智能化背景下新能源汽车供应链合作模式

doi:10.6040/j.issn.1671-9352.0.2025.159

摘要/Abstract

摘要： 本文构建了包含智能系统供应商和新能源汽车制造商的二级供应链模型。针对制造商主导和供应商主导的合作模式,本文利用Stackelberg博弈方法得到了供应链成员的均衡决策和利润,进一步分析了新能源汽车供应链的合作模式选择问题。研究发现:(1)当销售收入分配比例和研发成本系数都超过一定阈值时,智能系统供应商主导模式下产品的智能化水平更高;(2)智能化研发成本系数和弹性系数对于均衡决策具有重要影响;(3)对于制造商和供应商而言,两种合作模式的选择受到销售收入分配比例的影响。在供应商模式下,通过设置合理的销售收入分配比例,可以使得制造商和供应商都获得更高的利润,即实现双赢结果。

关键词: 智能化, 新能源汽车, 供应链, 合作模式, 销售收入分配

Abstract: This paper constructs a two-tier supply chain model involving an intelligent system supplier and a new energy vehicle(NEV)manufacturer. Focusing on cooperation modes led by the manufacturer and the supplier, this study employs the Stackelberg game approach to derive the equilibrium strategies and profits of supply chain members, and further examines the selection of cooperation modes in the NEV supply chain. The findings reveal that:(1)When the sales revenue allocation ratio and the R& D cost coefficient exceed a certain threshold, the supplier-led mode results in a higher level of product intelligentization;(2)The R& D cost coefficient and elasticity coefficient exert a significant impact on equilibrium decisions;(3)For both the manufacturer and the supplier, the choice between cooperation modes is influenced by the sales revenue allocation ratio. Under the supplier-led mode, by setting a reasonable sales revenue allocation ratio, both the manufacturer and the supplier can achieve higher profits, thereby realizing a win-win outcome.

Key words: intelligentization, new energy vehicle, supply chain, cooperation mode, sales revenue allocation

中图分类号:

F272

朱梦萍,罗立娇,王启飞. 智能化背景下新能源汽车供应链合作模式[J]. 《山东大学学报(理学版)》, 2026, 61(8): 132-144.

ZHU Mengping, LUO Lijiao, WANG Qifei. Supply chain cooperation modes for new energy vehicles under the background of intelligentization[J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2026, 61(8): 132-144.

