Optimal Decisions of Electric Vehicle Closed-Loop Supply Chain under Government Subsidy and Varied Consumers’ Green Awareness

Abstract

The emerging operating mode of new automobile forces in the context of China brings up new problems for the development of the EV CLSC, which are the market position shift inside the loop and government policy and consumer awareness of changes outside it. Aiming at promoting the development of the EV CLSC, this study integrates the influence of internal and external factors, analyzes their joint impact on the performance of the EV CLSC, and explores the optimal CLSC structure. Specifically, this study develops five game theory models considering different CLSC structures and consumers’ green awareness under government subsidy and varied channel leaderships. Combining theoretical analysis with numerical simulation, the study reveals the performance of the EV CLSC and indicates the optimal CLSC decisions for different players. The result suggests that an EV manufacturer should develop an EV CLSC by itself considering the elimination of double marginalization. When a third-party player is incorporated, the EV manufacturer should undertake the collection effort by itself to optimize the benefit for both the EV manufacturer and the third-party player, especially considering the increasing green awareness of consumers. And a lift of each player’s channel power would always be a wise choice for each other. For the government which has the goals of promoting both the EV industry and the end-of-life treatment of obsolete EVs, a series of trade-offs including the CLSC structure and channel leadership should be considered prudently. This study contributes to the comprehensive understanding of the optimal decisions of the EV CLSC, and will benefit the development of the EV CLSC.

1. Introduction

Under the goal of Carbon Neutralization, the volume of electric vehicles (EVs) grows rapidly [1,2,3]. It is reported that the number of EVs had reached 8.104 million in China by the end of June, 2022, accounting for 80.93% of the total number of new energy vehicles [4]. Because of battery packs, and the various metals and plastics of EVs, as the peak of obsolete EVs approaches, the concerns for the environment, resources, and human health issues have spread widely [5,6]. Under such a context, it becomes more important to accelerate the establishment of an EV closed-loop supply chain (CLSC) in order to achieve the proper treatment of obsolete EVs in China.

The rise of EVs has given birth to a large number of emerging enterprises, including Tesla, NIO, XPENG and so on. It is concluded that the aforementioned new automobile forces occupy an important share in the EV market [2,4]. Different from the traditional automobile manufacturers, the new automobile forces prefer selling EVs mainly online instead of through the traditional 4S auto shop in a forward supply chain (FSC). Such a new operating mode will lead to a shift in players’ market position in the EV CLSC on the one hand, and on the other, the emphasis on low-carbon development and the increase in consumers’ green awareness are affecting and reshaping the development of the EV CLSC in China [7,8,9,10,11]. The above new changes call for specific concerns for the EV CLSC.

There is abundant research on CLSC development from various aspects, including channel power structures, competition, different collectors, collection effort implementation, different collection cost structures and so forth [12,13,14,15,16]. Focusing on EVs, the influence of different government policies, like recycling subsidies, research and development subsidies, and product subsidies, and deposit-refund policies, are discussed widely [17,18,19,20,21]. The impact of channel structure is also a focal point [22]. In summary, the above studies failed to consider the power shift in the EV industry, and rarely discussed the synchronous influence of both inner and outer factors of the supply chain. Theoretically, this study integrates the influence of internal and external factors, analyzes their joint impacts on the performance of the EV CLSC, and explores the optimal CLSC structure. The results of this study can benefit the development of the EV CLSC under complex future conditions.

The rest of this study is organized as follows. Section 2 summarizes a comprehensive literature review. Section 3 develops the models and provides the equilibrium results. Thereafter the influence of government subsidy and consumers’ green awareness, as well as the comparison of all the models, are analyzed in Section 4. Finally, we present our conclusion in Section 5.

2. Literature Review

Three streams of the literature closely related to this study are reviewed. They are: CLSC management, consumers’ green awareness and impact of government subsidies.

2.1. CLSC Management

A growing literature in CLSC management focuses on CLSC performance under different contexts and varied conditions. Focusing on different channel structures, the basic model is developed to explore the performance of different players in a centralized-decision model and a decentralized-decision model [23,24]. Savaskan et al. first modeled and compared different collectors (the manufacturer or the retailer or the third party, respectively) in a CLSC [25]. Xiong and Yan analyzed the channel structure’s impact on the sales of remanufactured goods and concluded that selling remanufactured goods through a manufacturer-owned e-channel dominates remanufactured sales through a third party [26]. Zhao et al. studied the optimal pricing strategies for EV batteries in three different recycling channels [22]. Saha et al. proposed a closed-loop SC in which the manufacturer has three alternative ways of collecting obsolete products [27]. Giri et al. proposed a CLSC that uses the retailer and e-channels simultaneously to sell products [28]. Taleizadeh et al. studied the performance of a CLSC with different channel structures [29]. Considering the collection effort aimed at promoting consumers’ participation in collection activity, Guo et al. analyzed the influence of different collection-effort implementers and proposed coordination strategies in one supply chain [15]. Jian et al. modeled the collection effort implemented by two independent entities and derived the optimal decisions and members’ profits in various collaborative models [30]. Asghari et al. examined a single-stage green CLSC in which the green manufacturer, retailer, and collector try to reform the environmental effects of their operations, products, and services across the value chain according to their environmental responsibilities [31]. Focusing on the influence of different channel leaderships, Choi et al. investigated the performance of a CLSC which consists of a retailer, a collector, and a manufacturer [32]. Gao et al. analyzed the influence of different channel power on a CLSC with price- and effort-dependent demand [12]. Jin et al. explored how various channel power structures affect the pricing decisions and coordination in competitive online and offline recycling channels [33]. However, it is noted that the above studies failed to analyze the performance of a CLSC with different channel structures, different collection implementers and varied channel leaderships simultaneously.

