JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE) ›› 2026, Vol. 61 ›› Issue (8): 52-63.doi: 10.6040/j.issn.1671-9352.0.2025.128

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Altruistic preference and government subsidy policies on the closed-loop supply chain of power batteries

XIAO Min1, GAO Dashun1, HE Xinhua1, XIE Fuji2   

  1. 1. School of Economics and Management, Shanghai Maritime University, Shanghai 201306, China;
    2. Antai College of Economics and Management, Shanghai Jiao Tong University, Shanghai 200030, China
  • Published:2026-08-12

Abstract: In order to analyze the impact of altruistic preference(AP)and government subsidy on the closed-loop supply chain(CLSC)of power batteries, this paper constructs a CLSC of power batteries composed of the battery manufacturer, retailer, and third-party recycler. In the context of the battery manufacturer exhibiting AP towards the third-party recycler, this paper utilizes game theory to establish three decision models: without subsidy policy, subsidy for battery manufacturer in eco-design, and subsidy for third-party recyclers in recycling cost. The research results show that:(1)AP of the battery manufacturer can increase the recycling rate and social welfare, and maintain the stability of the supply chain system, but at the cost of the manufacturers profits;(2)When the government implements a subsidy policy for the recycling cost of the third-party recycler, the recycling rate of used power batteries is the highest. However, when the battery manufacturer exhibits strong AP, the recycling cost subsidy policy may have adverse effects on social welfare;(3)In the model of the government providing subsidy for the battery manufacturer in eco-design, social welfare is significantly higher than in the other two models, but the recycling rate of used power batteries is the lowest.

Key words: power battery, closed-loop supply chain, altruistic preference, eco-design subsidy, recycling cost subsidy