参考文献

[1] 骆轶琪. 汽车行业智能化下半场:整车与芯片等核心环节生态协同成关键[EB/OL]. 21世纪经济报道,(2024-05-31)[2025-04-01]. https://m.21jingji.com/article/20240531/herald/bf8b2be5c8b68b84f9acd7214d40601c.html. Luo Yiqi. In the second phase of intelligentization within the automotive industry: synergistic collaboration across core segments such as complete vehicles and chips has become crucial to the development of the ecosystem[EB/OL]. 21st Century Business Herald,(2024-05-31)[2025-04-01]. https://m.21jingji.com/article/20240531/herald/bf8b2be5c8b68b84f9acd-7214d40601c.html.
[2] Gu X Y, Ieromonachou P, Zhou L, et al. Developing pricing strategy to optimise total profits in an electric vehicle battery closed loop supply chain[J]. Journal of Cleaner Production, 2018, 203: 376-385.
[3] 李思凝,陈凯. 竞争环境下新能源汽车嵌入技术服务的定价策略[J]. 系统管理学报, 2020, 29(3): 561-572. Li Sining, Chen Kai. Pricing strategy of new energy vehicle embedded technical service providers under competitive environment[J]. Journal of Systems & Management, 2020, 29(3): 561-572.
[4] Yu Y, Zhou D, Zha D, et al. Joint optimization of charging facility investment and pricing in automobile retail supply chain and coordination[J]. Computers & Industrial Engineering, 2021, 157: 107321.
[5] 易余胤,陈健. 不同供应链模式下“以旧换新燃油”和“以旧换新能源”定价策略[J]. 管理工程学报, 2023, 37(3): 80-91. Yi Yuyin, Chen Jian. Pricing strategies for "trade-in for new fuel vehicles" and "trade-in for new energy vehicles" programs under different supply chain models[J]. Journal of Industrial Engineering and Engineering Management, 2023, 37(3): 80-91.
[6] 王田,邓世名. 以电动汽车供应链为依托的充电站建设模式研究[J]. 中国管理科学, 2018, 26(10): 152-163. Wang Tian, Deng Shiming. Optimal building policies of charging stations with automobile supply chain analysis[J]. Chinese Journal of Management Science, 2018, 26(10): 152-163.
[7] 刘杰,王煜鑫,张景宣. 换电模式下考虑政府补贴和权力结构的电动汽车供应链减排决策研究[J]. 工业工程与管理, 2024, 29(6): 141-152. Liu Jie, Wang Yuxin, Zhang Jingxuan. Research on emission reduction decision of electric vehicle supply chain considering government subsidy and power structure under battery swapping mode[J]. Industrial Engineering and Management, 2024, 29(6): 141-152.
[8] 卢志平,姚逸飞,陆成裕. 差异供应链结构下新能源电动汽车换电模式定价策略[J]. 系统工程, 2022, 40(2): 27-37. Lu Zhiping, Yao Yifei, Lu Chengyu. Pricing strategy of new energy electric vehicle battery swapping mode under differential supply chain structure[J]. Systems Engineering, 2022, 40(2): 27-37.
[9] 杜建国,王文轩. 不同权力结构下新能源汽车换电供应链定价决策研究[J]. 软科学, 2024, 38(2): 124-133. Du Jianguo, Wang Wenxuan. Pricing decision of NEV battery swapping supply chain under different power structures[J]. Soft Science, 2024, 38(2): 124-133.
[10] 邱泽国,郑艺,徐耀群. 新能源汽车动力电池闭环供应链回收补贴策略: 基于演化博弈的分析[J]. 商业研究, 2020(8): 28-36. Qiu Zeguo, Zheng Yi, Xu Yaoqun. Closed-loop supply chain recycling subsidy strategy of new energy vehicle power battery: an analysis based on evolutionary games[J]. Commercial Research, 2020(8): 28-36.
