补贴-惩罚政策下废旧动力电池的回收决策研究

doi:10.16381/j.cnki.issn1003-207x.2020.2326

摘要/Abstract

摘要：

通过构建动力电池生产商（以下简称电池商）和新能源汽车制造商（以下简称汽车商）关于废旧动力电池回收决策的演化博弈模型，分别在政府不干预和实施补贴-惩罚政策两种情形下，分析了影响电池商和汽车商选择回收与否的因素以及二者均决定回收的条件，并运用系统动力学模型仿真。研究结果表明：（1）在政府不干预情形下，当电池商的回购价大于电池商和汽车商各自单位回收价和回收成本之和的最大值时，二者均回收废旧动力电池。（2）在政府实施补贴-惩罚政策情形下，电池商的回购价不受政府惩罚的影响。与不干预情形相比，政府单位补贴增大会使电池商的最低回购价降低。（3）政府实施补贴-惩罚政策时，当单位补贴大于阀值时，电池商和汽车商选择回收废旧动力电池策略。（4）政府实施补贴-惩罚政策能够明显缩短电池商和汽车商开展废旧动力电池回收的时间。此研究可以为政府促进电池生产企业和新能源汽车制造企业回收废旧动力电池提供参考。

关键词: 补贴-惩罚政策, 废旧动力电池回收, 演化博弈, 系统动力学

Abstract:

The total number of retired power batteries in my country is about 200000 tons in 2020， and by 2025， it will reach 780000 tons. If these waste power batteries are not effectively recycled， not only the recycling of metal resources such as lithium and cobalt will not be realized， but it will also increase environmental pollution. Therefore， how to use government power to urge related enterprises to take the responsibility of recycling waste power batteries is an urgent problem to be solved.Although the existing literature studies the recycling and treatment of waste power batteries， most of them stay at the policy level. It is the most common to encourage enterprises to participate in the recycling of waste power batteries through subsidy policies. Blindly providing subsidies incentives increases the fraudulent behavior of enterprises. The government’s punishment curbs the fraudulent behavior of enterprises. The government subsidy-punishment factor is taken into account， and the issue of recycling enterprises’ selection of waste power battery recycling strategies is explored under the government subsidy-punishment policy. The main body of the recycling decision we choose to study is the power battery supplier and the new energy vehicle manufacturer. At present， the main recycling entities in my country are power battery suppliers （such as Tianjin Lishen， Honeycomb Energy Technology）， new energy vehicle manufacturers （such as BYD， Geely， Changan）， and third-party recycling enterprises （such as GEM， etc.）. The recycling qualifications of third-party recycling enterprises are uneven. There are fewer formal third-party recycling enterprises， and more studies on third-party recycling. Therefore， the third-party recycling enterprises are not our research objects. In terms of research methods， most literature assumes that the main body of power battery recycling is completely rational. In fact， the power battery manufacturer and the new energy vehicle manufacturer cannot obtain timely information on the recycling market， nor can they accurately predict changes in the external environment. They can only make decisions based on existing information resources and under conditions of limited rationality. The method of evolutionary game is adopted to explore the selection of recycling strategies for waste power batteries when the main body of recycling is bounded rationality.An evolutionary game model is developed for the power battery manufacturer （hereinafter referred to as the battery supplier） and the new energy vehicle manufacturer （hereinafter referred to as the vehicle manufacturer）， and the factors that affect the recycling choices of battery and the condition for choosing recycling strategies when the government non-intervention and the government implementation of subsidy-punishment policies are analyzed. The correctness of the relevant conclusions is verified through the simulation of the SD model. The findings include the following：（i） If the repurchase price of the battery supplier is satisfied $m a x {C S + P S, C S + P M} < P < Δ$ when without government intervention， they choose the recycling strategy. （ii） When the government implements the subsidy-penalty policy， the repurchase price is not influenced by the government punishment. Compared with the non-intervention situation of the government， the minimum repurchase price decreases with the increase of government subsidies. （iii） When the government implements the subsidy-punishment policy， the battery supplier and the battery manufacturer choose recycling strategy if the government subsidies are greater than the threshold. （iv） The government’s subsidy-penalty policy significantly shortens the time it takes for these to carry out the business of recycling waste power batteries. This research provides some ideas for the government to promote the recycling of waste power batteries by the battery supplier and the vehicle manufacturer.Some management insights based on the research results are provided. The effect of the government's subsidy-punishment policy is affected by the cost recovery of the battery supplier and the vehicle manufacturer. Therefore， the government can increase investment in technology for the dismantling of waste power batteries and use information technology to reduce recycling costs. Not only can it save the government part of the subsidy costs and better play the role of the subsidy-punishment policy， it can also reduce the waste of metal resources and environmental pollution.Our research has certain limitations. The model we designed only considers the game between the battery supplier and the vehicle manufacturer on the recycling of waste power batteries. The tripartite game needs to be further studied if the third-party recycler participates in recycling. In addition， how consumers’ green behavior and environmental awareness affect the strategic choices of the main body of power battery recycling also need to be further explored.

Key words: subsidy-penalty policy, recycling of used power batteries, evolutionary game, system dynamics

中图分类号:

F224

王文宾,刘业,钟罗升,戚金钰,仝鹏. 补贴-惩罚政策下废旧动力电池的回收决策研究[J]. 中国管理科学, 2023, 31(11): 90-102.

Wen-bin WANG,Ye LIU,Luo-sheng ZHONG,Jin-yu QI,Peng TONG. Research on Recovery Decision of Waste Power Battery under Subsidy-Penalty Policy[J]. Chinese Journal of Management Science, 2023, 31(11): 90-102.