2.2. Consumers’ Green Awareness

Consumers play an important role in the supply chain considering their demand decisions. Boztepe concluded that environmental awareness, green product features, green promotion activities and green price affect green purchasing behaviors of consumers in a positive way [34]. Ayodele et al. empirically investigated the effect of green awareness on consumers’ purchase intentions for environmentally friendly electrical products [35]. Lu et al. explored the influence on the corporate image of enterprises of consumer responses to a company’s social responsibility programs [36]. Yenipazarli and Vakharia modeled a segmented consumer market with different preferences, where the market consists of green and brown products [37]. Heydari et al. provided an analytical approach to address channel coordination and pricing issues in a green supply chain under consumer environmental awareness [10]. Hosseini-Motlagh et al. analyzed the impact of marketing efforts on recycling decisions in a CLSC [38]. Pathak et al. evaluated optimal pricing and effort decisions for Closed-Loop Dual-Channel Supply Chain scenarios [39]. Tao et al. examined the optimal channel structure of a green supply chain consisting of one manufacturer and one retailer considering consumers’ green awareness [40]. Nielsen et al. considered a positive relation between green-technology investment and consumer demand, and analyzed supply-chain performance in a two-period green supply chain [41]. To the best knowledge of the authors, there has been limited study as yet trying to model the relation of the demand for new products with consumers’ green awareness, where the consumers’ green awareness is influenced by the collection effort. And no studies have analyzed the influence of consumers’ green awareness and different CLSC structures simultaneously in an EV CLSC so far.

2.3. Government Subsidy

Government policy plays an important role in industrial development and public services [42,43] (Zhang et al., 2023; Huang et al., 2021). Many studies have been conducted to reveal the influence of government subsidy on a CLSC [44,45,46]. Focusing on a vehicle CLSC, Gu et al. analyzed the subsidy mechanism of new energy vehicles and the recycling problem of a spent EV battery [17]. Wang et al. compared four kinds of subsidies for recycling and reuse of auto parts, where the subsidies included direct subsidy, a recycling subsidy, a research and development subsidy, and a product subsidy [18]. Li et al. applied system dynamics to evaluate the influence of several recycling-subsidy policies on recycling effect and economic benefits [47]. Allevi et al., 2018, focused on the impact of government policy on recycling decisions in a CLSC [48]. Based on a new-energy vehicle CLSC, Zhao et al. studied the impact of different government subsidy objectives on enterprise profits and supply-chain competitiveness [22]. Liu and Wang studied the optimal decisions of the government and supply-chain members under different government subsidy policies (no subsidy, subsidy for the new energy vehicle manufacturer and subsidy for consumers) and their impact on profits and social welfare [9]. Zhu and Li investigated the pricing mechanism of dual-channel power-battery recycling models under different government subsidies [19]. Several studies also focused on the influence of deposit–refund policy or punishment on an EV CLSC [8,20,21]. However, the joint impacts of government subsidy and consumers’ green awareness on the EV CLSC, and the optimal CLSC structures and optimal channel leaderships for different players under the joint impacts, still remain to be explored.

Above all, three main contributions are provided by this study. Firstly, unlike studies which consider a single factor, this study considers multiple factors in a CLSC simultaneously, including government subsidy, consumers’ green awareness, different EV CLSC channel structures, varied collection-effort implementers and different channel leaderships (

Table 1. Summary of the difference between the existing studies and this study.

Source of the Research	Main Topics
	EV	CLSC	Gover. Subsidy	Consumers’ Green Awareness	Collection Effort	Varied Collection Effort Implementers	Different Channel Structures	Different Channel Leaderships
[25] Savaskan et al., 2004		✓			✓	✓	✓
[32] Choi et al., 2013		✓					✓	✓
[12] Gao et al., 2016		✓			✓			✓
[27] Saha et al., 2016		✓					✓
[28] Giri et al., 2017		✓					✓	✓
[29] Taleizadeh and Sadeghi, 2018							✓	✓
[30] Jian et al., 2019					✓	✓
[48] Allevi et al., 2018		✓	✓
[45] Wan and Hong, 2019		✓	✓
[41] Nielsen et al., 2019			✓	✓				✓
[8] Li et al., 2020	✓	✓
[19] Zhu and Li, 2020	✓	✓	✓
[38] Hosseini-Motlagh et al., 2020		✓			✓
[21] Wang et al., 2021	✓	✓						✓
[9] Liu and Wang, 2021	✓	✓	✓				✓
[10] Heydari et al., 2021				✓
[40] Tao et al., 2022				✓			✓
[31] Asghari et al., 2022		✓		✓	✓
[39] Pathak et al., 2022		✓		✓	✓		✓	✓
This study	✓	✓	✓	✓	✓	✓	✓	✓

). Secondly, besides considering the direct feedback of consumers on their green awareness, this study also considers the diffusion of the influence of green awareness throughout the entire supply chain. Thirdly, instead of analyzing either from an internal or external level, this study jointly analyzes the influence of the operating mode inside and policy and consumer awareness outside the EV CLSC. Taking all of the above into account, five game-theoretic models are developed. The five models are different in EV CLSC channel structures, collection-effort implementers and channel leaderships. This study analyzes the joint impacts of the external and internal factors on the EV CLSC through theoretical analysis and numerical simulation, compares the outcomes of the above models, and concludes with the optimal EV CLSC structures.

3. Materials and Methods

This study considers three EV CLSC structures that varied in CLSC channel structures and collection-effort implementers. Accordingly, five game-theoretical models are established by incorporating different channel leaderships (Figure 1). In Model D, the EV manufacturer sells EVs in an FSC; meanwhile it conducts a collection effort and implements collection activity directly in the reverse supply chain (RSC). In Model O/ON and Model OS/OSN, the manufacturer is responsible for selling EVs while a third-party player is outsourced to implement collection activity. However, the collection effort aiming at promoting consumers’ participation in collection is conducted by the third-party player in Model O/ON while it is conducted by the manufacturer in Model OS/OSN. The difference between Model O (Model OS) and Model ON (Model OSN) is that the former CLSC is under an M-leader game where the EV manufacturer has a dominant position, while in the latter model, the CLSC is under a Nash game where the EV manufacturer and the third-party player have equal channel power. In all the models, the government subsidy paid to the EV manufacturer and the influence of consumers’ green awareness on the demand for new EVs are considered.

