Low-complexity energy-aware sensor selection for noise reduction in distributed microphone networks

1.   Introduction

With increasing global concerns over climate change, the push for new energy vehicles (NEVs) has become a pivotal aspect of policy agendas worldwide. The government’s ambitious carbon peak and neutrality targets in China highlight the key role of the NEV sector. However, the widespread adoption of NEVs faces significant hurdles, primarily due to shortcomings in charging infrastructure, such as uneven distribution of facilities, low utilization of charging piles, high fees, and safety concerns. The ease of access and convenience offered by charging infrastructures are crucial for consumer acceptance of NEVs, and resolving these issues is vital for the sector’s advancement^[1].

This study explores the collaboration between automotive companies and third-party private charging-pile-sharing platforms (hereinafter referred to as PCP-sharing platforms, following Wang et al.^[2]), exemplified by Teld, a platform offering PCP-sharing services. Teld’s partnerships with nearly 70 NEV manufacturers, including industry giants such as BYD, Xpeng, and Lotus, showcase how cooperation functions in practice. These partnerships allow owners of the associated brands to easily locate and use charging piles and check their real-time availability, thus improving the EV charging experience. However, this benefit is not extended to customers of brands that have not partnered with Teld. Additionally, Teld’s development of diverse charging equipment and co-branded sites helps automotive companies quickly expand their charging networks at lower costs ¹.

Such collaborations offer multiple advantages. Automotive companies can improve their electric vehicle (EV) charging solutions and customer loyalty by leveraging the technology and networks of platforms, such as Teld, while reducing the costs and risks related to developing charging infrastructure through a sharing economy model^[3]. Conversely, PCP-sharing platforms benefit from their association with automotive companies by gaining increased visibility, credibility, a broader service range, and a larger customer base, enhancing their market competitiveness and profitability. In China, successful collaborations between platforms (such as Star Charge, State Grid, and YKC) and automakers (such as BAIC, Xpeng, GAC, and BYD) demonstrate that partnerships constitute an effective strategy for navigating the complexities of charging infrastructure in the NEV industry.

Nonetheless, while promising, the cooperative model between PCP-sharing platforms and automotive companies is not without its challenges. These platforms face profitability pressures, diminished consumer charging experiences, and low utilization rates of charging infrastructure, posing risks to the model’s long-term sustainability and growth^[4]. Thus, examining the nature and implications of such collaboration becomes crucial.

This cooperative framework introduces new platform revenue channels through commission-based arrangements, wherein automotive companies pay a specified percentage of their revenue to the platform. Post-collaboration, automotive companies generate additional revenue from fees charged to their consumers to provide higher-quality after-sales charging services. The rate of this commission is pivotal for fostering successful cooperation. Furthermore, these partnerships influence the platform’s pricing strategies, significantly impacting the PCP-sharing industry’s business model and overall profitability. Ensuring charging safety and maintaining high-quality standards are vital for building consumer trust, underscoring the importance of platforms’ capabilities to enhance charging safety through collaboration with automotive companies.

Additionally, cooperation-induced cross-side network effects are expected to significantly alter the dynamics for platforms, consumers, and PCP suppliers. After cooperation, platforms are likely to experience increased utilization rates of charging piles by broadening their consumer base, which, in turn, benefits PCP suppliers. However, this expansion could increase consumer waiting times, negatively impacting user experiences^[5]. Cross-side network effects also mean that supply will grow, disproportionately advantaging consumers over suppliers, necessitating an in-depth analysis of these shifts in supply-demand dynamics and their implications for consumer and supplier surplus.

In light of these considerations, this study aims to delve into the economic mechanisms underpinning the cooperation between PCP-sharing platforms and automobile companies, elucidating the societal benefits of such partnerships and their potential impacts on charging service quality. The primary research question explores the effects of such cooperation on the platform’s operational efficiency and market performance.

To this end, we develop a theoretical Stackelberg game model reflecting the operational realities of PCP-sharing platforms to assess the impact of cooperation on platform profitability and social welfare, encompassing consumer and supplier welfare, as well as environmental outcomes, in which PCP-sharing platforms are the leaders and automotive companies are the followers ². Our model involves a PCP-sharing platform, an automobile company, PCP suppliers sharing idle charging piles, and EV drivers renting these facilities ³. It examines decision-making processes both with and without cooperation, including pricing strategies for drivers and suppliers, charging quality for drivers of cooperative brands, and additional fees. This research comprehensively evaluates how the cooperative model affects consumer charging quality, the economic effects of the platform, and overall social welfare, including environmental considerations.

Our findings enrich the literature by illuminating the economic dynamics of cooperation between PCP-sharing platforms and automotive companies, incorporating considerations of consumer delay sensitivity and service quality heterogeneity into operational management strategies, and providing practical insights for the management and operation of sharing platforms.

The remainder of this paper is structured as follows: Section 2 reviews the relevant literature. Section 3 describes the development of our theoretical model and an equilibrium analysis. Section 4 presents an empirical examination of the effects of cooperation on the platform. Section 5 discusses the implications of cooperation for social welfare. Finally, Sections 6 and 7 offer conclusions and policy recommendations, respectively.

2.   Literature review

This study intersects three distinct and related areas of literature: strategies for platform cooperation, consumer heterogeneity analysis, and operations of sharing platforms.

2.1   Strategies for platform cooperation

The discourse on platform cooperation strategies extends across various scholarly domains, illustrating a diverse range of academic interests. Initial research endeavors concentrated on the modalities of cooperation under traditional business models, with Ghosh and Morita investigating the economic outcomes of cooperative ventures, especially in the context of horizontal and vertical product differentiation^[6]. Subsequent studies have broadened the scope to examine the multifaceted economic impacts of cooperation. These include the challenges faced by original equipment manufacturers in partner selection^[7], potential synergies between luxury fashion brands and rental platforms^[8], and the complex relationships between comprehensive retail platforms and social service providers^[9]. Additional research has delved into service order allocation within supply chains^[10], partnerships between airlines and high-speed rail services^[11], optimal strategies for manufacturers in product-sharing ecosystems^[12], the effects of horizontal cooperation among online retailers^[13], and logistics platforms’ alliances with suppliers^[14].

The burgeoning field of on-demand service platforms has also captured scholarly attention, with studies exploring profit-sharing mechanisms in competitive bilateral platforms^[15], conditions fostering mutual interests in on-demand service ecosystems^[16], and the nuances of pricing, investment, and profit-sharing in collaborations between bilateral platforms and social media^[17]. Investigations have further focused on the dynamics of partnerships between online food delivery services and restaurants^[18], competitive interactions between ride-sharing services and car rental companies^[19], cooperative strategies within online travel platforms^[20], and the effects of collaboration between taxi-hailing platforms and car rental services^[21].

This paper contributes to the existing corpus of literature on platform cooperation by offering two significant enhancements. First, it shifts the traditional focus from merely augmenting supply to address the increasing demand to a more nuanced examination of how such cooperation can boost user engagement and profitability within PCP-sharing platforms. Second, it broadens the scope of analysis beyond economic benefits to include considerations of social welfare improvements, notably environmental benefits. Through a comprehensive theoretical model, this study aims to elucidate the consequences of demand shifts triggered by the cooperation between a PCP-sharing platform and a company, thus providing a novel perspective on platform cooperation strategies.

