Competition and Cooperation in Ride-Sharing Platforms: A Game Theoretic Analysis of C2C and B2C Aggregation Strategies

Abstract

The aggregation of ride-sharing platforms has forced traditional ride-sharing platforms to decide whether to join or leave these emerging platforms. This study presents a stylized model analyzing the demand, supply, and profit of two self-operated platforms, C2C platforms (such as DiDi and Uber) and B2C platforms, considering aggregation platform awareness and commissions. The study investigates the conditions under which the self-operated platforms should employ the entry strategy based on the optimization method and Cournot game theory, as well as exploring the reasons why self-operated platforms choose to withdraw after joining. The results show that in order to avoid competition, B2C platforms adopt an entry strategy, while C2C platforms adopt a non-entry strategy. Only during the off-peak period, when the awareness of the aggregation platform is very high and the level of competition between the two types of platforms is very intense, will both types of platforms adopt an entry strategy, but C2C platforms may experience a significant loss of market share, leading to a decline in social welfare. Furthermore, even if the self-operated platform chooses to withdraw, social welfare will still increase if the two self-operated platforms adopt the best strategy. The study contributes to sustainable development by promoting efficient resource allocation, reducing redundant competition, and improving overall market efficiency, thereby fostering a more sustainable urban transportation system.

1. Introduction

The global ride-sharing market has rapidly developed, intensifying competition among major platforms. In the United States, Uber and Lyft compete for market share through different pricing and service strategies [1]; in Southeast Asia, Grab and Go-Jek offer diverse services tailored to local needs, achieving differentiated competition [2]; in Europe and Africa, Uber and Bolt engage in fierce competition [3]; and in the Indian market, Ola and Uber frequently adjust their pricing and service types to vie for market share [4]. Global ride-sharing platforms build differentiated mobility networks based on the needs of different regions, presenting a pattern of both competition and cooperation. The competition and cooperation among ride-sharing platforms are mainly achieved through integration strategies, which have gradually evolved from simple service integration to more complex alliances and cross-platform collaborations. For example, Uber has partnered with Viator and Omio to expand its business into the tourism and dining sectors [5]; Ola, on the other hand, has launched the Ola Money payment and Ola Play app in India to provide a personalized travel experience. These strategies not only help the platform expand its user base and enhance loyalty but also optimize resource allocation through collaboration, thereby improving social welfare.

The ride-sharing market in China has evolved into a highly competitive and dynamic landscape. The development of the Chinese ride-sharing market is shown in Figure 1, with DiDi navigating challenges posed by both B2C platforms and aggregation platforms. Once holding a dominant 91% market share with over 550 million registered users, DiDi began expanding internationally to regions such as Taiwan, Brazil, Mexico, and New Zealand in 2017. However, its collaboration with Amap, a navigation application that launched the “Easy Travel Platform” aggregation service, shifted to competition due to strategic conflicts. Amap’s integration of multiple ride-hailing providers, including DiDi, gradually reduced its reliance on DiDi’s services. Following regulatory challenges in 2021, DiDi’s market share dropped from over 90% to 69%, creating opportunities for competitors like Amap, CaoCao, and T3 Travel to grow. Despite this, DiDi’s ride-hailing business demonstrated resilience, achieving 3.004 billion and 871 million rides in domestic and international markets, respectively, during the second quarter of 2024, with year-on-year growth rates of 12.3% and 39.1% [6]. Meanwhile, the rise of aggregation platforms from companies such as Meituan, Baidu, and Huawei has further intensified competition, with aggregation platforms now holding a 27% market share. The mobile application interfaces of Amap and DiDi are shown in Figure 2. Against the backdrop of slowing user growth, DiDi continues to compete by leveraging price, service, and technological innovations. As Amap integrates various ride-hailing providers and offers competitive pricing, DiDi focuses on its proprietary services, raising questions about whether self-operated platforms like DiDi should join or withdraw from aggregation platforms.