3.1. Model Description

In this study, the following hypothesis are always held. A single EV manufacturer and collector in the EV CLSC are considered. The EVs have the same lifespan and the collected EVs have the same residual value.

In the same way as the studies of [26,49], we assume a negative linear demand function of EVs with regard to selling price. It is concluded that environmental awareness and green promotion activities affect green purchasing behaviors of consumers in a positive way [34,35]. Therefore, a positive impact of consumers’ green awareness on demand is considered, wherein the impact is measured as a ratio of the collection effort conducted by the EV CLSC. In total, the demand is denoted as following Equation (1).

$$q_s=\alpha -\beta p+\delta \tau$$

(1)

where $\alpha$, $\beta$, $\delta$ > 0 and are all constants (

Table 2. Notations and definitions.

Parameter	Definition
$p$	Selling price of one new EV
$p_c$	Collection price of one obsolete EV
$p_t$	Transfer price of one obsolete EV paid by the manufacturer
$p_r$	Treatment revenue of one obsolete EV
$c_m$	Manufacture cost for one new EV
$q_s$	Demand for new EVs
$q_c$	Collection quantity of obsolete EVs
$\tau$	Collection effort extent
$\eta$	Scaling parameter
$\alpha$	Base market size
$\beta$	Price elasticity
$\delta$	Consumers’ green awareness
$K$	Minimum collection quantity
$M$	Influence of collection price on collection quantity
$N$	Influence of collection effort on collection quantity
$s$	Government subsidy
${\pi }_m$, ${\pi }_t$	Overall profit of EV manufacturer or third-party player
$p^D$,${p_c}^D$,${\tau }^D$,${q_s}^D$,${q_c}^D$	Equilibrium results in Model D
$p^O$,${{ p}_c}^O$,${p_c}^O$,${\tau }^O$,${q_s}^O$,${q_c}^O$	Equilibrium results in Model O
$p^{OS}$,${{ p}_c}^{OS}$,${p_c}^{OS}$,${\tau }^{OS}$,${q_s}^{OS}$,${q_c}^{OS}$	Equilibrium results in Model OS
$p^{ON}$,${{ p}_c}^{ON}$,${p_c}^{ON}$,${\tau }^{ON}$,${q_s}^{ON}$,${q_c}^{ON}$	Equilibrium results in Model ON
$p^{OSN}$, ${{ p}_c}^{OSN}$, ${p_c}^{OSN}$, ${\tau }^{OSN}$, ${q_s}^{OSN}$, ${q_c}^{OSN}$	Equilibrium results in Model OSN

).

Similar to the studies of [12,25], the collection quantity is positively influenced by the collection price and collection effort. The collection quantity in this study is formulated as Equation (2).

$$q_c=K+M{p}_c+N\tau$$

(2)

$K$ is presented to capture the minimum collection quantity without the influence of the collection price and collection effort.

The profit of the manufacturer consists of two parts in this study. One is from the sale of new EVs in an FSC while the other is the treatment of obsolete EVs in an RSC. In all the models, the manufacturer runs the FSC by itself. It sets the selling price of new EVs as $p$ with a manufacturing cost $c_m$. The profit of the manufacturer in the FSC is formulated as $(p-c_m)q_s$. In China, several incentive measures including subsidies have been launched to promote the EV CLSC [7,8,9]. This study considers a subsidy ($s$) issued according to the collected quantity of EVs.

In Model D, the manufacturer collects obsolete EVs and implements the collection effort by itself in a reverse supply chain. Therefore, the overall profit of the manufacturer in Model D is formulated in Equation (3):

$${\pi }_m=(p-c_m)q_s+(s+p_r-p_c)q_c-\frac{1}{2}\eta {\tau }^2$$

(3)

where the convex increasing investment-cost form of the collection effort is commonly applied [12,44,49].

In Model O/ON and Model OS/OSN, the manufacturer outsources collection activity to a third-party player by offering a transfer price $p_t$. The third-party player provides the collection price in order to gain obsolete EVs.

Since the third-party player implements the collection effort in Model O/ON, the overall profits of the two players in Model O/ON are denoted in Equations (4) and (5).

$${\pi }_m=(p-c_m)q_s+(s+p_r-p_t)q_c$$

(4)

$${\pi }_t=(p_t-p_c)q_c-\frac{1}{2}\eta {\tau }^2$$

(5)

Considering the manufacturer responsible for conducting the collection effort in Model OS/OSN, the overall profits are presented as below (Equations (6) and (7)):

$${\pi }_m=(p-c_m)q_s+({s+p}_r-p_t)q_c-\frac{1}{2}\eta {\tau }^2$$

(6)

$${\pi }_t=(p_t-p_c)q_c$$

(7)

3.2. Model Development

All the proofs are summarized in Supplementary Materials. Since all the defined parameters are non-negative numbers in this study, $4\beta \eta \left(2M\eta -N^2\right)-N^2{\delta }^2>0$, $2M\beta \eta -M{\delta }^2-2N^2\beta >0$ and $M\eta -N^2>0$ always hold.