2.2   Consumer heterogeneity

The exploration of consumer heterogeneity on sharing platforms, especially in the context of waiting time sensitivity, occupies a notable niche within the academic discourse. Research has delved into how consumer delay sensitivity influences strategies for profit-maximization among manufacturers^[22], the optimization of a company’s price/lead-time offerings^[23], the competitive dynamics between just-in-time service platforms^[24], and the formulation of optimal pricing and wage policies on on-demand service platforms^[25]. Afeche and Pavlin^[26], along with Bai et al.^[27], further expanded on this theme, examining customers’ preferences with diverse valuations for immediate service versus their tolerance for delay costs.

In parallel, the literature surrounding consumer service quality heterogeneity offers valuable insights for this study. Investigations have focused on the impact of service quality competition on customer loyalty^[28], the trade-off between delivering superior search results and maximizing revenue^[29], optimal pricing and service quality for customers with varied quality sensitivities^[30], and strategic considerations for platform quality investment^[31]. Furthermore, studies have explored the design and pricing of discretionary service lines in markets characterized by diverse customer sensitivities to service quality^[32], along with strategies for managing quality on two-sided platforms and the differentiation in services provided by the supply side^{[33, 34]}.

Although existing research often addresses consumers’ delay sensitivity and service quality heterogeneity as distinct focus areas, few studies comprehensively integrate these dimensions. Anand et al.^[35] highlighted a positive correlation between service quality and service time, suggesting an intertwined relationship between these metrics. This study aims to bridge this gap by concurrently considering both consumer delay sensitivity and service quality heterogeneity, offering a fresh theoretical perspective and actionable insights for managing PCP-sharing platforms. While Zhong et al.^[36] have also explored dual heterogeneity in platform matching systems, the current research uniquely examines the implications of this dual consumer heterogeneity for the cooperative strategies between PCP-sharing platforms and automotive companies and its consequential impact on various consumer segments, thereby enriching the discourse on platform cooperation strategies.

2.3   Operation of sharing platforms

The expansion of the sharing economy has attracted significant scholarly interest in the dynamics of pricing and wage strategies within sharing platforms. Analytical models have been proposed to delineate optimal pricing and wage rates^[27], with further inquiries into the welfare of agents and the complex interactions between price, wages, labor supply, customer delay, and demand^[37]. Competitive forces in two-sided platforms have also been a focal point, leading to the development of pricing game models between platforms and studies on balanced bilateral pricing, market share, and platform profits^{[38, 39]}. Spatial dynamics in pricing strategies for online services, particularly ride-hailing, have been examined^{[40, 41]}, alongside the effects of network externalities on price competition between platforms^[42]. Consideration of supplier preference heterogeneity in pricing mechanisms^[43], diverse pricing schemes for on-demand services^[44], and the strategic behaviors of passengers and drivers have enriched the discourse^[45]. A notable study by He et al.^[46] emphasized real-world platform operations and the adaptation of pricing mechanisms amid supply-demand discrepancies.

Quality management within sharing platforms, aimed at boosting the user experience and market competitiveness, has been another area of focus. The role of quality differences in impacting platform profits and social welfare within the sharing economy has been explored^[47]. Liu et al.^[48] and Zhang et al.^[49] delved into how platforms can adjust commission rates and service prices and match quality to influence service provision and equilibrium.

The literature on two-sided platforms extends to examining the broader social impacts of platform operations. Studies have considered the implications of innovations such as autonomous vehicles for platform economics and social welfare^[50], and the broader welfare effects of competition and cooperation among platforms on various stakeholders^{[21, 24, 37, 51]}. In particular, Cachon et al.^[52] concluded, contrary to mainstream views, that stakeholders can all benefit from surge pricing. Zeng and He^[53] further reported that the economic effects of the sharing economy could conflict with the welfare of affected communities.

In summary, despite the extensive examination of pricing mechanisms within two-sided platforms, the exploration of quality management within sharing platforms remains somewhat less developed. This study seeks to enrich the existing corpus of knowledge by integrating analyses of both pricing mechanisms and quality management within platforms, particularly through the lens of external business cooperation. It aims to assess how partnerships, such as those with emerging PCP-sharing platforms, impact platform operations, with a focus on how changes in demand influence pricing and quality management strategies. This approach marks a strategic departure from previous studies such as Lin et al.^[21], which concentrated on supply-side changes. Our research builds upon the principles of consumer delay sensitivity and service quality heterogeneity, examining how cooperation influences platform decisions on charging quality and the resulting variations in consumer surplus among individuals with differing sensitivities to charging quality. This comprehensive approach offers novel insights into the interplay between pricing, quality management, and external business cooperation in the context of the sharing economy.

3.   Model development

This study delves into the strategic interaction between a PCP-sharing platform (e.g., Teld) and an automobile manufacturer (e.g., BYD). It examines how the platform strategically manages pricing, the quality of service delivered to consumers, and the compensation paid to PCP suppliers. This strategic management is crucial for consumers with sensitivities to price, waiting time, and charging quality, as well as the PCP suppliers, who prioritize their charging piles’ income and utilization rates. Our analysis focuses on whether the platform will cooperate with the automobile company and explores the potential ramifications of such a partnership on the interests of all stakeholders, including consumers, PCP suppliers, and overall social welfare. This paper uses superscripts $nc$ and $c$ to distinguish between non-cooperative and cooperative scenarios, respectively. The notation used in this study is outlined in Table 1.

Table  1.  Notation for the model.

Parameter	Definition
Decision variables
$p_s$	Unit price charged to consumers by the PCP-sharing platform
$p_d$	Unit price paid to suppliers by the PCP-sharing platform
$x$	Charging quality variation for consumers of the cooperative brand
Nondecision variables
$\bar \lambda$	Number of potential consumers from the cooperative brand engaging in the PCP-sharing platform
$\bar \lambda_0$	Number of potential consumers from other brands engaging in the PCP-sharing platform
$\phi$	Probability of consumers from the cooperative brand seeking the PCP-sharing platform’s service
$\phi_0$	Probability of consumers from other brands seeking the PCP-sharing platform’s service
$\lambda$	Consumers from the cooperative brand engaging in the PCP-sharing platform
$\lambda_0$	Consumers from other brands engaging in the PCP-sharing platform
$\Lambda$	Total consumer demand
$v$	Utility perceived by consumers post service
$e$	Service utility increases for consumers of the cooperative brand after cooperation
$T$	Waiting time
$c$	Cost incurred by consumers per unit of waiting time
$CS$	Consumer surplus
$\bar \eta$	Number of potential suppliers engaging in the PCP-sharing platform
$\epsilon$	Probability of suppliers engaging in the PCP-sharing platform
$\eta$	Suppliers engaging in the PCP-sharing platform
$\mu$	Average service rate of PCPs on the PCP-sharing platform
$\rho$	Utilization rate of PCPs on the PCP-sharing platform
$r$	Reservation wage for suppliers
$PS$	Supplier surplus
$C$	Cost for the PCP-sharing platform to increase/decrease one unit of quality
$\Pi_p$	The profit of the platform
$p_0$	Additional charges imposed on its consumers by the automobile company after cooperation
$\Pi_o$	The profit of the automobile company
$\gamma$	Commission rate
$\delta$	The degree of environmental impact from one charging process
$f$	Increase/decrease in environmental impact per-unit change in charging quality
$E$	Environmental effects

 | Show Table

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We examine a scenario where a PCP-sharing platform can cooperate with a specific automobile company.The game sequence diagram can be found in Fig. 1. The relationships between the four entities involved in the model are shown in Fig. 2. Without such cooperation, the platform functions independently, serving NEV owners. In this independent operation mode, the platform must strategically determine the per-unit charging price $p_s$ ($p_s \geq 0$) for vehicle owners and the compensation rate $p_d$ ($p_d \geq 0$) to be paid to PCP suppliers. At this point, the automobile company proactively addresses its consumers’ charging concerns by constructing proprietary charging stations or offering charging piles as complimentary gifts. This approach contrasts with merely transferring the charging issue to car owners. Consequently, it is inferred that, in the absence of collaborative efforts, consumers of other brands are required to utilize the platform to rent charging piles, whereas consumers of this company are exempt from this necessity.