As shown in Figure 3, the business models of the ride-sharing market are divided into two categories: the aggregation model (such as Amap and Meituan), which relies on its own user activity to cooperate with online car-hailing platforms and matches supply and demand information, and the self-operated model, which directly recruits vehicles and drivers and operates independently [7]. According to the source of vehicles, the self-operated model can also be subdivided into two types. In the C2C model (such as Uber and DiDi), the platform does not regard drivers and vehicles as their own assets, does not pay wages or insurance to drivers, and distributes the social vehicle supply through the mobile Internet. In the B2C model (such as Caocao and T3 Travel), the platform purchases vehicles and hires drivers to ensure service quality. In the self-operated model, the online car-hailing platform directly matches drivers and passengers, while the aggregation model indirectly matches drivers and passengers and directly matches online car-hailing platforms and passengers. Self-operated platforms dominate the ride-sharing market with their high market share and awareness. With the rise of aggregation platforms such as Amap, market competition is becoming increasingly fierce. Thus, when a high-profile self-operated platform such as DiDi enters an aggregation platform, how will its market competition strategy be adjusted? This study aims to understand the impact of the emergence of aggregation platforms on the operating strategies of self-operated platforms and the resulting passenger demand, platform profits, and social welfare by exploring the influencing factors of traditional self-operated platforms entering aggregation platforms. Traditional e-commerce platforms transfer part of their profits, and entering more familiar aggregation e-commerce platforms can expand brand awareness [8]. However, in the field of ride-sharing, the access of self-operated platforms to aggregation platforms may lead to the loss of their promotion commissions and customer churn.

The following research questions are addressed in this work.

(1)

How do the aggregation platforms influence the entry strategies of self-operated platforms, and what factors drive self-operated platforms to withdraw from the market?

(2)

How do aggregation platforms impact prices, demand, and market dynamics, especially through commission ratios?

(3)

How do platform competition and cooperation shape strategies and social welfare as consumers adopt aggregation platforms?

To answer these questions, this study made several assumptions about the ride-sharing market and constructed the supply, demand, and profit functions of B2C and C2C platforms under different entry strategy combinations. Using optimization methods and Cournot game theory, this study derived equilibrium price, equilibrium profit, consumer surplus, and social welfare for both types of platforms across peak and off-peak periods. The ride-sharing market has been extensively studied by other scholars. For instance, two-period models based on the Stackelberg framework have been used to describe competition between heterogeneous ride-sharing platforms, focusing on pricing strategies and demand allocation [9]. Another study employed mathematical modeling to analyze the role of third-party platform integration, shedding light on competitive dynamics and strategies in the ride-sharing market [10]. Research on dynamic multi-regional macro-fundamental diagram models has provided congestion mitigation and sustainable travel strategies, emphasizing the role of platform design in market dynamics [11]. Additionally, investigations into the impact of immediate matching strategies on equilibrium and efficiency in two-sided markets have offered managerial insights into supply–demand coordination for ride-sharing platforms [12]. Under different market conditions, ride-hailing platforms’ cooperation and competition strategies are influenced by various factors, including market structure, platform characteristics, and consumer demand. In fragmented markets, cooperation can optimize resource utilization by sharing demand and supply, improving performance metrics such as reducing passenger pickup times and increasing driver earnings [13]. In markets with platform asymmetry, platforms with larger market shares or different fleet compositions can use cooperation to balance supply–demand gaps, particularly in asymmetric duopoly scenarios where one platform can utilize the surplus capacity of another [9,13]. Consumer demand sensitivity also plays a crucial role in strategy selection. For instance, in markets with high price sensitivity, cooperation can stabilize prices and improve service quality, benefiting both platforms and consumers [14]. Additionally, cooperation can enhance service performance by pooling resources to optimize indicators such as driver availability and passenger acceptance rates [15]. Regarding social welfare, cooperation typically leads to win–win outcomes for platforms, consumers, and societal welfare in partially covered markets. However, in fully covered markets, cooperation may reduce social welfare, necessitating evaluation based on market coverage [16]. In monopolistic markets, as the number of platforms increases, the market gradually transitions from monopoly to perfect competition. This shift limits monopolistic profits and promotes pricing strategies that are more socially beneficial. However, intensified competition may lead to market fragmentation [17]. In duopolistic environments, intense price competition often occurs, and capacity constraints can exacerbate this phenomenon [18]. While capacity sharing can alleviate some competitive pressure, it may also intensify price competition, benefiting drivers and passengers but reducing platform profits [19]. In highly competitive markets, platforms may collaborate to offer joint services, but such strategies may undermine profits in supply-side competition [20]. As a result, platforms often adopt dynamic pricing models to balance supply and demand, optimizing among consumer surplus, platform profits, and social welfare [21].