[11] 谢家平,李璟,杨非凡, 等. 新能源汽车闭环供应链的多级契约决策优化[J]. 管理工程学报, 2020, 34(2): 180-193. Xie Jiaping, Li Jing, Yang Feifan, et al. Decision-making and coordination optimized for multi-stage closed-loop supply chain of new energy vehicle[J]. Journal of Industrial Engineering and Engineering Management, 2020, 34(2): 180-193.
[12] 马亮,刘玉洁,朱浩. 闭环供应链视角下新能源汽车电池双渠道回收契约设计[J]. 科技管理研究, 2021, 41(20): 184-193. Ma Liang, Liu Yujie, Zhu Hao. Design of dual-channel recycling contract for new energy vehicle batteries from the perspective of closed-loop supply chain[J]. Science and Technology Management Research, 2021, 41(20): 184-193.
[13] 丁军飞,浦徐进,曹雨馨,等. EPR制度下新能源汽车闭环供应链的回收成本分担机制研究[J]. 中国管理科学, 2024, 32(12): 257-268. Ding Junfei, Pu Xujin, Cao Yuxin, et al. Cost-sharing mechanism for closed-loop supply chain of new energy vehicles under EPR[J]. Chinese Journal of Management Science, 2024, 32(12): 257-268.
[14] Gu X Y, Zhou L, Huang H F, et al. Electric vehicle battery secondary use under government subsidy: a closed-loop supply chain perspective[J]. International Journal of Production Economics, 2021, 234: 108035.
[15] 周兴建,黎继子,李菲,等. 基于Blockchain的新能源汽车动力电池回收供应链模式[J]. 计算机集成制造系统, 2023, 29(4): 1386-1398. Zhou Xingjian, Li Jizi, Li Fei, et al. Recycling supply chain mode of new energy vehicle power battery based on Blockchain technology[J]. Computer Integrated Manufacturing Systems, 2023, 29(4): 1386-1398.
[16] 罗春林. 基于政府补贴的新能源汽车供应链策略研究[J]. 管理评论, 2014, 26(12): 198-205. Luo Chunlin. Supply chain analysis for electric vehicle under government's subsidy[J]. Management Review, 2014, 26(12): 198-205.
[17] 申成然,李林芝. 新能源背景下考虑政府补贴的汽车供应链决策研究[J]. 数学的实践与认识, 2019, 49(8): 79-88. Shen Chengran, Li Linzhi. Strategy research of government subsidy to the automotive supply chain under the background of new energy[J]. Mathematics in Practice and Theory, 2019, 49(8): 79-88.
[18] 张鹤立,淳伟德,燕汝贞,等. 考虑差异化补贴的新能源汽车闭环供应链决策研究[J]. 工程管理科技前沿, 2023, 42(2): 67-74. Zhang Heli, Chun Weide, Yan Ruzhen, et al. Study of closed-loop supply chain decision-making of the new energy vehicles considering differentiated subsidies[J]. Frontiers of Science and Technology of Engineering Management, 2023, 42(2): 67-74.
[19] 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.
[20] 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.
[21] Zhang H L, Chun W D, Yuan X M, et al. The governance of irresponsible new energy vehicle members considering differentiated subsidies[J]. Sustainable Cities and Society, 2024, 104: 105289.
[22] Zhu X X, Chiong R, Wang M M, et al. Is carbon regulation better than cash subsidy? The case of new energy vehicles[J]. Transportation Research Part A: Policy and Practice, 2021, 146: 170-192.