Figure  1.  The decision timeline. This diagram illustrates the Stackelberg game sequence of the model.

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Figure  2.  Modeling framework under non-cooperative and cooperative scenarios. This diagram illustrates the relationships between the four parties involved in this study.

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In the cooperative scenario, the automobile company collaborates with the platform to address its consumers’ charging needs, thereby providing more convenient and higher-quality charging services. This partnership offers superior customer support and service responsiveness, alongside potential additional services such as regular inspections or priority access rights. To avail themselves of these added conveniences and services, consumers of the automobile company may be required to make advance payments or pay additional fees at the time of vehicle purchase. This upfront payment can be regarded as an investment in future services and conveniences, thereby enhancing the overall service experience $e$. Consequently, the automobile company introduces an additional price $p_0$ ($p_0 \geq 0$) for their car buyers, which encompasses extra services or discounts related to platform charging. This strategy aims to bolster the company’s sales, expand market potential, and increase the platform’s revenue ⁴. The company agrees with a profit-sharing arrangement to facilitate cooperation, denoted as the commission rate $\gamma$. The platform optimizes prices: $p_s$, $p_d$ ($p_s \geq 0$, $p_d \geq 0$) and adjusts charging quality $x$ via intelligent charging management systems ⁵. Note that we assume that $x$ can be negative, implying that after cooperation, the platform may not necessarily improve the charging quality provided to the consumers of the cooperative brand but may decrease it. Moreover, to safeguard the interests of these consumers, it has been stipulated that the variable $x$ should not be excessively small. Consequently, a lower bound for $x$ is established. Therefore, $x>\hat{x}$ ⁶.

To increase the precision of this research, we elucidate the distinction between charging experience $e$ and charging quality $x$. Service experience e encompasses all stages of the user’s interaction with the charging process, including locating charging stations, booking, payment, charging, and post-use feedback. In contrast, charging quality $x$ pertains to the technical aspects and performance during the charging process, such as charging safety, charging rate, and equipment status.

The primary focus of this study is to address consumer charging issues through collaborative efforts. The platform, as an industry pioneer, enters the market to establish a comprehensive charging network, thereby possessing extensive charging stations and data resources. With its first-mover advantage, the platform excels in charging technology, payment systems, and user interfaces and has instituted corresponding technical and service standards that collaborating companies must adhere to. For instance, in collaborations such as ChargePoint with traditional car manufacturers, the platform typically spearheads the deployment and operation of charging infrastructure, whereas car manufacturers engage in the market through collaboration ⁷. Consequently, this study designates the platform as the leader and the automobile company as the follower.

In our analytical framework, we establish foundational assumptions to streamline our exploration. We posit that consumers and suppliers act rationally and are equipped to assess critical information accurately, influencing their participation decisions on the platform. This includes variables such as the price paid by consumers on the platform, $p_s$, the fee received by private charging pile owners for sharing their charging piles, $p_d$, the waiting time for consumers, $T$, the charging quality obtained by consumers of cooperative brands, $x$, and the utilization rate of the PCP on the platform, $\rho$. Moreover, to sharpen the focus of our investigation, we normalize the consumer’s charging quantity per unit of time and the average service duration to one. This standardization allows us to concentrate on strategic interactions and the implications of decision-making processes within the PCP-sharing platform and its cooperative dynamics with automotive firms.

3.1   Consumer decision analysis

In line with Zhong et al.^[51] and Lin et al.^[21], we assume that potential customers randomly drive at the platform at a certain exogenous speed during the planning period. We categorize customers into two distinct groups based on their reported preferences: other brand consumers and cooperative brand consumers. Importantly, the sensitivity to charging quality may vary within each group. Cooperative brand consumers may exhibit greater sensitivity to service quality because of the additional costs ($p_0$) and the promise of superior charging quality ⁸. This does not imply that consumers of other brands are universally indifferent to charging quality. Rather, in comparison with cooperative brand consumers, they are less sensitive to charging quality and more concerned with the price they must pay and the waiting time involved ⁹. Each consumer can decide whether to join or exit the platform. Without cooperation, we assume that only consumers from non-partnered brands will be present. In other words, cooperation between the PCP-sharing platform and the automobile company will attract consumers with greater sensitivity to service quality to join the platform.

We assume that the potential total number of consumers from this cooperative brand and other brands in the market is denoted as $\bar{\lambda }$ and $\bar{\lambda _0}$, respectively, where $\bar {\lambda_0 }> \bar{\lambda } > 0$. Each consumer must decide whether to participate in the platform.

Initially, ascertain the average waiting time expression: Assuming that $\eta$ denotes the supply of sharing charging piles, $\mu$ represents the average service rate of charging piles, and $\Lambda$ signifies the customer demand rate, then under the non-cooperative (cooperative) conditions, $\Lambda =\lambda _0$ ($\Lambda =\lambda +\lambda _0$). Consequently, akin to Taylor^[25], Bai et al.^[27], and Benjaafar et al.^[37], we employ the following expression to delineate the waiting time:

This article exclusively focuses on scenarios where $\Lambda < \eta \mu$. Furthermore, the waiting time expression has the following common properties: (i) When the actual arrival rate of consumers $\Lambda$ increases, the waiting time $T$ increases and takes the form of a convex function. Conversely, when the number of participating suppliers $\eta$ increases, $T$ decreases and follows a convex function. (ii) In the limits where $\lim {{\eta \to \infty}}$, $\lim {{\mu \to \infty}}$, or $\lim {{\Lambda \to 0}}$ occur, $\lim {{T \to 0}}$. Conversely, when $\lim {{\Lambda \to \eta \mu}}$, $\lim {{T \to \infty}}$. (iii) The waiting time $T$ reflects the nature of the economy of scale, indicating that even with a proportional increase in demand, $T$ decreases in supply.

The net utility function for consumers of other brands can be expressed as the difference between the utility gained from receiving platform services and the costs in terms of price and time, as shown in the following formula:

where $c$ represents the unit waiting time cost. A rational consumer with utility $v$ will seek services if and only if $U(v)_0 \geq 0$, and the uniform distribution on [0, 1] is followed by $v$. Assume that $\phi _0$ represents the probability of consumers from other brands seeking the PCP-sharing platform’s service, then, $\phi _0= 1- c\times T -p_s$.