• Model D

In Model D (Figure 2), the manufacturer decides the selling price ($p$), the collection price ($p_c$) and the collection effort ($\tau$) simultaneously in order to maximize its overall profit Equation (8).

$$\underset{p, p_c,\mathit{\tau }}{\max }{\pi }_m=(p-c_m)q_s+(s+p_r-p_c)q_c-\frac{1}{2}\eta {\tau }^2$$

(8)

Since $\frac{{\partial }^2{\pi }_m}{\partial p^2}=-2\beta <0$, $\frac{{\partial }^2{\pi }_m}{\partial {p_c}^2}=-2M<0$, $\frac{{\partial }^2{\pi }_m}{\partial {\tau }^2}=-\eta <0$, ${\pi }_m$ is concave in $p$, $p_c$ and $\tau$. There exists a specific set of $p$, $p_c$ and $\tau$ making ${\pi }_m$ the maximum.

Set $\frac{\partial {\pi }_m}{\partial p}=0$, $\frac{\partial {\pi }_m}{\partial p_c}=0$, $\frac{\partial {\pi }_m}{\partial \tau }=0$, the $p^D$, ${p_c}^D$, ${\tau }^D$, ${q_s}^D$, ${q_c}^D$ in the equilibrium state can be solved (

Table 3. Equilibrium results.

Model	Equilibrium Results
Model D	$\left\{\begin{array}{c}{p}^D=\frac{\alpha \left(2M\eta -N^2\right)+KN\delta +\left(2M\beta \eta -2M{\delta }^2-N^2\beta \right)c_m+MN\delta \left(s+p_r\right)}{2\left(2M\beta \eta -M{\delta }^2-N^2\beta \right)}\\ {p_c}^D=\frac{-N\alpha \delta -K\left(2\beta \eta -{\delta }^2\right)+N\beta \delta c_m+\left(2M\beta \eta -M{\delta }^2-2N^2\beta \right)\left(s+p_r\right)}{2\left(2M\beta \eta -M{\delta }^2-N^2\beta \right)}\\ {\tau }^D=\frac{M\alpha \delta +KN\beta -M\beta \delta c_m+MN\beta \left(s+p_r\right)}{2M\beta \eta -M{\delta }^2-N^2\beta }\\ {q_s}^D=\beta \frac{\alpha \left(2M\eta -N^2\right)+KN\delta -\left(2M\beta \eta -N^2\beta \right)c_m+MN\delta \left(s+p_r\right)}{2\left(2M\beta \eta -M{\delta }^2-N^2\beta \right)}\\ {q_c}^D=M\frac{N\alpha \delta +K\left(2\beta \eta -{\delta }^2\right)-N\beta \delta c_m+\left(2M\beta \eta -M{\delta }^2\right)\left(s+p_r\right)}{2\left(2M\beta \eta -M{\delta }^2-N^2\beta \right)}\end{array}\right.$
Model O	$\left\{\begin{array}{c}{p}^O=\frac{2\alpha \eta \left(2M\eta -N^2\right)+KN\delta \eta +\left(4M\beta {\eta }^2-2N^2\beta \eta -N^2{\delta }^2\right)c_m+MN\delta \eta \left(s+p_r\right)}{4\beta \eta \left(2M\eta -N^2\right)-N^2{\delta }^2}\\ {p_t}^O=\frac{N\alpha \delta \left(2M\eta -N^2\right)+K(N^2{\delta }^2+2N^2\beta \eta -4M\beta {\eta }^2)-N\beta \delta \left(2M\eta -N^2\right)c_m+2M\beta \eta \left(2M\eta -N^2\right)\left(s+p_r\right)}{M\left[4\beta \eta \left(2M\eta -N^2\right)-N^2{\delta }^2\right]}\\ {p_c}^O=\left(M\eta -N^2\right)\frac{N\alpha \delta \left(2M\eta -N^2\right)+K(N^2{\delta }^2+2N^2\beta \eta -4M\beta {\eta }^2)-N\beta \delta \left(2M\eta -N^2\right)c_m+2M\beta \eta \left(2M\eta -N^2\right)\left(s+p_r\right)}{M\left(2M\eta -N^2\right)\left[4\beta \eta \left(2M\eta -N^2\right)-N^2{\delta }^2\right]}-\frac{K\eta }{2M\eta -N^2}\\ {\tau }^O=N\frac{N\alpha \delta \left(2M\eta -N^2\right)+K(N^2{\delta }^2+2N^2\beta \eta -4M\beta {\eta }^2)-N\beta \delta \left(2M\eta -N^2\right)c_m+2M\beta \eta \left(2M\eta -N^2\right)\left(s+p_r\right)}{\left(2M\eta -N^2\right)\left[4\beta \eta \left(2M\eta -N^2\right)-N^2{\delta }^2\right]}+\frac{KN}{2M\eta -N^2}\\ {q_s}^O=\beta \frac{2\alpha \eta \left(2M\eta -N^2\right)+KN\delta \eta -\left(4M\beta {\eta }^2-2N^2\beta \eta \right)c_m+MN\delta \eta \left(s+p_r\right)}{4\beta \eta \left(2M\eta -N^2\right)-N^2{\delta }^2}\\ {q_c}^O=M\eta \frac{N\alpha \delta \left(2M\eta -N^2\right)+K(N^2{\delta }^2+2N^2\beta \eta -4M\beta {\eta }^2)-N\beta \delta \left(2M\eta -N^2\right)c_m+2M\beta \eta \left(2M\eta -N^2\right)\left(s+p_r\right)}{\left(2M\eta -N^2\right)\left[4\beta \eta \left(2M\eta -N^2\right)-N^2{\delta }^2\right]}+\frac{KM\eta }{2M\eta -N^2}\end{array}\right.$