[23] Zhou D Q, Yu Y, Wang Q W, et al. Effects of a generalized dual-credit system on green technology investments and pricing decisions in a supply chain[J]. Journal of Environmental Management, 2019, 247: 269-280.
[24] 孙慧芳,王阳. “双积分”政策下新能源汽车供应链横向竞合研发博弈[J]. 数学的实践与认识, 2020, 50(22): 67-77. Sun Huifang, Wang Yang. The horizontal competition and R & D game of new energy vehicles supply chain under the "double credits" policy[J]. Mathematics in Practice and Theory, 2020, 50(22): 67-77.
[25] 胡文婕,马成霖,赵骅,等. “双积分”政策下的汽车竞合供应链策略选择[J]. 系统工程学报, 2024, 39(1): 109-127. Hu Wenjie, Ma Chenglin, Zhao Hua, et al. The strategic choice of co-opetition automobile supply chain under "dual-credit" policy[J]. Journal of Systems Engineering, 2024, 39(1): 109-127.
[26] Pu J C, Chun W D, Yang H. Low carbon strategy and coordination for a two-echelon automotive supply chain considering dual credit policy[J]. Computers & Industrial Engineering, 2024, 192: 110229.
[27] Li J Z, Ku Y Y, Yu Y, et al. Optimizing production of new energy vehicles with across-chain cooperation under China's dual credit policy[J]. Energy, 2020, 194: 116832.
[28] Xu Z R, Li Y, Li F F. Electric vehicle supply chain under dual-credit and subsidy policies: technology innovation, infrastructure construction and coordination[J]. Energy Policy, 2024, 195: 114339.
[29] Yi Y X, Zhang M, Zhang A X, et al. Can "dual credit" replace "subsidies" successfully -based on analysis of vehicle supply chain decisions under the digital transformation of technology[J]. Energy Economics, 2024, 130: 107303.
[30] 于晓辉,叶兆兴,李敏. 补贴退坡-双积分政策下两级供应链生产决策优化分析[J]. 运筹与管理, 2021, 30(3): 42-49. Yu Xiaohui, Ye Zhaoxing, Li Min. Production decision optimizing analysis of two-level supply chain under subsidy back-slope and double integral policy[J]. Operations Research and Management Science, 2021, 30(3): 42-49.
[31] 唐金环,杨芳,徐家旺,等. 双积分制下考虑消费者偏好的二级汽车供应链生产与定价问题研究[J]. 工业工程与管理, 2021, 26(1): 121-129. Tang Jinhuan, Yang Fang, Xu Jiawang, et al. A production and pricing research on two-echelon automotive supply chains considering consumer preference under dual-credit regulation[J]. Industrial Engineering and Management, 2021, 26(1): 121-129.
[32] 刘丛,刘洁,邵路路,等. “双积分” 政策下新能源汽车制造商激励供应商创新的契约选择研究[J]. 管理学报, 2022, 19(6): 928-937. Liu Cong, Liu Jie, Shao Lulu, et al. Contract design to incentive supplier innovation under dual-credit policy[J]. Chinese Journal of Management, 2022, 19(6): 928-937.
[33] 卢超,王倩倩,陈强. “双积分” 政策下考虑价格、减排和续航的汽车供应链协调[J]. 系统工程理论与实践, 2021, 41(10): 2595-2608. Lu Chao, Wang Qianqian, Chen Qiang. Automobile supply chain coordination considering auto price, emission reduction and the mileage range in one charge under the "double points" policy[J]. Systems Engineering-Theory & Practice, 2021, 41(10): 2595-2608.