[1] 中华人民共和国生态环境部. 《中国应对气候变化的政策与行动2023年度报告》[EB/OL].(2023-10-27)[2024-05-28]. https://www.mee.gov.cn/ywgz/ydqhbh/wsqtkz/202310/t20231027_1044178.shtml. Ministry of Ecology and Environment of the Peoples Republic of China. Chinas policies and actions to address climate change 2023 annual report[EB/OL].(2023-10-27)[2024-05-28]. https://www.mee.gov.cn/ywgz/ydqhbh/wsqtkz/202310/t20231027_1044178.shtml.
[2] 中华人民共和国中央人民政府. 《四部委关于印发汽车产品生产者责任延伸试点实施方案的通知》[EB/OL].(2021-05-26)[2024-05-28]. https://www.gov.cn/zhengce/zhengceku/2021-06/10/content_5616601.html. Central Peoples Government of the Peoples Republic of China. Circular of the four ministries on the issuance of the pilot implementation program for the extension of producer responsibility for automotive products [EB/OL].(2021-05-26)[2024-05-28]. https://www.gov.cn/zhengce/zhengceku/2021-06/10/content_5616601.html.
[3] 曹晓刚,曹博威,闻卉. 考虑公平关切的混合回收渠道闭环供应链决策研究[J]. 中国管理科学, 2026, 34(4): 243-255. Cao Xiaogang, Cao Bowei, Wen Hui. Closed-loop supply chain decision of hybrid recycling channels considering fairness concerns[J]. Chinese Journal of Management Science, 2026, 34(4): 243-255.
[4] Zhao X, Peng B H, Zheng C Y, et al. Closed-loop supply chain pricing strategy for electric vehicle batteries recycling in China[J]. Environment, Development and Sustainability, 2022, 24(6): 7725-7752.
[5] Loch C H, Wu Y Z. Social preferences and supply chain performance: an experimental study[J]. Management Science, 2008, 54(11): 1835-1849.
[6] 杨双鹏,马丽,王永明. 多重行为偏好下的供应链契约及协调研究[J]. 工业工程, 2022, 25(3): 58-65. Yang Shuangpeng, Ma Li, Wang Yongming. A research on supply chain contract coordination under multiple behavioral preferences[J]. Industrial Engineering Journal, 2022, 25(3): 58-65.
[7] 代应,林金钗,覃燕红,等. 利他偏好下低碳供应链批发价格契约协调机制[J]. 计算机工程与应用, 2017, 53(11): 252-259. Dai Ying, Lin Jinchai, Qin Yanhong, et al. Low-carbon supply chain coordination considering altruism under contract of wholesale price[J]. Computer Engineering and Applications, 2017, 53(11): 252-259.
[8] 林志炳. 基于利他属性的双渠道供应链研究[J]. 中国管理科学, 2014, 22(12): 126-134. Lin Zhibing. Analysis of dual channel supply chain based on altruism[J]. Chinese Journal of Management Science, 2014, 22(12): 126-134.
[9] 姜吉坤,李宇,王威昊. 利他行为对动态供应链服务和定价决策的影响[J]. 山东大学学报(理学版), 2022, 57(5): 97-110. Jiang Jikun, Li Yu, Wang Weihao. Influence of altruistic behaviors upon service and pricing decisions of dynamic supply chain[J]. Journal of Shandong University(Natural Science), 2022, 57(5): 97-110.
[10] 焦琰,汪传旭,王元巍,等. 建议零售价下利他偏好对双渠道供应链定价决策的影响[J]. 山东大学学报(理学版), 2021, 56(1): 103-110. Jiao Yan, Wang Chuanxu, Wang Yuanwei, et al. Pricing decision of dual-channel supply chain considering altruistic preferences under reference price effect[J]. Journal of Shandong University(Natural Science), 2021, 56(1): 103-110.
[11] 姚锋敏,谭琦,李涛. 信息不对称下考虑利他偏好的供应链绿色设计与定价决策[J]. 计算机集成制造系统, 2025, 31(3): 1070-1084. Yao Fengmin, Tan Qi, Li Tao. Green design and pricing decisions of supply chain considering altruistic preference under asymmetric information[J]. Computer Integrated Manufacturing Systems, 2025, 31(3): 1070-1084.
[12] Rong L Q, Xu M Z. Impact of altruistic preference and government subsidy on the multinational green supply chain under dynamic tariff[J]. Environment, Development and Sustainability, 2022, 24(2): 1928-1958.
[13] Yang R, Tang W S, Zhang J X. Technology improvement strategy for green products under competition: the role of government subsidy[J]. European Journal of Operational Research, 2021, 289(2): 553-568.
[14] 尚文芳,滕亮亮. 考虑政府补贴和销售努力的零售商主导型绿色供应链博弈策略[J]. 系统工程, 2020, 38(2): 40-50. Shang Wenfang, Teng Liangliang. Game strategy considering government subsidies and sales efforts in retailer-led green supply chain[J]. Systems Engineering, 2020, 38(2): 40-50.
[15] Joshi B V, Vipin B, Ramkumar J, et al. Impact of policy instruments on lead-acid battery recycling: a system dynamics approach[J]. Resources, Conservation and Recycling, 2021, 169: 105528.
[16] Liu H H, Li T Y, Leong G K. Choice of competitive strategy of formal and informal sectors in recycling WEEE with fund subsidies: service or price?[J]. Journal of Cleaner Production, 2022, 372: 133717.
