《山东大学学报(理学版)》 ›› 2026, Vol. 61 ›› Issue (8): 52-63.doi: 10.6040/j.issn.1671-9352.0.2025.128
• • 上一篇
肖敏1,高大顺1,何新华1,谢富纪2
XIAO Min1, GAO Dashun1, HE Xinhua1, XIE Fuji2
摘要: 为了分析利他偏好行为和政府补贴政策对动力电池闭环供应链的影响,通过构建由电池制造商、零售商、第三方回收商组成的动力电池闭环供应链,在电池制造商对第三方回收商具有利他偏好行为的背景下,运用博弈论分别建立了无补贴政策、对电池制造商生态设计补贴、对第三方回收商回收成本补贴三种决策模型。研究结果表明:(1)电池制造商的利他偏好行为可以提高回收率和社会福利,促进供应链系统的稳定,但会以损失自身利润为代价;(2)政府对第三方回收商实行回收成本补贴政策时,废旧动力电池的回收率最高。然而,当电池制造商具有较强的利他偏好时,回收成本补贴政策会对社会福利产生不利的影响;(3)在政府对电池制造商进行生态设计补贴的情形下,社会福利显著高于另外两种情形,但是此时的废旧动力电池的回收率最低。
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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rf的Hessian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)] |
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