This implies $p_s=1-\phi _0-c\times T$. When the consumer’s utility is $v \geq p_s+c \times T=1-\phi _0$, their utility is $v-p_s-c \times T$. The consumer surplus refers to the net utility that consumers derive from seeking services on a platform after the price they pay and the delay costs they incur are subtracted. It represents the net benefit obtained by the consumers. Therefore, consumer surplus can be determined as follows:

By analogy, in the cooperative scenario, when calculating the net utility for consumers of the cooperative brand, in addition to considering the costs of price and time for charging on the platform, the upfront payment made for better services and the quality of charging provided by the platform are also included. Similar to common assumptions in the literature^[54–56], charging quality is normalized, meaning that one unit of mass $x$ results in one unit of utility. Therefore, the net utility for consumers of the cooperative brand is as follows:

Here, the condition $e>1$ indicates the expectation that consumers from the cooperative brand on the platform will enjoy an enhanced service experience. $x$ is the charging quality for consumers of the cooperative brand. A consumer will opt for services if $U(v) \geq 0$.

Assume that $\phi^c$ represents the probability of consumers from the cooperating brand seeking the PCP-sharing platform’s service, then: $\phi ^c=1-\dfrac{c \times T+p_s+p_0-x}{e}$. This implies that $p_s = e - e \times \phi^c - c \times T - p_0 + x$. The utility derived by the consumer is $e \times v - p_s - p_0 - c \times T + x$ when $v \geq \dfrac{c \times T + p_s + p_0 - x}{e}$. Consequently, the consumer surplus under the cooperative brand can be ascertained via the following formula:

In conclusion, the total consumer surplus can be computed as follows: When there is no cooperation, the company independently addresses the charging problems for its consumers. At this point, only consumers of other brands utilize the platform, and the total consumer surplus is $CS^{nc} = {cs}^{nc}_0$. In the case of cooperation, the total consumer surplus is $CS^{c} = {cs}^c_0 + cs^c$, representing the sum of the consumer surplus for both types of consumers.

3.2   Supplier decision analysis

The unit service price announced by the platform and the utilization of their charging piles on the platform are equally important factors that determine the actual revenue of PCP suppliers. In line with Lin et al.^[21], we assume that charging orders are distributed equally among PCPs. Let $\rho$ denote the PCP utilization rate on the platform in a steady state. Hence, the utilization of PCPs on the platform is given by:

The net utility for suppliers who share their PCPs on the platform is similarly represented by the difference between the total utility gained from sharing and their reservation wage. The total utility is influenced by the fees paid by the platform, the utilization rate of their PCP on the platform, and the service rate of the PCP. Therefore, the net utility can be expressed as:

where $r$ is the reservation wage, which varies by individual supplier. Given that the reservation wage $r$ is uniformly distributed in the range of [0, 1], a rational supplier with a reservation wage $r$ will participate in the platform if and only if $U(r) \geq 0$. Assuming that $\epsilon$ is the probability of the PCP supplier participating in the platform, then: $\epsilon =\rho \times \mu \times p_d$. When the reservation wage of the PCP supplier is $r \leq \rho \times \mu \times p_d$, their utility is $\rho \times \mu \times p_d-r$. Supplier welfare quantifies the net utility that PCP owners derive from sharing their charging piles on the platform. It is calculated as the total utility generated from the sharing activity minus the reservation wage, which represents the opportunity cost or the income they would have forgone had they not participated in the sharing arrangement. Therefore, the surplus of the PCP supplier is as follows:

The supply of PCPs is $\eta =\epsilon \bar{\eta }$, where $\bar{\eta}$ is the number of potential suppliers in the market.

3.3   Platform strategy and equilibrium analysis

In the non-cooperative scenario, the profit of the automobile company is normalized to zero, establishing a baseline in the absence of cooperation. This allows any profit changes resulting from cooperation to reflect its actual impact, free from interference from other factors. This assumption appropriately emphasizes the importance of focusing on the incremental benefits or additional gains brought about by cooperation in the research.

Consequently, the primary objective for the platform is to configure its pricing and compensation scheme to maximize expected profits, a goal succinctly captured by the following profit maximization formula:

Like a typical sharing platform, the PCP-sharing platform profits by earning a price difference in the non-cooperative scenario.

Moreover, in addition to earning a price difference, the platform can also receive a commission from the company to facilitate cooperation in the cooperative scenario. However, at this point, the platform must bear the cost of providing quality service to the cooperative brand’s consumers. Therefore, as a leader, the platform determines its prices and charging quality to maximize expected profit:

Additionally, we assume that $C$ is the cost the platform requires to improve/reduce one unit of charging quality. Moreover, the variable production cost of a product with quality $x$ often has quadratic properties. Owing to these properties, the development cost of improving the charging quality by $x$ units can be expressed as $\dfrac{1}{2} C x^2$.

Then, as a follower, the company establishes its pricing strategy ($p_0$) to maximize expected profit: $\Pi _0^c=(1-\gamma) p_0 \lambda$. Within the framework of this study, in the cooperative scenario, its profit mainly comes from the additional fee $p_0$ charged for guaranteeing a greater service experience for the cooperating brand’s consumers. By employing backward induction, given $p_s$, $p_d$, and $x$, and substituting them into the company’s profit function, we obtain the optimal decision for the enterprise: $p_0 = \dfrac{1}{2} \left(e + x + \phi_0 - 1\right)$. Additionally, we can conclude that:

to prepare for the analysis of platform decisions.

Theoretically, automotive companies invariably benefit from cooperation, as this aligns with the real-world scenario where they opt for cooperation to circumvent the high costs associated with building their own charging stations. The impact of cooperation on platforms, however, remains more ambiguous. Consequently, we will shift our research focus to PCP-sharing platforms.

4.   Cooperation’s impact on platform profits

In the subsequent research, we examine the prerequisites for a singular optimal solution within our model, delving into the market dynamics conducive to the platform’s inclination toward embracing cooperation. Following this foundational analysis, our investigation extends to the ramifications of such cooperation on a multitude of facets: the strategic decisions made by the platform, the surplus experienced by consumers, the surplus accruing to PCP suppliers, and the overarching environmental implications. Moreover, we scrutinize the repercussions stemming from alterations in exogenous variables, specifically how these modifications influence the profit margins of the involved stakeholders.

First, in non-cooperative and cooperative scenarios, the platform’s objective functions are reorganized as follows:

Lemma 1. In cases of non-cooperation and cooperation, the relevant property of the profit function concerning $(\Lambda^{nc}, \epsilon^{nc})$ and $(\Lambda^{c}, \epsilon^{c}, x^{c})$ implies the existence and uniqueness of the optimal solution. They are subject to the satisfaction of the following first-order conditions:

The proof of Lemma 1 is given in the Appendix.

4.1   Conditions for the platform to accept cooperation

Given the complexity of the optimal solutions delineated in this study, a theoretical analysis of the platform’s optimal decisions is challenging. Therefore, we resort to a suite of numerical simulations to probe the platform’s propensity for cooperation and to discern the subsequent effects on its operations post-cooperation. Concurrently, we delve into service experience, market size, and other exogenous factors to unravel their influence on the platform’s strategic decisions and operational dynamics. To ensure that the experimental results have some versatility and robustness, we conduct a series of numerical experiments by changing the main parameters to obtain more reliable research conclusions.

