scenario. Manufacturer prefers a myopic retailer because it can squeeze the retailer’s profit margins， consolidate the leadership and increase the share of profits. The results of the paper can provide implications for firms and policymakers.

Key words: cap-and-trade, differential game, consumers’ green preference, green goodwill, myopic

中图分类号:

F224

姚凡军,肖汉,高野,高红伟. 碳配额交易政策下考虑消费者偏好和成员行为的供应链微分博弈研究[J]. 中国管理科学, 2024, 32(1): 231-241.

Fanjun Yao,Han Xiao,Ye Gao,Hongwei Gao. A Differential Game Study of Supply Chain Considering Consumers' Green preference and Member's Behavior under Cap-and-trade Policy[J]. Chinese Journal of Management Science, 2024, 32(1): 231-241.

图/表 11

表1

分散决策模式策略关于各关键参数的比较静态分析"

参数	$γ$	$μ$	$k$	$τ$	$θ$	$σ$
$A N$	$↗$	$↘$	$↘$	$↘$	$↗$	$↘$
$w N$	$↗$	$↗$	—	$↗$	—	$↗$
$p N$	$↗$	$↗$	—	$↗$	—	$↗$

表1

表2

零售商短视分散决策模式策略关于各关键参数的比较静态分析"

参数	$γ$	$μ$	$k$	$τ$	$θ$	$σ$
$A O$	$↗$	$↘$	$↘$	$↘$	$↗$	$↘$
$w O$	$↗$	$↗$	—	$↗$	—	$↗$
$p O$	$↗$	$↗$	—	$↗$	—	$↗$

表2

表3

集中决策模式策略关于各关键参数的比较静态分析"

	$γ$	$μ$	$k$	$τ$	$θ$	$σ$
$A C$	$↗$	$↘$	$↘$	$↘$	$↗$	$↘$
$p C$	$↗$	$↗$	—	$↗$	—	$↗$

表3

图1

图2

图3

图4

图5

表4

消费者绿色偏好系数σ敏感性分析"

参数	$σ = 0.2$	$σ = 0.4$	$σ = 0.6$	$σ = 0.8$	$σ = 1$	参数	$σ = 0.2$	$σ = 0.4$	$σ = 0.6$	$σ = 0.8$	$σ = 1$
$w N$	4.453	4.542	4.609	4.661	4.704	$w O$	4.603	4.814	4.982	5.120	5.237
$A N$	5.238	4.397	3.816	3.386	3.053	$A O$	5.614	4.918	4.397	3.989	3.660
$p N$	6.305	6.438	6.538	6.617	6.681	$p O$	6.249	6.354	6.438	6.507	6.566
$G ∞ N$	6.117	5.733	5.715	5.853	6.066	$G ∞ O$	6.412	6.026	5.941	5.997	6.126
$π M N$	36.814	38.014	39.353	40.652	41.863	$π M O$	47.219	48.138	49.442	50.863	52.291
$π R N$	24.197	21.756	20.638	20.127	19.927	$π R O$	19.300	16.904	15.114	13.712	12.580
$π S C N$	61.011	59.770	59.991	60.779	61.790	$π S C O$	66.519	65.042	64.556	64.575	64.871
$D N$	2.772	2.380	2.210	2.132	2.098	$D O$	3.008	2.645	2.466	2.371	2.320
$π R O / π R N$	0.798	0.777	0.732	0.681	0.631	$A O / A N$	1.072	1.118	1.152	1.178	1.199
$π M O / π M N$	1.283	1.266	1.256	1.251	1.249	$p O / p N$	0.991	0.987	0.985	0.983	0.983
$w O / w N$	1.034	1.060	1.081	1.098	1.113	$D O / D N$	1.085	1.111	1.116	1.112	1.106

表4

表5

碳配额交易价格τ敏感性分析"

参数	$τ = 0.2$	$τ = 0.4$	$τ = 0.6$	$τ = 0.8$	$τ = 1$	参数	$τ = 0.2$	$τ = 0.4$	$τ = 0.6$	$τ = 0.8$	$τ = 1$
$w N$	4.401	4.489	4.578	4.666	4.754	$w O$	4.759	4.831	4.902	4.975	5.047
$A N$	4.465	4.272	4.083	3.896	3.712	$A O$	5.095	4.865	4.640	4.418	4.201
$p N$	6.427	6.459	6.491	6.524	6.557	$p O$	6.327	6.363	6.399	6.435	6.471
$G ∞ N$	5.877	5.786	5.697	5.608	5.520	$G ∞ O$	6.170	6.064	5.959	5.855	5.752
$π M N$	35.886	37.264	38.683	40.143	41.643	$π M O$	47.819	48.244	48.764	49.367	50.079
$π R N$	23.918	22.476	21.092	19.763	18.488	$π R O$	17.513	16.725	15.950	15.188	14.440
$π S C N$	59.804	59.740	59.775	59.906	60.131	$π S C O$	65.332	64.969	64.714	64.555	64.519
$D N$	2.458	2.367	2.278	2.191	2.105	$D O$	2.757	2.648	2.541	2.436	2.334
$π R O / π R N$	0.732	0.744	0.756	0.769	0.781	$A O / A N$	1.141	1.139	1.136	1.134	1.132
$π M O / π M N$	1.333	1.295	1.261	1.230	1.203	$p O / p N$	0.984	0.985	0.986	0.986	0.987
$w O / w N$	1.081	1.076	1.071	1.066	1.062	$D O / D N$	1.122	1.119	1.115	1.112	1.109