[17] Wang Z, Huo J Z, Duan Y R. Impact of government subsidies on pricing strategies in reverse supply chains of waste electrical and electronic equipment[J]. Waste Management, 2019, 95: 440-449.
[18] Yu H, Chang X Y, Liu W J. Cost-based subsidy and performance-based subsidy in a manufacturing-recycling system considering product eco-design[J]. Journal of Cleaner Production, 2021, 327: 129391.
[19] 楼高翔,雷鹏,马海程,等. 不同回收补贴政策下新能源汽车动力电池闭环供应链运营决策研究[J]. 管理学报, 2023, 20(2): 267-277. Lou Gaoxiang, Lei Peng, Ma Haicheng, et al. Research on operation decision of closed-loop supply chain of new energy vehicle power battery under different recycling subsidy policies[J]. Chinese Journal of Management, 2023, 20(2): 267-277.
[20] 贾俊秀,赵学科. 政府补贴下新能源汽车供应链电池续航能力及回收策略[J]. 系统工程学报, 2022, 37(3): 330-343. Jia Junxiu, Zhao Xueke. Battery endurance and recycling strategies of a new energy vehicle supply chain under government subsidies[J]. Journal of Systems Engineering, 2022, 37(3): 330-343.
[21] Xiao S Q, Chang X Y, Chen M H. Altruistic preference and government subsidies in a manufacturing-recycling system with eco-design[J]. Journal of Cleaner Production, 2022, 359: 132095.
[22] Liu Z, Li K W, Li B Y, et al. Impact of product-design strategies on the operations of a closed-loop supply chain[J]. Transportation Research Part E: Logistics and Transportation Review, 2019, 124: 75-91.
[23] 龚本刚,高一凌,刘志,等. 政府基金政策下动力电池闭环供应链回收渠道选择[J]. 计算机集成制造系统, 2023, 29(9): 3123-3137. Gong Bengang, Gao Yiling, Liu Zhi, et al. Selection of recycling channels in power battery closed-loop supply chain under government fund policy[J]. Computer Integrated Manufacturing Systems, 2023, 29(9): 3123-3137.
[24] Zhang M, Wu W Q, Song Y. Study on the impact of government policies on power battery recycling under different recycling models[J]. Journal of Cleaner Production, 2023, 413: 137492.
[25] 王文宾,张梦,赵蕾,等. 第三方回收商公平关切下闭环供应链决策模型[J]. 系统工程学报, 2019, 34(3): 409-421. Wang Wenbin, Zhang Meng, Zhao Lei, et al. Decision-making model of closed-loop supply chain based on third-party collectors fairness concern[J]. Journal of Systems Engineering, 2019, 34(3): 409-421.
[26] Chen C K, Ulya M A. Analyses of the reward-penalty mechanism in green closed-loop supply chains with product remanufacturing[J]. International Journal of Production Economics, 2019, 210: 211-223. 附录: 无补贴情形下均衡解的证明。 首先求解零售商关于零售价格p和第三方回收商关于回收率τ的二阶偏导为(ə2Πr)/(əp2)=-2b<0,(ə2Πt)/(əτ2)=-h(a+ek-bp)2<0,即Πr、Πt分别是关于p、τ的凹函数,联立(əΠr)/(əp)=0和(əΠt)/(əτ)=0得到p和τ的反应函数p=(a+ek+bw)/(2b), τ=(2(rf-Ct+φe))/(h(a+ek-bw)),代入式(1),求得电池制造商的效用函数关于批发价格w和转移回收价格rfHessian矩阵Hm=[(ə2Um)/(əw2)(ə2Um)/(əwərf) (ə2Um)/(ərfəw)(ə2Um)/(ər2f)] =[-b 0 0(λ-2)/h] 。由于0<λ<1,所以可得(ə2Um)/(əw2)(ə2Um)/(ər2f)-(ə2Um)/(əwərf)(ə2Um)/(ərfəw)=(b(2-λ))/h>0,即Hessian矩阵负定。因此Um分别是关于w、rf的凹函数。联立(əUm)/(əw)=0和(əUm)/(ərf)=0得到w、rf的反应函数,再代入式(1),可以得到关于e的二阶偏导为(ə2Um)/(əe2)=(4bφ2+h(2-λ)(k2-4b μ))/(4bh(2-λ)),此时可得效用函数为凹函数的判定条件为4bφ2+h(2-λ)(k2-4b μ)<0,同时为保证回收率τ>0,应使得(a-bCm)[φ2+h μ(2-λ)] t)。最后计算(əUm)/(əe)=0, 求得动力电池的生态设计水平e,代入各反应函数可得无补贴情形下的均衡结果。 命题1的证明 (əwN*)/(əs)=(2h kφB9)/(B22)>0,(əpN*)/(əs)=(3h kφB9)/(B22)>0,(əeN*)/(əs)=(4bhφB9)/(B22)>0。 (əτN*)/(əs)=(h μA1B9)/(b(A1B7+ kφA2)2)>0,(ərN*f)/(əs)=(-h(hA3+4b φ2)B9)/(B22 )>0。 推论1的证明 (əΠ N*m)/(əλ)=(-h2λA3B29)/(B32 )<0,(əΠ N*r)/(əλ)=(-2h bB9(A1B7+ A2))/(B32 )>0,(əΠ N*t)/(əλ)=(h2A3B29)/(B32 )>0, (əΠ N*sc)/(əλ)=(h2A3B29(1-λ)-2h kφbB9(A1B7+ kφA2))/(B32 )>0。 命题6的证明 由wR*-wN*=(2h kφs(2-λ)B9)/(B2B5)>0, wM*-wR*=(4bhk2s(λ-2)(A1B8- kφA2))/(2bB5(B2-A3A4s))>0,可得到wM*>wR*>wN*。 由eR*-eN*=(4bh φs(2-λ)B9)/(B2B5)>0, eM*-eR*=(4bhks(λ-2)(A1B8- kφA2))/(B5(B2-A3A4s))>0,可得到eM*>eR*>eN*。 由pR*-pN*=(3h kφs(2-λ)B9)/(B2B5)>0, pM*-pR*=(24bhk2s(λ-2)(A1B8- kφA2))/(4b[2B5(B2-A3A4s)] )>0,可得到pM*>pR*>pN*。 由rR*f-rN*f=(4bh φ2s(λ-1)B9)/(B2B5)<0, rM*f-rRf=(-4bh kφs(λ-1)(A1B8- kφA2))/(B5(B2-A3A4s))<0,可得到rN*f>rR*f>rM*f。 由τR*N*=(bh μ s(2-λ)A1B9)/(b2(A1B7+ kφA2)(A1B8- kφA2))>0、 τN*M*=(b μ s(φA1-kA2)B6)/(b2(A1B7+ kφA2)(A1B8- kφA2))>0,可得到τR*N*M*。 参数的指代含义为A1=a-bCm, A2=Δ-Ct, A3=k2-4b μ, A4=h(2-λ), A5=k2-4b μ+4b μ s, A6=Ct-λCt+Δ, A7=3a+bCm, B1=A4(A3Cm-2 μ A1)-2 kφA2, B2=4b φ2+A3A4, B3=A4(CmA3-3 μ A1)-3 kφA2, B4=hkφ(1-λ)A1+hA3A6, B5=4b φ2+A4A5, B6=4b φA2+kA1A4, B7=A4 μ-φ2, B82+A4 μ(1+s), B9= kφA1-A3A2, B10=sCmk2A4
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