In the investigation, the parameter $\bar{\lambda}$ has been deduced, drawing upon the production volume metrics of BYD. As of November 24, 2023, this volume notably reached a milestone of 6 million units ¹⁰. Considering its growth momentum, we set $\bar{\lambda} \in [6,7,8,9,10]$. The determination of the parameter $\bar{\lambda_0}$ is anchored in the user registration data from BYD’s partner, Teld. With the service vehicle count reaching 16 million, the selected range for $\bar{\lambda_0}$ is conservatively established $[11,12,13,14,15]$ ¹¹. For the parameter $\bar{\eta}$, in 2022, the cumulative number of private charging infrastructure units in China exceeded 3.4 million. Consequently, we take $\bar{\eta} \in [5,7.5, 10,12.5,15]$ to represent this growing trend ¹². Based on the research of Jacob and Roet-Green^[57], the waiting time cost is set between [3, 4, 5, 6, 7]. Similarly, following Lin et al.^[21], we define $\mu \in [5,7.5,10,12.5,15]$, and drawing from Hafezi and Zolfagharinia^[55] as well as the unique characteristics of the NEV charging process, we establish the quality improvement cost parameter $C \in [15,17.5, 20, 22.5, 25]$. Furthermore, we set the parameters $e \in [1.25, 1.5, 1.75, 2, 2.25]$, $\gamma \in [0.1, 0.3, 0.5, 0.7,0.9]$ as proportions. These ranges are based on prior studies and reflect relative system dynamics. We obtained 375737 simulation results in this section based on the parameter values above. According to the numerical simulation results, the platform accepts cooperation in most cases (370580 instances). In the scenario where cooperation was declined, there were only 5157 instances, accounting for 1.37% of the total.

Fig. 3 illustrates the range of values for various parameters and their frequency distributions when cooperation with the platform is declined. The horizontal axis represents eight exogenous variables, with the color for each variable corresponding to its parameter values in ascending order from left to right. For example, in the case of $\bar{\lambda}$, the five colors from left to right represent $\bar{\lambda}$ values of 6, 7, 8, 9, and 10, respectively, with the same logic applied to other parameters. These values are not explicitly labeled in the figure to maintain its clarity and aesthetic appeal. The vertical axis indicates the frequency of different parameter values under the scenario where cooperation declined (based on 5157 simulation results). In summary, Fig. 3 illustrates how three key factors significantly impact the likelihood of cooperation: the improvement in service utility for the cooperative brand’s consumers ($e$), the potential consumer base of the cooperative brand ($\bar {\lambda}$), and the cost of quality variation ($C$). Specifically, a lower $e$, $\bar {\lambda}$, and minimized $C$ correspond to a decreased willingness of the platform to cooperate due to insufficient benefits or heightened risks.

Figure  3.  Why does the refusal to cooperate? This diagram shows the frequency distribution of different values of exogenous variables when the platform refuses to cooperate.

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The service experience of cooperative brands ($e$) is especially critical; high $e$ enhances the likelihood of platform cooperation by attracting drivers (consumers) and increasing profits, whereas low $e$ diminishes it. The potential consumer base of the cooperative brand ($\bar {\lambda}$) plays a vital role. A lower $\bar {\lambda}$ reduces the platform’s appeal and limits opportunities for user base expansion, whereas greater $\bar {\lambda}$ attracts more users and increases profits after cooperation. In post-cooperation scenarios, even when the platform incurs low direct costs ($C$) due to reduced charging quality, the indirect consequences, such as eroded consumer trust and damaged brand reputation, could result in overall losses exceeding the immediate financial benefits derived from cooperation. This situation is particularly acute when these direct costs are minimal. However, the impact on consumer interests due to compromised charging quality is profound, leading the platform to forgo cooperation despite seemingly low initial expenses. Among these factors, service experience ($e$) is the most crucial in influencing cooperation. When $e$ is very low (e.g., $e = 1.25$), the platform refuses cooperation in 4527 instances. When the value of $e$ exceeds a certain threshold $\hat{e}$ (in this study, $\hat{e} = 1.75$), the platform is more inclined to accept cooperation. Therefore, when the platform can provide a greater service experience for the cooperative brand’s consumers, it gains greater confidence in accepting cooperation. In addition, when the number of potential consumers from other brands engaging in the platform ($\bar{\lambda_0}$) is high, it tends to discourage the platform from accepting cooperation.

In conclusion, lower service experience associated with cooperative brands, the size of their potential consumer base, and the costs entailed by quality variations predispose the platform to decline cooperation offers. This reluctance stems from the prospect of insufficient benefits or escalated risks. It becomes imperative for platforms to judiciously evaluate market potential and the implications of quality changes, selecting partners and cooperation modalities that bolster profitability and competitive edge.

4.2   Platform decision-making

In the preceding segment, we delineated the circumstances that prompted platforms to embrace cooperative endeavors. This segment delves into the repercussions of such cooperation on pivotal decision-making variables, remarkably, the price to consumers ($p_s$), fees remitted to charging pile suppliers ($p_d$), and charging quality ($x$). Our discourse focuses on PCP-sharing platforms’ strategies for regulating pricing and charging standards. These elements are instrumental in harmonizing and apportioning benefits across platforms, consumers, suppliers, and partner entities. Consequently, discerning and refining the alterations in $p_s$, $p_d$, and $x$ after cooperation is paramount for the PCP sharing domain. Our investigation reveals that post-cooperation, platforms are inclined to escalate the prices charged to consumers ($p_s$) and the fees disbursed to PCP providers ($p_d$). Simultaneously, there is a discernible decline in the caliber of charging services ($x$) rendered to consumers of the cooperative brand.

For simplicity and clarity, we categorize the variables into the following three groups:

(i) Based on the above analysis, variables that significantly affect cooperation include $\bar {\lambda}$, $e$, and $C$. We choose the following test values for illustration: $\bar {\lambda} \in [6,7,8,9,10]$, $\bar {\lambda_0} = 11$, $\bar {\eta} =7.5$, $c =4$, $e \in [1.5,\,2,\,2.5,\,3,\,3.5]$, $\gamma =0.9$, $\mu =10$, $C \in [15,17.5,20,22.5,25]$. These values are selected to demonstrate the impact of such variables.

(ii) The variables with less impact on cooperation include $c$, $\gamma$, and $\mu$. We choose the following test values for illustration: $\bar {\lambda} = 8$, $\bar {\lambda_0} = 13$, $\bar {\eta} = 10$, $c \in [3,4,5,6,7]$, $e = 1.75$, $\gamma \in [0.1,0.3,0.5,0.7,0.9]$, $\mu \in [5,7.5,10,12.5,15]$, $C = 20$. These values are selected to demonstrate the impact of such variables.

(iii) The variables related to potential market size include $\bar {\lambda_0}$, $\bar {\lambda}$, and $\bar {\eta}$. We choose the following test values for illustration: $\bar {\lambda} \in [6,7,8,9,10]$, $\bar {\lambda_0} \in [11,12,13,14,15]$, $\bar {\eta} \in [5,7.5, 10, 12.5,15]$, $c = 7$, $e = 1.75$, $\gamma = 0.7$, $\mu = 15$, $C = 20$. These values are selected to demonstrate the impact of such variables.