Model OS	$\left\{\begin{array}{c}{p}^{OS}=\frac{\alpha \left(4M\eta -N^2\right)+KN\delta +\left(4M\beta \eta -4M{\delta }^2-N^2\beta \right)c_m+MN\delta \left(s+p_r\right)}{2(4M\beta \eta -2M{\delta }^2-N^2\beta )}\\ {p_t}^{OS}=\frac{-N\alpha \delta -K(2\beta \eta -{\delta }^2)+N\beta \delta c_m+(2M\beta \eta -M{\delta }^2-N^2\beta )\left(s+p_r\right)}{2(4M\beta \eta -2M{\delta }^2-N^2\beta )}\\ {p_c}^{OS}=\frac{-3N\alpha \delta -3K(2\beta \eta -{\delta }^2)+3N\beta \delta c_m+(2M\beta \eta -M{\delta }^2-2N^2\beta )\left(s+p_r\right)}{2(4M\beta \eta -2M{\delta }^2-N^2\beta )}\\ {\tau }^{OS}=\frac{2M\alpha \delta +KN\beta -2M\beta \delta c_m+MN\beta \left(s+p_r\right)}{4M\beta \eta -2M{\delta }^2-N^2\beta }\\ {q_s}^{OS}=\beta \frac{\alpha \left(4M\eta -N^2\right)+KN\delta -\left(4M\beta \eta -N^2\beta \right)c_m+MN\delta \left(s+p_r\right)}{2(4M\beta \eta -2M{\delta }^2-N^2\beta )}\\ {q_c}^{OS}=M\frac{2N\alpha \delta +2K(2\beta \eta -{\delta }^2)-2N\beta \delta c_m+N^2\beta \left(s+p_r\right)}{2(4M\beta \eta -2M{\delta }^2-N^2\beta )}\end{array}\right.$
Model ON	$\left\{\begin{array}{c}{p}^{ON}=\frac{\alpha \left(3M\eta -N^2\right)+KN\delta +\left(3M\eta -N^2\right)\beta c_m+MN\delta \left(s+p_r\right)}{2\beta (3M\eta -N^2)}\\ {p_t}^{ON}=\frac{\left(2M\eta -N^2\right)\left(s+p_r\right)-K\eta }{3M\eta -N^2}\\ {p_c}^{ON}=\frac{\left(M\eta -N^2\right)\left(s+p_r\right)-2K\eta }{3M\eta -N^2}\\ {\tau }^{ON}=\frac{MN\left(s+p_r\right)+KN}{3M\eta -N^2}\\ {q_s}^{ON}=\beta \frac{\alpha \left(3M\eta -N^2\right)+KN\delta -\left(3M\eta -N^2\right)\beta c_m+MN\delta \left(s+p_r\right)}{2\beta (3M\eta -N^2)}\\ {q_c}^{ON}=M\frac{M\eta \left(s+p_r\right)+K\eta }{3M\eta -N^2}\end{array}\right.$
Model OSN	$\left\{\begin{array}{c}{p}^{OSN}=\frac{N\alpha (3M\beta \eta -3M{\delta }^2-N^2\beta )+K\delta \left(3M\beta \eta +N^2\beta \right)+N\beta c_m(3M\beta \eta -N^2\beta )+M{N}^2\beta \delta \left(s+p_r\right)}{N\beta \left[6M\beta \eta -3M{\delta }^2-2N^2\beta \right]}\\ {p_t}^{OSN}=\frac{-N\alpha \delta -K(2\beta \eta -{\delta }^2)+N\beta \delta c_m+(4M\beta \eta -2N^2\beta -2M{\delta }^2)\left(s+p_r\right)}{6M\beta \eta -3M{\delta }^2-2N^2\beta }\\ {p_c}^{OSN}=\frac{-2N\alpha \delta -2K(2\beta \eta -{\delta }^2)+2N\beta \delta c_m+(2M\beta \eta -M{\delta }^2-2N^2\beta )\left(s+p_r\right)}{6M\beta \eta -3M{\delta }^2-2N^2\beta }\\ {\tau }^{OSN}=\frac{-3MN\alpha \delta +2K\left(3M\beta \eta +N^2\beta \right)+3MN\beta \delta c_m+2M{N}^2\beta \left(s+p_r\right)}{N\left[6M\beta \eta -3M{\delta }^2-2N^2\beta \right]}\\ {q_s}^{OSN}=\beta \frac{N\alpha (3M\beta \eta -3M{\delta }^2-N^2\beta )+K\delta \left(3M\beta \eta +N^2\beta \right)-N\beta c_m(3M\beta \eta -3M{\delta }^2-N^2\beta )+M{N}^2\beta \delta \left(s+p_r\right)}{N\beta \left[6M\beta \eta -3M{\delta }^2-2N^2\beta \right]}\\ {q_c}^{OSN}=M\frac{N\alpha \delta +2K(2\beta \eta -{\delta }^2)-N\beta \delta c_m+(2M\beta \eta -M{\delta }^2)\left(s+p_r\right)}{6M\beta \eta -3M{\delta }^2-2N^2\beta }\end{array}\right.$