表5

表6

碳配额eˉ敏感性分析"

参数	$e ˉ = 1$	$e ˉ = 2$	$e ˉ = 3$	$e ˉ = 4$	$e ˉ = 5$	参数	$e ˉ = 1$	$e ˉ = 2$	$e ˉ = 3$	$e ˉ = 4$	$e ˉ = 5$
$w N$	4.578	4.578	4.578	4.578	4.578	$w O$	4.902	4.902	4.902	4.902	4.902
$A N$	4.083	4.083	4.083	4.083	4.083	$A O$	4.640	4.640	4.640	4.640	4.640
$p N$	6.491	6.491	6.491	6.491	6.491	$p O$	6.399	6.399	6.399	6.399	6.399
$G ∞ N$	3.878	4.787	5.697	6.606	7.515	$G ∞ O$	4.183	5.071	5.959	6.846	7.734
$π M N$	22.476	30.580	38.683	46.786	54.889	$π M O$	31.164	39.964	48.764	57.564	66.364
$π R N$	15.988	18.540	21.092	23.643	26.195	$π R O$	15.950	15.950	15.950	15.950	15.950
$π S C N$	38.464	49.12	59.775	70.429	81.084	$π S C O$	47.114	55.914	64.714	73.514	82.314
$D N$	1.551	1.915	2.278	2.642	3.006	$D O$	1.784	2.162	2.541	2.919	3.298
$π R O / π R N$	0.998	0.860	0.756	0.675	0.609	$A O / A N$	1.136	1.136	1.136	1.136	1.136
$π M O / π M N$	1.387	1.307	1.261	1.230	1.209	$p O / p N$	0.986	0.986	0.986	0.986	0.986
$w O / w N$	1.071	1.071	1.071	1.071	1.071	$D O / D N$	1.150	1.129	1.115	1.105	1.097