For brevity and clarity, $\Delta$ is employed herein to denote the disparity in values pre- and post-cooperation, assuming constancy in exogenous variables. For example, we define the difference between the price charged to consumers after cooperation and those charged under the same conditions without cooperation as $p_s^c - p_s^{nc}$, denoted as $\Delta p_s$. This notation will be consistently used throughout.

Notably, most changes indicated by $\Delta p_s > 0$, $\Delta p_d > 0$, and $\Delta x < 0$ suggest that cooperation leads to escalated consumer prices, increased fees for PCP suppliers, and reduced service quality for the consumers of cooperative brand. Fig. 4 delineates the impact of key external factors on platform decision-making post-cooperation, as elaborated earlier. Following cooperation, heightened charging demand from new consumers prompts the platform to raise payments to PCP supplies, thereby fostering more significant participation in PCP sharing. This necessitates increased consumer prices to offset the financial burden of higher fees.

Figure  4.  The impact of cooperation on platform decision-making.

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Addressing the broader implications while safeguarding the cooperative brand consumer interests, it is assumed that the platform incurs maintenance costs even as service quality declines. Reducing service quality, while seemingly counterintuitive, is consistent with the platform’s strategic approach to quality management. Enhanced quality does not necessarily correlate with increased engagement from cooperative brand consumers, particularly considering the simulation results showing extended waiting time post-cooperation. Therefore, the platform gives considerable thought to consumer tolerance for delays. A preference among consumers for shorter waiting times could prompt platforms to deliberately reduce charging quality as a strategic maneuver to broaden their user base.

Interestingly, this study’s analysis indicates that the reduction in service quality for cooperative brand consumers post-cooperation could paradoxically increase the likelihood of consumer participation from other brands. This shift in perception, whereby consumers of non-cooperative brands perceive an improvement in charging quality (despite no objective change) relative to costs on the platform, could bolster their satisfaction and brand loyalty. This counterintuitive outcome highlights the nuanced dynamics of consumer behavior and market perception, underscoring the importance of strategic quality management within platform operations.

4.3   Platform user scale

Investigating the operational dynamics following cooperation in PCP-sharing ecosystems is pivotal for elucidating and advancing the sector’s evolution. Amidst prevailing challenges such as diminished profitability and suboptimal utilization rates of PCPs, a thorough analysis is essential to determine how partnerships with automotive manufacturers can bolster platform revenues and enhance overall efficiency.

It is commonly posited that such cooperation attracts novel consumer segments and invigorates the engagement of PCP providers via cross-network externalities inherent to dual-sided markets. Therefore, our analytical emphasis is on assessing the ramifications of cooperation between PCP-sharing platforms and automobile firms on platform profitability, the augmentation of consumer engagement, and the proliferation of PCP suppliers.

In general, cooperation enhances demand and supply, leveraging automobile companies’ influence to broaden the consumer base. This expansion and cross-network externalities contribute to a greater supply of PCPs. Fig. 5 illustrates the impact of external variables on platform profits and the participation of drivers and the PCP suppliers post-cooperation. Specifically, a post-cooperation increase in service experience ($e$) and the potential consumer base of cooperative automotive brands ($\bar {\lambda}$) bolsters both demand and supply, resulting in higher platform profits. In contrast, elevated post-cooperation quality improvement costs ($C$) dampen these increases, adversely affecting profits. Additionally, a higher commission rate ($\gamma$) contributes to expanding the user base and profit generation, although it is not the determinant of successful cooperation.

Figure  5.  The impact of cooperation on the platform user scale.

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In a broader framework, we posit that the burgeoning NEV sector confers advantages on PCP-sharing platforms, a stance corroborated by simulation outcomes. However, the effect of the consumer bases of other automobile brands on the supply dynamics is complex. Following a cooperative initiative, the availability of PCPs surges in response to the influx of prospective consumers from different brands. However, as the prospective consumer pool of the partnering brand swells, the contribution of potential consumers from other brands to supply expansion ceases to follow a straightforwardly increasing trajectory. Instead, this influence begins to wane, displaying a downward trend. What starts as a positive effect of other brands’ consumers on the supply of PCPs gradually diminishes or may even invert, becoming a detrimental impact as the market reach of the cooperating brand escalates.

5.   Cooperation’s impact on social welfare

In conclusion, platforms typically pursue cooperative efforts to increase profits and enhance user engagement. In the aftermath of such cooperation, platforms tend to escalate prices for drivers, increase fees provided to PCP providers, and diminish the quality of charging services available to consumers affiliated with the cooperative brand.

These adjustments inject a degree of unpredictability into the welfare of both consumers and suppliers. The precise repercussions of these changes, instigated by cooperation, on the surpluses enjoyed by consumers and suppliers are intricate. Our exploration is geared toward uncovering whether cooperation can benefit both stakeholders, striving to achieve an outcome that is beneficial for all parties involved.

5.1   Consumers

This research delves into the dynamics of cooperation between PCP-sharing platforms and automobile manufacturers, specifically, its influence on consumer surplus, emphasizing demand-side considerations. It examines consumer sensitivity to delays and the diversity in charging quality, distinguishing between consumers of cooperative brands and non-cooperative brands. The study assesses the effect of such cooperation on the aggregate consumer surplus and the surpluses of distinct consumer cohorts, investigating the role of various external variables and their impacts.

In contrast to non-cooperation scenarios, consumers face elevated prices, slightly extended waiting periods, and diminished service quality, particularly those affiliated with cooperative brands. Intriguingly, despite these drawbacks, the aggregate consumer surplus continues to increase. This improvement stems from the prioritized access and accelerated charging times granted to consumers of cooperative brands, notwithstanding the compromises in quality. For consumers of other brands, the degradation in service quality for cooperative brand consumers paradoxically opens up more opportunities for participation, thereby augmenting their surplus.

The prolongation of waiting times is attributed to a surge in demand for charging services. The decline in service quality, on the other hand, mirrors a strategic maneuver by the platform. This strategy is not aimed at curtailing costs but rather at orchestrating a balance among diverse consumer groups and averting substantial user attrition. Figs. 6 and 7 are illustrative, detailing the post-cooperation effects of various external variables on the surpluses of three distinct consumer groups—specifically, consumers of cooperative brands, consumers of other brands, and aggregate consumers—alongside the implications for consumer pricing, waiting durations, and the quality of service meted out to consumers of cooperative brands.

Figure  6.  The impact of cooperation on consumers.

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Figure  7.  The impact of cooperation on three types of consumers.

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As the service experience ($e$) improves and the platform begins cooperating with the company, the quality provided to consumers of the cooperative brand decreases compared with that in the non-cooperation scenario, accompanied by an increase in waiting time. Changes in prices charged to consumers exhibit distinctive trends: Under conditions conducive to cooperation, such as high-quality cost or a more extensive potential consumer base of cooperative automotive brands, $\Delta p_s$ increases as the service experience improves. Conversely, despite the improved service experience, the price increment is reduced. In cases involving additional quality change costs, there may be a need to raise prices post-cooperation to compensate for losses, resulting in a positive price difference between cooperation and non-cooperation. Additionally, for a cooperative brand with a large market base, the platform may attract more consumers by lowering prices, even with an improved service experience, to gain competitiveness.