).

• Model O under M-Leader (Model O)

In Model O (Figure 3), the manufacturer decides the selling price ($p$) and the transfer price ($p_t$) firstly, then the third-party player sets the collection price ($p_c$) and the collection effort ($\tau$) so as to maximize its overall profit Equation (9).

$$\left\{\begin{array}{c}\underset{p, p_t}{\max }{\pi }_m=(p-c_m)q_s+(s+p_r-p_t)q_c\\ s.t. \underset{p_c,\mathit{\tau }}{\max }{\pi }_t=(p_t-p_c)q_c-\frac{1}{2}\eta {\tau }^2\end{array}\right.$$

(9)

The equilibrium results can be solved by backward induction. First, we solve $p_c$ and $\tau$ by letting $\frac{\partial {\pi }_t}{\partial p_c}=0$ and $\frac{\partial {\pi }_t}{\partial \tau }=0$. Thereafter, the $p$ and $p_t$ can be derived by substituting $p_c$ and $\tau$ in ${\pi }_m$ and setting $\frac{\partial {\pi }_m}{\partial p}=0$ and $\frac{\partial {\pi }_m}{\partial p_t}=0$.

Therefore, the equilibrium results in Model O can be calculated (Table 3).

• Model OS under M-Leader (Model OS)

In Model OS (Figure 4), the manufacturer decides the selling price ($p$), the transfer price ($p_t$) and the collection effort ($\tau$) firstly, then the third-party player sets the collection price ($p_c$) to collect obsolete EVs Equation (10).

$$\left\{\begin{array}{c}\underset{p, p_t,\mathit{\tau }}{\max }{\pi }_m=(p-c_m)q_s+(s{+p}_r-p_t)q_c-\frac{1}{2}\eta {\tau }^2\\ s.t. \underset{p_c}{\max }{\pi }_t=(p_t-p_c)q_c\end{array}\right.$$

(10)

Likewise, first, we solve $p_c$ by letting $\frac{\partial {\pi }_t}{\partial p_c}=0$. Thereafter, the $\tau$, $p$ and $p_t$ can be derived by substituting $p_c$ in ${\pi }_m$ and setting $\frac{\partial {\pi }_m}{\partial \tau }=0$, $\frac{\partial {\pi }_m}{\partial p}=0$ and $\frac{\partial {\pi }_m}{\partial p_t}=0$.

And the equilibrium state in Model OS is summarized as in Table 3.

• Model O under Nash Game (Model ON)

In Model ON (Figure 5), the manufacturer decides the selling price ($p$) and the transfer price ($p_t$), and the third-party player sets the collection price ($p_c$) and the collection effort ($\tau$) simultaneously Equation (11).

$$\left\{\begin{array}{c}\underset{p, p_t}{\max }{\pi }_m=(p-c_m)q_s+(s+p_r-p_t)q_c\\ \underset{p_c,\mathit{\tau }}{\max }{\pi }_t=(p_t-p_c)q_c-\frac{1}{2}\eta {\tau }^2\end{array}\right.$$

(11)

The equilibrium results can be solved by letting $\frac{\partial {\pi }_t}{\partial p_c}=0$, $\frac{\partial {\pi }_t}{\partial \tau }=0$, $\frac{\partial {\pi }_m}{\partial p}=0$ and $\frac{\partial {\pi }_m}{\partial p_t}=0$.

Therefore, the equilibrium results in Model ON can be calculated (Table 3).

• Model OS under Nash Game (Model OSN)

In Model OSN (Figure 6), the manufacturer decides the selling price ($p$), the transfer price ($p_t$) and the collection effort ($\tau$), and the third-party player sets the collection price ($p_c$) to collect obsolete EVs simultaneously (Equation (12)).

$$\left\{\begin{array}{c}\underset{p, p_t,\mathit{\tau }}{\max }{\pi }_m=(p-c_m)q_s+(s{+p}_r-p_t)q_c-\frac{1}{2}\eta {\tau }^2\\ \underset{p_c}{\max }{\pi }_t=(p_t-p_c)q_c\end{array}\right.$$

(12)

Likewise, first, we solve the results by letting $\frac{\partial {\pi }_t}{\partial p_c}=0$, $\frac{\partial {\pi }_m}{\partial \tau }=0$, $\frac{\partial {\pi }_m}{\partial p}=0$ and $\frac{\partial {\pi }_m}{\partial p_t}=0$.

And the equilibrium state in Model OSN is summarized in Table 3.

3.3. Equilibrium Results

Based on the backward induction, all the equilibrium results are calculated and summarized in Table 3.

4. Results and Discussion

4.1. Theoretical Analysis

Proposition 1. 

The government subsidy would promote collection effort regardless of the CLSC structure and channel leadership. ($\frac{\partial {\tau }^D}{\partial s}>0$, $\frac{\partial {\tau }^O}{\partial s}>0$, $\frac{\partial {\tau }^{OS}}{\partial s}>0$, $\frac{\partial {\tau }^{ON}}{\partial s}>0$, $\frac{\partial {\tau }^{OSN}}{\partial s}>0$).

The results are identical with the study of Wang et al., who modelled a competitive dual-channel reverse supply chain [46]. In an EV CLSC, as the participation increases, the EV manufacturer can receive more subsidy from the government; consequently it has more enthusiasm for implementing the collection effort directly in Model D, Model OS and Model OSN. Even though the EV manufacturer would not implement the collection effort directly, it prefers offering a higher transfer price to the third-party player in order to promote the collection effort in Model O and Model ON. The increased transfer price along with a higher government subsidy ($\frac{\partial {p_t}^O}{\partial s}>0$, $\frac{\partial {p_t}^{ON}}{\partial s}>0$) demonstrates the deduction.

Proposition 2. 

The government subsidy has a positive influence on both the demand for new EVs and collection quantity of obsolete EVs in all the five models. ($\frac{\partial {q_s}^D}{\partial s}>0$,$\frac{\partial {q_s}^O}{\partial s}>0$,$\frac{\partial {q_s}^{OS}}{\partial s}>0$,$\frac{\partial {q_s}^{ON}}{\partial s}>0$,$\frac{\partial {q_s}^{OSN}}{\partial s}>0$;$\frac{\partial {q_c}^D}{\partial s}>0$,$\frac{\partial {q_c}^O}{\partial s}>0$,$\frac{\partial {q_c}^{OS}}{\partial s}>0$,$\frac{\partial {q_c}^{ON}}{\partial s}>0$,$\frac{\partial {q_c}^{OSN}}{\partial s}>0$).

Proposition 2 indicates the “chain effect” in the EV CLSC induced by government subsidy. It is not surprising that a government subsidy targeted on the collection quantity can promote the collection quantity of obsolete EVs directly. However, it is worthwhile to find that government subsidy can enlarge the demand for new EVs indirectly, reflecting the “chain effect” of the government subsidy. The chain effect is noted in many studies. For instance, Allevi et al. concluded that carbon emission regulation launched for one player can affect the performance of all the players in one CLSC [48]. Since the government subsidy is paid according to the collection quantity of obsolete EVs, it will motivate the EV manufacturer to invest in the collection effort directly or indirectly in order to enlarge the collection quantity in the five models. Combining with the collection effort and consumers’ green awareness, consequently the demand for new EVs can be promoted along with the “chain effect”. Proposition 2 shows that government subsidy has a positive influence on the expansion of the EV CLSC.