[34] 吉清凯,胡祥培,赵达. 有限产能下智能电子产品供应链的产量博弈模型[J]. 系统工程理论与实践, 2018, 38(10): 2578-2586. Ji Qingkai, Hu Xiangpei, Zhao Da. Quantity competition in intelligent electronics supply chains with limited capacity[J]. Systems Engineering-Theory & Practice, 2018, 38(10): 2578-2586.
[35] 张冲,朱祎,袁玥. 平台数据授权和技术投资下的智能供应链决策[J]. 计算机集成制造系统, 2025, 31(3): 1059-1069. Zhang Chong, Zhu Yi, Yuan Yue. Smart supply chain decision under platform digital empowerment and technology investment[J]. Computer Integrated Manufacturing Systems, 2025, 31(3): 1059-1069.
[36] 苏菊宁,杨泽君,王奕婷,等. 智联产品服务供应链研发运维多阶段联合优化与协调[J]. 中国管理科学, 2022, 30(9): 162-171. Su Juning, Yang Zejun, Wang Yiting, et al. The multi-stage joint optimization and coordination of R & D and maintenance in smart connected product service supply chain[J]. Chinese Journal of Management Science, 2022, 30(9): 162-171.
[37] 肖芳,袁开福,王盼盼,等. 不同权力结构下汽车供应链定价与智能水平决策[J]. 计算机集成制造系统, 2024, 30(9): 3341-3353. Xiao Fang, Yuan Kaifu, Wang Panpan, et al. Pricing and intelligence level strategies in automobile supply chain under different power structure[J]. Computer Integrated Manufacturing Systems, 2024, 30(9): 3341-3353.
[38] Ma J H, Ding X, Zhao L, et al. A time-based pricing game considering echelon utilization in the battery leasing market[J]. Studies in Nonlinear Dynamics & Econometrics, 2026, 30(1): 141-157.
[39] Zhu J H, Feng T W, Lu Y, et al. Optimal government policies for carbon-neutral power battery recycling in electric vehicle industry[J]. Computers & Industrial Engineering, 2024, 189: 109952.
[40] 东方财富网. 赛力斯: 2024年年度报告[EB/OL].(2025-04-01)[2025-04-20]. https://data.eastmoney.com/notices/detail/601127/AN202503311649710345.html. Eastmoney.com. SERES: 2024 Annual Report[EB/OL].(2025-04-01)[2025-04-20]. https://data.eastmoney.com/notices/detail/601127/AN202503311649710345.html. 附录命题1的证明根据逆向归纳法,首先求式(2)关于p的二阶导(ə²πM_m(p,I))/(əp²)=-2 β<0,则πM_m(p,I)是关于p的凹函数。由一阶条件(əπM_m)/(əp)=0,可得p=(α+(c+w)β+γI)/(2 β)。将p=(α+(c+w)β+γI)/(2 β)代入式(1)中,求出式(1)关于w的二阶导(d²πM_s(w))/(dw²)=-β<0,则πM_s(w)是关于w的凹函数,由一阶条件(dπM_s(w))/(dw)=0,可得w=(2α-2c β+k βI²+2γI)/(4 β)。将w=(2α-2c β+k βI²+2γI)/(4 β)代入p=(α+(c+w)β+γI)/(2 β)中,得到p=(6α+2c β+k βI²+6γI)/(8β)。将w=(2α-2c β+k βI²+2γI)/(4 β)和p=(α+(c+w)β+γI)/(2 β)代入式(2),得到πM_m(I)=([2α-2c β+2γI-k βI²] ²)/(64 β)。在实践中制造商的边际利润为正,需要保证p-w-c=(2α-2c β+2γΙ-k βΙ²)/(8β)>0,即2α-2c β+2γΙ-k βΙ²>0。因此,最大化πM_m(I)即等价于最大化2α-2c β+2γI-k βI²。定义f(I)=2α-2c β+2γI-k βI²,可得(df(I))/(dI)=2γ-2k βI且(d²f(I))/(dI²)=-2k β<0。可知f(I)为关于I的凹函数,根据上述一阶条件,可得I ^{M^*}=γ/(k β)。将I^{M^*}=γ/(k β)代入w=(2α-2c β+k βI²+2γI)/(4 β)和p=(6α+2c β+k βI²+6γI)/(8β)中,可得w^{M^*}=(2k β(α-c β)+3γ²)/(4k β²), p^{M^*}=1/8(2c+(6kα β+7γ²)/(k β²))。将I^{M^*}、w^{M^*}、 p^{M^*}代入式(1)、(2),可得π^{M^*}_s=([2k β(α-c β)+γ²] ²)/(32k² β³), π^{M^*}_m=([2k β(α-c β)+γ²] ²)/(64k² β³)。命题2的证明根据逆向归纳法,首先求式(4)关于p的二阶导(d²πS_m(p))/(dp²)=-2 β(1-σ)<0,可知π^S_m(p)是关于p的凹函数。