The elevation in quality-related costs leads to decreased profits for the overall consumer base and those affiliated with other brands. Nevertheless, it boosts the profits for consumers tied to cooperative brands. This increased expense plays a crucial role in counteracting price increases, waiting time increases, and the deterioration of service quality. An increase in commission rates tempers the price increases while broadening the benefits for all consumer groups, including those associated with the cooperative brand and others.

Moreover, when contrasted with the non-cooperation paradigm, an expansion in the scale of PCPs ($\bar \eta$) enhances profits across the board. The growth in the pool of potential consumers from other brands ($\bar{\lambda_0}$) specifically benefits these consumers, albeit it does not favor consumers of cooperative brands. Nonetheless, from the perspective of overall consumer surplus, an increase in $\bar{\lambda_0}$ generally yields a positive outcome. Conversely, the effects of enlarging the potential consumer base of the cooperative brand ($\bar{\lambda}$) on consumer surplus are more nuanced. While consumer surplus typically climbs alongside $\bar{\lambda}$, under certain conditions marked by a low $\bar{\eta}$ and a great $\bar{\lambda_0}$, a marginal hike in $\bar{\lambda}$ might precipitate a negligible alteration in consumer surplus ($\Delta CS$). This indicates that under particular circumstances, the influence of $\bar{\lambda_0}$ is markedly pronounced, highlighting intricate interactions among various factors.

The influence of service experience ($e$) on consumer surplus post-cooperation emerges as a critical aspect. To further unpack the significance of $e$, our forthcoming analysis will meticulously examine its effect on the aggregate consumer surplus, the surplus of consumers of the cooperative brand, and that of consumers from other brands, both before and after cooperation. The parameters chosen for this detailed exploration include the following: $\bar{\lambda }= 8$, $\bar{\lambda_0} = 11$, $\bar{\eta} = 7.5$, $c = 7$, $e \in [1.25:0.05:2.95]$, $\gamma = 0.7$, $\mu = 15$, $C = 20$.

Fig. 8 elucidates the effect of service experience on consumer surplus for three distinct consumer categories before and after the initiation of platform cooperation, as well as delineating the disparities in consumer surplus among various consumer groups, both in cooperative and non-cooperative contexts. Additionally, Fig. 8 illustrate the differential impact on consumer surplus between the two brand categories, which varies with the service experience level ($e$), denoted as ${cs}^{c}-{{cs}}^c_0$. To encapsulate, the ramifications of an enhanced service experience on the surpluses of the three consumer groups post-cooperation, alongside the broader influence of cooperation on the welfare of both general and brand-specific consumers, can be summarized as follows:

Figure  8.  The impact of service experience on consumer surplus.

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First, consumers associated with cooperative brands experience a notable enhancement in service experience, which translates into heightened satisfaction and value, thereby increasing their surplus. For these consumers, cooperation emerges as beneficial, with an improved service experience directly proportional to the increase in their benefits when contrasted with scenarios lacking cooperation.

Second, for consumers of other brands, the increased service experience extended to cooperative brand consumers might escalate their substitution costs, potentially diminishing their consumer surplus. Therefore, an enhanced service experience under cooperation may result in more significant losses for these consumers than situations without cooperation. The disparity in consumer surplus between consumers of cooperative and other brands, represented as ${cs}^{c}-{{cs}}^c_0$, begins at a negative value, increases with service experience, and eventually becomes a positive domain. This trajectory suggests that an augmented service experience unfurls benefits for cooperative brand consumers as the service experience increases.

Finally, the overarching consumer surplus nonetheless experiences growth. With the improvement in the service experience, cooperation has been validated as advantageous for the consumer populace, translating improved service experience into broader benefits than non-cooperative scenarios do.

5.2   Suppliers

To scrutinize the ramifications of cooperation for all involved parties, we conducted an inquiry that begins with assessing its impact on consumers. Previous findings underscore that cooperation serves the interests of consumers, with service experience ($e$) playing a crucial role in this dynamic. We then broaden our analysis to encompass the effects of cooperation on PCP suppliers. These suppliers are vital cooperative partners for the platform, as their surplus influences their readiness to commit and continue their involvement in sharing endeavors. Furthermore, we delve into the feasibility of creating a scenario where cooperation yields benefits not only for the platform and its consumers but also for PCP suppliers. Such an examination is vital for understanding the platform’s operational efficiency, consumer contentment, and broader implications for social welfare.

Compared with complex impacts on consumers, cooperation consistently benefits suppliers. Cooperation positively impacts PCP suppliers by increasing fees and boosting utilization rates, culminating in an overall increase in supplier surplus. Fig. 9 elucidates the influence of different parameters on the surplus of suppliers, the fees they earn, and the utilization rates of PCPs after platforms enter into cooperative agreements. A higher level of service experience ($e$) during cooperation translates into greater profits for suppliers, owing to increased fees and utilization rates. An upsurge in the commission rate ($\gamma$) further bolsters supplier profits. Additionally, an expanded potential consumer base of the cooperative brand ($\bar{\lambda}$) and a reduced scale of PCPs ($\bar{\eta}$) drive up supplier profits by increasing the price increment and their PCPs’ utilization rate. The effect of an increased number of potential consumers from other brands ($\bar{\lambda_0}$) on the PCP utilization rate exhibits a non-monotonic pattern but generally tends toward higher profits for suppliers.

Figure  9.  The impact of cooperation on suppliers.

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In summary, such cooperative endeavors create a mutually beneficial scenario for platforms, consumers, and suppliers. Our investigation highlights the importance and favorable impacts of cooperation between PCP-sharing platforms and automotive companies. In most scenarios, this partnership results in positive outcomes for all parties involved. Specifically, cooperation increases platform profits and diversifies revenue streams, increasing the utilization rate of PCPs— thereby benefiting suppliers and fostering the expansion of PCP sharing. Additionally, it addresses charging needs while guaranteeing a satisfactory service experience for consumers affiliated with cooperative brands, which leads to a surge in consumer surplus. Fundamentally, the cooperation between PCP-sharing platforms and automotive firms represents a triple-win strategy, enhancing the economic benefits for the platform and improving the well-being of consumers and suppliers alike. This approach underscores the potential for the PCP-sharing industry to deliver greater social benefits, providing crucial insights for theoretical exploration and practical enhancements within the sector.

5.3   Environmental effects

Our comprehensive analysis shows that cooperation can refine platforms’ operational efficiency, expand user demographics, and increase profits for both platforms and their partnering companies. Nevertheless, the charging activities associated with NEVs might entail environmental downsides. The augmentation in platform user engagement following cooperation could heighten greenhouse gas emissions, thus exerting detrimental effects on the environment. Furthermore, EV charging is capable of inducing harmonic pollution, which can precipitate significant increases in current and voltage within power transmission systems, leading to energy inefficiencies.

Given these considerations, thoroughly investigating the environmental implications of such cooperation to ensure that the NEV charging sector advances sustainably becomes crucial. Consequently, we commit to a detailed analysis to understand this impact in depth. This effort aims to identify and implement more effective strategies to lessen adverse environmental outcomes while promoting a scenario that benefits all involved parties.