4.2. Numerical Simulation

The numerical simulation is undertaken to study the following three questions in this section: (1) the influence of the government subsidy on the overall profits of the EV manufacturer and the third-party player; (2) the impact of consumers’ green awareness on the EV CLSC; (3) comparison of the five models under the joint impacts.

The data are mainly derived from the studies of [8,9] and set as follows: $\alpha =\mathrm{100,000}$, $c_m=$106,466, $p_r=$34,848, $\beta =0.5$. Considering the constraints, we set $K=1000$, $M=0.8$, $N=0.5$, $\eta =10$, and let $\delta =0.2$, $s=5000$ in the base scenario. With the help of random function, a series of sensitivity studies are conducted and the following conclusions also hold; the details can be checked in the Supplementary Materials.

4.2.1. Influence of Government Subsidy on Overall Profits

Proposition 3. 

The increase in government subsidy can improve the overall profit of the EV manufacturer and the third-party player in all the models (Figure 7).

Proposition 3 concludes with the fundamental influence of the government subsidy and explains the reasons for its effectiveness. In China, several incentive measures including subsidies have been launched to promote the EV CLSC [7,8,9]. The government subsidy is an extrinsic incentive paid to the EV manufacturer directly according to the treatment quantity of obsolete EVs. It should be noted that high payback is the fundamental object for the players in the EV CLSC. For the profit-seekers in the EV CLSC, only if they engage in the EV CLSC deeply and broadly can they receive the high payback.

4.2.2. Influence of Consumers’ Green Awareness

Proposition 4. 

The increased green awareness of consumers will always benefit the whole EV CLSC in all the models but that in Model ON (Figure 8).

Consumers’ green awareness represents consumers’ positive response to the environmentally-friendly activity of the EV CLSC. It is defined as the positive relation between sales of new EVs and extent of the collection effort by the EV CLSC in this study. Currently, it is noted that consumers pay much attention to green consumption due to awareness of the deterioration of the environment and government initiatives [10,11]. Given the extent of the collection effort, the increase in consumers’ green awareness will apparently boost the sales of new EVs and the overall profit of the EV manufacturer directly in all the models. Due to the relation between consumers’ green awareness and the collection effort, the EV manufacturer prefers to devote itself to the collection effort so as to maintain the above benefits. As a result, the collection quantity and overall profit of the third-party player will be enlarged as well in Model D, Model OS and Model OSN, where the EV manufacturer undertakes the collection effort directly by itself. Even though the EV manufacturer does not participate in the collection effort, it can stimulate the third-party player by adjusting the transfer price taking its dominant position into account in Model O. Meanwhile, the dominant position of the EV manufacturer is non-existent in Model ON. Consequently, the collection quantity and overall profit of the third-party player can be promoted in Model O while being unaffected in Model ON as the consumers’ green awareness changes.

4.3. Comparison of the Models

Due to the elimination of double marginalization, the outcomes of Model D are higher than other models. Hereafter we mainly analyze the outcomes among the other four models.

4.3.1. Comparison of Different CLSC Structures

Firstly, Propositions 5 and 6 are derived by comparing the following pairs: Model O vs. Model OS; Model ON vs. Model OSN.

Proposition 5. 

(1)

The demand for new EVs grows much faster in Model OS than in Model O (in Model OSN than in Model ON) when the government subsidy and consumers′ green awareness increase (Figure 9a: Blue vs. Grey; Red vs. Green).

(2)

The collection quantity of obsolete EVs is always higher in Model OSN than in Model ON (Figure 9b: Blue vs. Grey).

(3)

The collection quantity of obsolete EVs is almost the same in Model O and Model OS. Combining with the sensitivity study, it is derived that whatever other parameters vary, Model O outperforms Model OS when consumers′ green awareness is relatively low (Figure 9b: Green vs. Red; Supplementary Materials).

Proposition 6. 

In terms of the overall profit of the EV manufacturer and the third-party player, Model OS performs better than Model O (Model OSN performs better than Model ON) when consumers’ green awareness increases. And the superiority is more obvious for the overall profit of the EV manufacturer when the government subsidy grows (Figure 9c,d): Blue vs. Grey; Red vs. Green).

Propositions 5 and 6 indicates the optimal decisions for different players. The results are partially identical with the study of Savaskan et al., who conclude that the agent closer to the customer is the most effective undertaker of product-collection activity for the manufacturer [25]. Under M-leader, for the EV manufacturer and the third-party player with the goal of improving their overall profits, the optimal CLSC structure is the same, that is, the EV manufacturer conducts the collection effort directly regardless of channel leadership (Proposition 6). The results are consistent with the results of Guo et al. and Wang et al., wherein they considered the collection effort implemented in a two-echelon reverse supply chain and concluded that the agent who is closer to the consumers is ineffective in promoting consumer participation in the collection effort [15,48]. Proposition 5(1) also indicates that the demand for new EVs can be enlarged when the collection effort is implemented by EV manufacturers.

Considering the inconsistency of the collection quantity and overall profit, there exists a trade-off for the government which has the responsibility to promote the EV industry and the end-of-life treatment of obsolete EVs as well. Taking all the above into account, corollary 1 can be derived.

Corollary 1. 

When a third-party player participates in an EV CLSC, the government can promote the development of the EV CLSC through publicizing the proper CLSC structure.