由一阶条件(dπ^S_m(p))/(dp)=0,可得p=1/2((α+γI)/β+c/(1-σ))。将p=1/2((α+γI)/β+c/(1-σ))代入式(3)中,得到利润 πS_s(I)=([c β+α(-1+σ)+γΙ(-1+σ)] {k βΙ²-[α+c β+Ι(γ+k βΙ)] σ+(α+γΙ)σ²})/(4 β(-1+σ)²)。(A1) 式(A1)是关于I的三次函数,基于一阶条件(dπ^S_s(I))/(dI)=0,可得2个驻点I₁=(Z+β A)/(3k βγ(1-σ))或I₂=(Z-β A)/(3k βγ(1-σ))。对于这2个驻点来说,只有当二阶导数小于0,利润函数取得最大值;否则,利润函数取得最小值。式(3)关于I的二阶导(d²π^S_s(I))/(dI²)=1/2[(γ²σ)/β-k(α+3γI)+(ck β)/(1-σ)] ,将I₁、I₂分别代入以上表达式,可得I₁对应的二阶导数为 -((k²[c β+α(-1+σ)] ²-(2k γ²[c β-2α(-1+σ)] (-1+σ)σ)/β+(γ⁴(-1+σ)²σ²)/(β²))^1/2)/(2(1-σ))<0, 对应π^S_s(I)的最大值;I₂对应的二阶导数为 ((k²[c β+α(-1+σ)] ²-(2k γ²[c β-2α(-1+σ)] (-1+σ)σ)/β+(γ⁴(-1+σ)²σ²)/(β²))^1/2)/(2(1-σ))>0, 对应πS_s(I)的最小值。因此I^{S^*}=I₁=(Z+β A)/(3k βγ(1-σ))。将I^{S^*}=(Z+β A)/(3k βγ(1-σ))代入p=1/2((α+γI)/β+c/(1-σ)),可得 p^{S^*}=(γ²(1-σ)σ+2k β(α+2c β-ασ)+β A)/(6k β²(1-σ))=(Y+β A)/(6k β²(1-σ))。将I^{S^*}、 p^{S^*}代入式(3)和式(4),可得供应链各成员的利润分别为 π^{S^*}_s=(3σ(X+β A)(Y+β A))/(108k² β³(1-σ)²)-((X+β A)(Z+β A)²)/(108k² β³(1-σ)³γ²), πS^*_m=({A β+2k β[-c β+α(1-σ)] +γ²(1-σ)σ}²)/(36k² β³(1-σ))=((A β+X)²)/(36k² β³(1-σ))。注 A=(k²[α(1-σ)-c β] ²+(γ⁴(1-σ)²σ²)/(β²)+(2k γ²(1-σ)σ(2α+c β-2ασ))/β)^1/2, X=2k β[α(1-σ)-c β] +γ²(1-σ)σ,Y=γ²(1-σ)σ+2k β(α+2c β-ασ), Z=k β[α(1-σ)-c β] +γ²(1-σ)σ。定理1的证明 ΔI=I ^M*-I ^{S^*}=(A β+k β[c β-α(1-σ)] - γ²(3-σ)(1-σ))/(3k βγ(σ-1)),由于(ə(ΔI))/(əA)=1/(3k γ(σ-1))<0,所以ΔI关于A单调递减,关于A的临界值为:(~overA)₁=(γ²(3-σ)(1-σ)+k β(α-c β-ασ))/β。因此,当A>(~overA)₁=(γ²(3-σ)(1-σ)+k β(α-c β-ασ))/β时,I ^{M^*}S^*;反之I ^{M^*}≥I ^{S^*}。注意到,A>(~overA)₁可以等价于A²>(~overA)²₁, A²-(~overA)²₁=(3γ²(-1+σ){2k β[α(1-σ)²-c β] +γ²(1-σ)(3-2σ)})/(β²)。 (1)在供应商模式下,供应商有较大的渠道权力确保其销售收入分配不低于一定比例。因此,α(1-σ)²-c β<0是一个合理的设定。在此情形下,A²-(~overA)²₁关于k单调递增,且临界条件为(~overk)=(γ²(1-σ)(3-2σ))/(2 β[c β-α(1-σ)²] )。当k>(~overk)时,有A²-(~overA)²₁>0,此时 I ^{M^*}S^*;否则,I ^{M^*}≥I ^{S^*}。 (2)当α(1-σ)²-c β>0时,I^{M^*}>I ^{S^*}恒成立。综合以上两种情况且进一步化简,可以得到当σ>1-((c β)/α)^1/2且k>(γ²(1-σ)(3-2σ))/(2 β[c β-α(1-σ)²] )时,I^{M^*}S^*;否则,I^{M^*}≥I ^{S^*}。定理2的证明 Δp=p^{M^*}-p^{S^*}=(4A β-γ²(1-σ)(21-4σ)+2k β[5α(-1+σ)+c β(5+3σ)] )/(24k β²(-1+σ)),(ə(Δp))/(əA)=1/(6k β(σ-1))<0,因此Δp关于A单调递减,关于A的临界值为(~overA)₂=(γ²(1-σ)(21-4σ)-2k β[c β(5+3σ)-5α(1-σ)] )/(4 β)。因此,当A>(~overA)₂=(γ²(1-σ)(21-4σ)-2k β[c β(5+3σ)-5α(1-σ)] )/(4 β)时,p^{M^*}S^*;反之,p^{M^*}≥p^{S^*}。定理3的证明 ΔD=D^{M^*}-D^{S^*}=(4A β+γ²[(7-4σ)σ-3] -2k β[c β(1+3σ)-α(1-σ)] )/(24k β(-1+σ)),(ə(ΔD))/(əA)=1/(6k(σ-1))<0,因此ΔD关于A单调递减,关于A的临界值为(~overA)₃=(γ²(1-σ)(3-4σ)+2k β[c β(1+3σ)-α(1-σ)] )/(4 β)。当A>(~overA)₃=(γ²(1-σ)(3-4σ)+2k β[c β(1+3σ)-α(1-σ)] )/(4 β)时,D^{M^*}S^*;反之,D^{M^*}≥D^{S^*}。定理4的证明 Δπm=π^{M^*}_m-π^{S^*}_m=([2k β(α-c β)+γ²] ²)/(64k² β³)-((A β+X)²)/(36k² β³(1-σ)),(ə(Δπm))/(əA)=(X+A β)/(18k² β²(σ-1))<0,因此,Δπm关于A单调递减,关于A的临界值为(~overA)₄=(3[2k β(α-c β)+γ²] (1-σ)^1/2)/(4 β)- X/β。因此,当A>(~overA)₄=(3[2k β(α-c β)+γ²] (1-σ)^1/2)/(4 β)- X/β时,π^{M^*}_m<π^{S^*}_m;反之,π^{M^*}_m≥π^{S^*}_m。

多维度评价

Viewed

Full text

Abstract

Cited

Shared

Discussed