We conceptualize the environmental impact attributed to platform-related charging activities before cooperation as follows:

Among these, $\delta$ is a coefficient used to gauge a single charge’s environmental impact. In this context, we assume a positive value for the coefficient. After cooperation, the environmental effect of platform charging is as follows:

In this context, $f$ symbolizes the enhancement or degradation in the environment as a direct consequence of the amelioration or decline in charging quality. It is hypothesized that increasing charging quality dampens environmental pollution, whereas reducing quality could exacerbate pollution levels. Additionally, we assume that $f$ is a positive figure, indicating that improvements in charging quality beneficially impact environmental conditions. Eqs. (15) and (16) indicate that, before and after cooperation, in addition to changes in consumer demand, the environmental impact changes primarily arise from the charging quality provided to cooperative consumers. Given the complexities involved in directly measuring the pollution generated during the charging process, we draw upon prior research to estimate values of $\delta \in [0.2, 0.3,0.4,0.5,0.6]$ and $f \in [0.2,0.25,0.3,0.35, 0.4]$. This range reflects the inherent variability and uncertainties in quantifying such effects. The categorization and values of the other parameters remain aligned with 4.1. For clarity, the findings are visually represented in Fig. 10.

Figure  10.  The impact of cooperation on the environment.

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Fig. 10 reveals that the escalation in charging demand and the compromise in service quality following cooperation contribute to increased environmental burdens. Notably, virtually every external variable’s effect on environmental pollution correlates with its influence on platform profitability and consumer surplus. Despite the potential for increased profitability for platforms and consumers under specific scenarios—such as modifications in commission rates or expanding the market for PCPs—cooperation could lead to a surge in environmental pollution. Nevertheless, specific variables, including the service rate ($\mu$), consumer waiting cost ($c$), and the potential scale of PCPs ($\bar{\eta}$), manifest impacts on the surplus of the supply side that diverge from the previously mentioned factors. This finding indicates that while reducing service rates or the potential scale of PCPs, or increasing consumer waiting costs, may diminish platform profits and consumer surplus, it can bolster the supply side’s welfare and alleviate environmental pollution. Fig. 10 shows a discernible environmental consequence stemming from the cooperative effort. Hence, our investigation serves as a crucial guide for policymakers in navigating the intricacies associated with cooperation between PCP-sharing platforms and automotive companies. Policymakers are urged to judiciously weigh all stakeholders’ interests and scrutinize various factors in crafting policies that foster the sustainable advancement of the NEV charging sector.

6.   Conclusions

This research thoroughly examines the viability of cooperation between PCP-sharing platforms and automotive companies by developing a mathematical model and applying numerical simulations. The key findings derived from this study are as follows:

The numerical simulations reveal a marked propensity for PCP-sharing platforms to seek cooperative arrangements. This finding indicates that automotive companies addressing their consumers’ charging issues through cooperation is a feasible approach. This tendency is corroborated by real-world cooperation within the charging-pile-sharing industry, exemplified by partnerships such as Teld with Toyota, Star Charge with Xpeng, and YKC with BYD. The analysis further indicates that factors such as decreased consumer service experience, lower quality costs, and diminished market potential for the cooperative brand can deter the likelihood of forging cooperative ventures

The outcomes of this study highlight that cooperation creates a win-win-win situation for platforms, drivers, and private charging pile suppliers. Following cooperation, platforms can increase prices and selectively adjust quality, fine-tuning the supply‒demand equilibrium. From the standpoint of consumers, despite facing higher prices, longer waiting times, and reduced charging quality from cooperative brands, there is a notable increase in overall consumer surplus ¹³. For suppliers, such cooperation leads to improved revenue streams and higher utilization rates of private charging piles, significantly enhancing supplier surplus ¹⁴.

In managing the trade-offs between consumer waiting time and the quality of charging provided to consumers of the cooperative brand, PCP-sharing platforms tend to compromise charging quality for consumers of the cooperative brand after they enter cooperation agreements. This approach may reduce waiting times, attract a wider audience of the cooperative brand’s consumers, or increase satisfaction and loyalty among consumers of other brands. Importantly, this study unequivocally eliminates the hypothesis of quality reduction for cost-cutting purposes.

The findings of this study indicate that tweaking the commission rate stands out as a potent lever to increase the earnings of PCP-sharing platforms, their users, and the suppliers of private charging piles. Specifically, under conditions where the service experience is superior, the market potential for the cooperative brand is somewhat favorable, the costs associated with quality are low, and the consumer base of other brands is expansive, the dynamics of cooperation favor benefiting the platform, drivers across all brands, and private charging pile suppliers. Nonetheless, the profit implications diverge between consumers associated with the cooperative brand and those linked to other brands. In scenarios characterized by elevated service rates, diminished consumer waiting costs, and a plentiful supply of private charging piles, the cooperative endeavor is poised to bolster the profit margins of both the platform at large and its consumer base, albeit at the potential expense of diminishing the profit margins for owners of private charging piles. This nuanced outcome underscores the importance of strategic considerations in fostering a cooperative model.

The conclusions drawn from this research highlight a nuanced understanding of the interplay between cooperation among PCP-sharing platforms and automobile companies and its broad-spectrum implications. Under certain conditions, while such partnerships can bolster platform and consumer benefits, they also potentially exacerbate environmental pollution and harm the interests of suppliers. This dual outcome underscores the complexity of integrating business growth with environmental stewardship.

7.   Implications

The insights garnered are invaluable for private charging-pile-sharing platforms, automotive companies, stakeholders, and policymakers, underpinning the pivotal essence of cooperation in driving growth and diversification in the sector. The study underscores the necessity of strategic considerations in partner selection, emphasizing market potential, service experience enhancement, and quality cost as critical determinants. Post-cooperation strategies that involve pricing adjustments and quality considerations for consumers of the cooperative brand emerge as crucial levers for optimizing the benefits derived from such partnerships. Correspondingly, for automotive companies, enhancing their market potential facilitates better cooperation, making it easier to address consumer charging issues and expand market share, creating a positive cycle.

For suppliers, the findings elucidate the advantageous impacts of cooperation, pointing to increased charges and utilization rates of charging piles as critical benefits. The study further delineates market conditions that could amplify these advantages for suppliers following cooperation. From the consumer perspective, this research diverges from previous studies by offering a nuanced categorization of consumers, factoring in delay sensitivity and the differential impacts of charging quality post-cooperation. A general predilection toward such partnerships is evident despite consumer responses to cooperation variability. However, the influence of various external variables may vary, necessitating bespoke strategies to cater to distinct market dynamics.

Moreover, contrary to concerns of potential collusion harming consumers, our research suggests that cooperation benefits both consumers and suppliers. This stance aligns with current governmental directives that promote the exploration of business cooperation models among charging operation companies, automobile companies, and Internet companies ¹⁵. However, the study also brings to light critical questions regarding regulatory interventions needed to enhance charging quality within cooperative frameworks, alongside considerations of the environmental implications and the varied impacts on the interests of different stakeholders. Such considerations call for a balanced approach in policy-making, aiming to foster industry growth while ensuring quality, sustainability, and equity among all parties involved.

While this study presents key findings, it also has certain limitations. First, the research scope was confined to one bilateral platform and one external cooperative company. However, cooperation dynamics between multi-platforms and multi-companies present an intriguing avenue for future investigations. Moreover, we adopted a uniform distribution for consumers’ service valuation and suppliers’ reservation wages to accentuate the model’s core features. Expanding the model to encompass a broader distribution spectrum could yield more profound insights.