表6

参考文献 30

1	乔晗，杨列勋，邓小铁. 碳排放信息披露情况对碳排放博弈的影响［J］.系统工程理论与实践， 2013， 33（12）： 3103-3111.
	Qiao H， Yang L X， Deng X T. Impacts of superiority about carbon emission information on carbon tariff game［J］.Systems Engineering-Theory & Practice， 2013， 33（12）： 3103-3111.
2	Benjaafar S， Li Y， Daskin M. Carbon footprint and the management of supply chains： insights from simple models［J］.IEEE Transactions on Automation Science and Engineering， 2012， 10（1）： 99-116.
3	Du S F， Ma F， Fu Z J， et al. Game-theoretic analysis for an emission-dependent supply chain in a ‘cap-and-trade’ system［J］.Annals of Operations Research， 2015， 228（1）： 135-149.
4	Xu X P， Zhang W， He P， et al. Production and pricing problems in make-to-order supply chain with cap-and-trade regulation［J］. Omega， 2017， 66： 248-257.
5	Toptal A， Özlü H， Konur D. Joint decisions on inventory replenishment and emission reduction investment under different emission regulations［J］.International Journal of Production Research， 2014，52（1）： 243-269.
6	Ghosh S K， Seikh M R， Chakrabortty M. Analyzing a stochastic dual-channel supply chain under consumers’ low carbon preferences and cap-and-trade regulation［J］. Computers & Industrial Engineering， 2020， 149： 106765.
7	Yang L， Hu Y J， Huang L J. Collecting mode selection in a remanufacturing supply chain under cap-and-trade regulation［J］.European Journal of Operational Research， 2020， 287（2）： 480-496.
8	Kuiti M R， Ghosh D， Basu P， et al. Do cap-and-trade policies drive environmental and social goals in supply chains： strategic decisions， collaboration， and contract choices［J］. International Journal of Production Economics， 2020， 223： 107537.
9	张令荣，杨子凡，程春琪.碳配额交易政策下闭环供应链的减排策略选择［J］.管理工程学报，2022，36（1）：172-180.
	Zhang L R， Yang Z F， Cheng C Q. Selection of emission reduction strategy for closed-loop supply chain under carbon cap-and-trade policy［J］. Journal of Industrial Engineering and Engineering Management， 2022，36（1）：172-180.
10	张桂涛，王广钦，赵欣语，等.碳配额交易体系下闭环供应链网络的生产与碳交易策略研究［J］.中国管理科学，2021，29（1）：97-108.
	Zhang G T， Wang G Q， Zhao X Y， et al. Production and carbon trading strategy of closed-loop supply chain network under cap-and-trade system［J］. Chinese Journal of Management Science， 2021，29（1）：97-108.
11	骆瑞玲，范体军，夏海洋.碳排放交易政策下供应链碳减排技术投资的博弈分析［J］.中国管理科学，2014，22（11）：44-53.
	Luo R L， Fan T J， Xia H Y. The game analysis of carbon reduction technology investment on supply chain under carbon cap-and-trade rules［J］. Chinese Journal of Management Science， 2014，22（11）：44-53.
12	崔春岳，张令荣，杨子凡，等.碳配额交易政策下基于收益共享契约的两阶段供应链协调［J］.中国管理科学，2021，29（7）：214-226.
	Cui C Y， Zhang L R， Yang Z F， et al. Two-stage supply chain coordination based on revenue sharing contract under carbon cap-and-trade［J］. Chinese Journal of Management Science， 2021，29（7）：214-226.
13	邹清明，胡李庆，邹霆钧.碳限额与碳交易机制下考虑公平关切的供应链定价与协调研究［J］.中国管理科学，2022，30（10）：142-154.
	Zou Q M， Hu L Q， Zou T J. Pricing and coordination of a supply chain with fairness concerns under carbon cap-and-trade mechanism［J］. Chinese Journal of Management Science， 2022，30（10）：142-154.
14	魏守道.碳交易政策下供应链减排研发的微分博弈研究［J］.管理学报，2018，15（5）：782-790.
	Wei S D. Differential game analysis on supply chain’s strategy of carbon emission reduction R&D under carbon trading policy［J］. Chinese Journal of Management， 2018，15（5）：782-790.
15	徐春秋，赵道致，原白云，等.上下游联合减排与低碳宣传的微分博弈模型［J］.管理科学学报，2016，19（2）：53-65.
	Xu C Q， Zhao D Z， Yuan B Y， et al. Differential game model on joint carbon emission reduction and low-carbon promotion in supply chains［J］. Journal of Management Sciences in China， 2016，19（2）：53-65.
16	Wang Y L， Xu X， Zhu Q H. Carbon emission reduction decisions of supply chain members under cap-and-trade regulations： a differential game analysis［J］. Computers & Industrial Engineering， 2021，162： 107711.
17	Yao F J， Gao H W， Jiang H， et al. Study on low-carbon supply chain coordination considering reference emission reduction effect［J］. Asia-Pacific Journal of Operational Research， 2021，38（5）： 2040022.
18	Xia L J， Bai Y W， Ghose S， et al. Differential game analysis of carbon emissions reduction and promotion in a sustainable supply chain considering social preferences［J］. Annals of Operations Research， 2022，310： 257-292.
19	武丹，杨玉香.考虑消费者低碳偏好的供应链减排微分博弈模型研究［J］.中国管理科学，2021，29（4）：126-137.
	Wu D， Yang Y X. Study on the differential game model for supply chain with consumers’ low carbon preference［J］. Chinese Journal of Management Science， 2021，29（4）：126-137.
20	Kalish S. Monopolist pricing with dynamic demand and production cost［J］. Marketing Science， 1983， 2（2）： 135-159.
21	Fibich G， Gavious A， Lowengart O. Explicit solutions of optimization models and differential games with nonsmooth （asymmetric） reference-price effects［J］. Operations Research， 2003， 51（5）： 721-734.
22	Popescu I， Wu Y. Dynamic pricing strategies with reference effects［J］. Operations Research， 2007， 55（3）： 413-429.
23	Martín-Herrán G， Taboubi S， Zaccour G. Dual role of price and myopia in a marketing channel［J］. European Journal of Operational Research， 2012， 219（2）： 284-295.
24	Chintagunta P K， Rao V R. Pricing strategies in a dynamic duopoly： a differential game model［J］. Management Science， 1996， 42（11）： 1501-1514.
25	Benchekroun H， Martín-Herrán G， Taboubi S. Could myopic pricing be a strategic choice in marketing channels？ A game theoretic analysis［J］. Journal of Economic Dynamics and Control， 2009， 33（9）： 1699-1718.
26	Ouardighi F E. Supply quality management with optimal wholesale price and revenue sharing contracts： a two-stage game approach［J］. International Journal of Production Economic， 2014， 156（51）： 260-268.
27	Andre F J， Sokri A， Zaccour G. Public Disclosure Programs vs. traditional approaches for environmental regulation： green goodwill and the policies of the firm［J］. European Journal of Operational Research， 2011， 212（1）： 199-212.
28	Yao F， Parilina E， Zaccour G， et al. Accounting for consumers’ environmental concern in supply chain contracts［J］. European Journal of Operational Research， 2022， 301（3）： 987-1006.
29	Huang J， Leng M G， Liang L P. Recent developments in dynamic advertising research［J］. European Journal of Operational Research， 2012， 220（3）： 591-609.
30	Jørgensen S， Zaccour G. A survey of game-theoretic models of cooperative advertising［J］. European journal of operational Research， 2014， 237（1）： 1-14.

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