图/表 12

表1

符号及其含义说明"

符号	含义
$Q$	市场中待回收的废旧动力电池回收量
$P S 、 P M$	电池商和汽车商对市场中废旧动力电池的回收价
$P$	电池商的回购价
$C S 、 C M$	电池商和汽车商回收废旧电池的单位成本
$Δ$	电池商使用回收的废旧动力电池创造的收益
$τ 1 、 τ 2$	电池商和汽车商的回收能力
$S$	政府对废旧电池回收量给予单位补贴
$F 1 、 F 2$	政府收取电池商和汽车商的环境治理费用
$λ$	电池商和汽车商回收量的分担比例

表1

表2

电池商和汽车商博弈支付矩阵"

博弈双方

汽车商

回收(Y) 不回收(N)

电池商

回收(Y)

不回收(N)

(π S Y Y, π M Y Y)

(π S Y N, π M N Y)

(π S N Y, π M Y N)

(π S N N, π M N N)

表2

表3

电池商和汽车商是否回收废旧动力电池的期望利润"

		电池商	汽车商
期望利润	回收	$E X = Y π S Y Y + (1 - Y) π S Y N$	$E Y = X π M Y Y + (1 - X) π M Y N$
	不回收	$E 1 - X = Y π S N Y + (1 - Y) π S N N$	$E 1 - Y = X π M N Y + (1 - X) π M N N$
	整体期望	$E S = X E X + (1 - X) E 1 - X$	$E M = Y E Y + (1 - Y) E 1 - Y$

表3

图1

图2

表4

矩阵J在各均衡点的行列式和迹的表达式"

均衡点	$d e t (J)$ 和 $t r (J)$ 表达式
(0,0)	$d e t (J) = ((Δ - P S - C S + S) τ 1 Q + F 1) ((P - P M - C M + S) τ 2 Q + F 2)$ $t r (J) = ((Δ - P S - C S + S) τ 1 Q + F 1) + ((P - P M - C M + S) τ 2 Q + F 2)$
(0,1)	$d e t (J) = - (τ 2 Q (Δ - P) (λ - 1) - τ 1 Q (Δ - P S - C S + S) (λ - 1)) ((P - P M - C M + S) τ 2 Q + F 2)$ $t r (J) = (τ 2 Q (Δ - P) λ - 1 - τ 1 Q (Δ - P S - C S + S) (λ - 1)) - ((P - P M - C M + S) τ 2 Q + F 2)$
(1,0)	$d e t (J) = - ((Δ - P S - C S + S) τ 1 Q + F 1) (P - P M - C M + S) λ τ 2 Q$ $t r (J) = - ((Δ - P S - C S + S) τ 1 Q + F 1) + λ τ 2 Q (P - P M - C M + S)$
(1,1)	$d e t (J) = (τ 2 Q (Δ - P) (λ - 1) - (Δ - P S - C S + S) (λ - 1) τ 1 Q) (P - P M - C M + S) λ τ 2 Q$ $t r J = - (τ 2 Q (Δ - P) (λ - 1) - τ 1 Q (Δ - P S - C S + S) (λ - 1)) - (P - P M - C M + S) τ 2 λ Q$
$(X , Y )$	$d e t (J) = M N$ 、 $t r (J) = 0$

表4

表5

政府不干预下电池商和汽车商局部均衡点判断"

情形	条件	均衡点	$d e t (J)$	$t r (J)$	局部均衡点
情形1	$Δ - P S < C S$ $P - P M < C M$	(0,0)	+	-	ESS
		(0,1)	-	+、-	鞍点
		(1,0)	-	+、-	鞍点
		(1,1)	+	+	不稳定点
情形2	$P - P M > C M$ $(Δ - P) τ 2 > (Δ - P S - C S) τ 1$	(0,0)	+、-	+、-	鞍点或不稳定点
		(0,1)	+	-	ESS
		(1,0)	+、-	+、-	鞍点或不稳定点
		(1,1)	-	+、-	鞍点
情形3	$Δ - P S > C S$ $P - P M < C M$	(0,0)	-	+、-	鞍点
		(0,1)	+、-	+、-	鞍点或不稳定点
		(1,0)	+	-	ESS
		(1,1)	+、-	+、-	鞍点或不稳定点
情形4	$m a x {C S + P S, C S + P M} < P < Δ$	(0,0)	+	+	不稳定点
		(0,1)	-	+、-	鞍点
		(1,0)	-	+、-	鞍点
		(1,1)	+	-	ESS

表5

图3

表6

政府实施补贴-惩罚政策时电池商和汽车商局部均衡点判断"

条件		均衡点	$d e t (J)$	$t r (J)$	局部均衡点
情形a	$S < m i n {S 1, S 2, S 3}$	(0,0)	+	-	ESS
		(0,1)	-	+、-	鞍点
		(1,0)	-	+、-	鞍点
		(1,1)	+	+	不稳定点
情形b	$m i n {S 1, S 2} < S S < m a x {S 4, S 3}$	(0,0)	+、-	+、-	鞍点或不稳定点
		(0,1)	+	-	ESS
		(1,0)	+	-	ESS
		(1,1)	+、-	+、-	鞍点或不稳定点
情形c	$S > m a x {S 2, S 3, S 4}$	(0,0)	+	+	不稳定点
		(0,1)	-	+、-	鞍点
		(1,0)	-	+、-	鞍点
		(1,1)	+、	-	ESS

表6

图4

图5

表7

电池商和汽车商局部稳定性分析"

$S$	均衡点
$S$	(0,0)	(0,1)	(1,0)	(1,1)
50	ESS	鞍点	鞍点	不稳定点
70
100
150	鞍点		ESS
250	不稳定点	ESS	鞍点	鞍点
350
420
440		鞍点		ESS
460		鞍点		ESS

表7

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