(1)

In order to improve economic benefits, the EV manufacturer should always be encouraged to implement the collection effort (Proposition 6);

(2)

In order to promote the end-of-life treatment of obsolete EVs, the optimal CLSC structure to be generalized depends on the channel leadership. Under the Nash game where the third-party player and EV manufacturer have equal channel power, the government should promote the EV CLSC where the EV manufacturer conducts the collection effort directly (Proposition 5(2)). Under the M-leader game where the EV Manufacturer has dominant power, the government should encourage the third-party player to undertake the collection effort directly when consumers’ green awareness is relatively low (Proposition 5(3)).

4.3.2. Comparison of Different Channel Leaderships

Secondly, Proposition 7 and 8 are derived by comparing the following pairs: Model O vs. Model ON; Model OS vs. Model OSN.

Proposition 7. 

The demand and collection quantity are higher under the Nash game than under the M-leader game regardless of the EV CLSC structure (Figure 9a,b): Grey vs. Green, Blue vs. Red).

Proposition 8. 

(1)

The overall profit of the EV manufacturer is higher under the M-leader game than under the Nash game regardless of the EV CLSC structure (Figure 9c: Grey vs. Green, Blue vs. Red).

(2)

The overall profit of the third-party player is higher under the Nash game than under the M-leader game regardless of the EV CLSC structure (Figure 9d: Grey vs. Green, Blue vs. Red).

It is indicated that different channel leaderships lead to different channel performances [10,50]. Propositions 7 and 8 present the optimal channel leadership for the development of the EV CLSC. For the EV manufacturers who always dominate the EV CLSC market (especially for the new automobile forces, Tesla, NIO, XPENG and so on, that sell new EVs directly most of time), apparently holding the dominant position is necessary for a higher overall profit (Proposition 8(1)). For the third-party players that are incorporated in the EV CLSC, a proposal for them is to improve their channel power in order to lift their overall profit as much as possible (Proposition 8(2)). For the government, corollary 2 can be derived as follows.

Corollary 2. 

When a third-party player participates in an EV CLSC, the government can promote the development of the EV CLSC through encouraging the proper channel leadership.

(1)

In order to promote the end-of-life treatment of obsolete EVs, the government would help improve the channel power of the third-party player through supporting large third-party enterprises instead of small-scale ones, or encouraging alliances of the latter ones (Proposition 7).

(2)

In order to improve economic benefits, the government can leave the EV manufacturer to maintain their dominant position considering the importance of the EV manufacturer in the EV CLSC (Proposition 8(1)).

Considering the elimination of double marginalization [39,41], the EV manufacturer should develop the EV CLSC by itself. When a third-party player is incorporated, for the EV manufacturer to undertake the collection effort directly would be a better choice for both the EV manufacturer and the third-party player, especially considering the increase in consumers’ green awareness. And a lift of each player’s channel power would always be a wise choice for each other. For the government which has the goals of promoting both the EV industry and the end-of-life treatment of obsolete EVs, a series of trade-offs including the CLSC structure and channel leadership should be considered prudently.

In summary, the study results can benefit both the government and the enterprise for better decision making. For governments, both a subsidy to enterprises and guidance to consumers are important. The result shows that the subsidy given to the EV recycling process can bring about spillovers to collection activities and EV consumption through a “chain effect”. Meanwhile, besides subsidies, governments should lay stress on the cultivation of consumers’ green awareness simultaneously. In addition, special concern should be given to the structural transformation of the EV industry from a new-EV consumption-oriented model to an obsolete-EV collection-oriented type, because the CLSC structure has significant influence on the profit of EV manufacturers and their collection quantities. For EV manufacturers, to be prepared for the construction of the CLSC in advance is necessary. On the one hand, it is suggested that EV manufacturers enhance their leading positions in the CLSC to increase the transfer price of the obsolete EVs collected. On the other, they are recommended to make an effort to promote the green awareness of consumers in order to increase the collection quantity.

5. Conclusions

The development of an EV CLSC becomes urgent in pace with the rapid expansion of the quantity of EVs. This paper applies a game theory model to study the performance of EV CLSCs under the joint impacts of government subsidy and consumers’ green awareness. Five game theory models that differ in CLSC channel structure, collection-effort implementer and channel leadership are developed. Combining theoretical analysis with numerical simulation, the following results are derived.

(1)

Government subsidy and increased green awareness of consumers both have positive influences on the EV CLSC.

(2)

Government subsidy for the treatment of obsolete EVs can not only promote collection quantity but also benefit the demand for new EVs in the market. The results demonstrate the “chain effect” of government subsidy on the EV CLSC.

(3)

The optimal CLSC decision varies for different players. For the EV manufacturer, considering the elimination of double marginalization, the EV manufacturer should develop the EV CLSC by itself. When a third-party player is incorporated, for the EV manufacturer to undertake the collection effort directly would be a better choice for both the EV manufacturer and the third-party player, especially considering the increase in consumers’ green awareness. And a lift of each player’s channel power would always be a wise choice for each other.

(4)

For the government which has the goals of promoting both the EV industry and the end-of-life treatment of obsolete EVs, a series of trade-offs including the CLSC structure and channel leadership should be considered prudently.

The emerging operating mode of new automobile forces in the context of China brings up new problems for the development of the EV CLSC, which are the market position shift inside the loop and government policy and changes in consumer awareness outside it. The results of this study reveal the impacts of government subsidy, consumers’ green awareness, collection effort, CLSC structure and channel power, and conclude with the optimal CLSC structure. The study contributes to the comprehensive understanding of the optimal decisions of the EV CLSC, and will benefit the efficient development of the EV CLSC.

The model developed in this paper has a few limitations that should be ameliorated in future research. Firstly, the symmetric information can be extended to asymmetric information, so as to explore the performance stability of different players in the CLSC. Secondly, the models of EV CLCS in this study considered a single collector; future studies could look at a circumstance with competition between different collectors. Moreover, an interesting extension to this work could includes consideration of coordination mechanisms, such as revenue sharing, profit sharing, and effort sharing.