Compared to these studies, our research is quite different. First, we refine entry and exit strategies by differentiating between B2C and C2C platform types, addressing a gap in prior studies that often treat ride-sharing platforms as homogeneous entities. While works such as Stackelberg-based models explore competition, they rarely examine dynamic entry and exit strategies, particularly when aggregation platforms are involved. Second, we compute equilibrium prices and demand while incorporating consumer awareness and aggregation platform commission rates. Notably, previous studies have largely overlooked the differentiation between peak and off-peak periods, which play a critical role in shaping platform competition. Urban traffic conditions usually show the characteristics of off-peak and peak periods [22]. However, in economically developed areas, due to dense populations and high traffic demand, peak hours often last longer; in contrast, in some economically underdeveloped areas, due to small populations, traffic congestion is relatively light, and there may not even be obvious peak periods [23]. In order to more comprehensively summarize the traffic characteristics of different cities, this article not only focuses on the off-peak and peak periods of a certain city but also fully considers the situation of cities with only peak periods or only off-peak periods, so as to systematically analyze the competition and cooperation strategies of the shared travel market in these cities. By addressing these aspects, including sustainability considerations such as environmental impact and social equity, our study enriches the understanding of platform dynamics and entry strategies under aggregation platforms, providing a more nuanced perspective of market interactions and their contributions to sustainable development.

The rest of this paper is organized as follows: Section 2 reviews the literature related to the study. Section 3 describes the basic framework of the problem, makes model assumptions, and establishes a model. Section 4 analyzes the equilibrium results of the C2C platform and the B2C platform under different circumstances. Section 5 mainly conducts decision analyses of self-operated platforms based on the equilibrium results in Section 4, while Section 6 draws final conclusions and prospects.

2. Literature Review

The literature related to the research problems addressed in this study includes three areas: competition and cooperation research on the agency model and retail model; research on the selection and mode of retail channels for manufacturers (suppliers); and optimization pricing decision research for on-demand service platforms.

This study focuses on competition and cooperation between the agency model and retail model. Considering the CPS alliance, the issue of whether self-operated platforms should enter aggregation platforms is a subdivision of research on the agency model and retail model. Under the agency model, retailers (middlemen) allow manufacturers (suppliers) to directly contact consumers through retail websites or platforms but charge a commission. Manufacturers can also make some key decisions regarding retail prices. When considered a manufacturer with both traditional and electronic channels, research has shown that whether an electronic channel retailer would open an agency model depends on the spillover effects between channels [24]. Additionally, the decision of whether an intermediary opens an agency model hinges on who has more information advantage regarding products among suppliers and intermediaries as well as the spillover effects among products [25]. In the above literature, whether to open a franchise mode is decided by retailers (middlemen), while the scenario of whether self-operated platforms should enter the aggregation platform belongs to the category of the supplier’s decision to join. This category of decision making has also been studied extensively. For instance, a game-theoretic model has been established to study a supply chain involving horizontal competition between two manufacturers supplying products of different quality brands to the same retailer [26]. Moreover, research analyzing the equilibrium strategy of manufacturers’ channel selection and retailers’ product line decision making through a game theory model has elucidated how manufacturer channel choices influence retailers’ brand strategies [27]. Starting with selective marketing strategies, advantageous suppliers producing differentiated products can determine the best online models under different distribution strategies [28]. Additionally, lower advertising costs have been identified as driving factors for online retailers and third-party companies to reach franchise agreements [29]. Further analysis using a two-stage game model has examined equilibrium price, service effort, and profit under different contractual scenarios. Under demand uncertainty, intermediaries choose whether or not to adopt a store–brand partnership based on the cost advantage of the service [30]. Lastly, the channel selection problem in the electronic retail market has been studied, indicating that when a reseller and an agent seller try a new hybrid retail strategy, the hybrid retail strategy can benefit all stakeholders if the proportion of market demand through the hybrid channel is small [31]. The above studies focused on the competition and cooperation between the agency model and retail model in product supply chains without involving the decision making of ride-sharing platforms’ entry (opening).

This study is also related to the selection and mode of retail channels for manufacturers (suppliers). With the emergence of aggregation platforms, self-operated platforms can choose whether to operate through their own software or to enter an aggregation platform. This decision essentially represents a choice between different retail channel modes. There is a great deal of relevant literature in this field. For instance, research on platform private brand competition indicates that significant channel advantages and high logistics levels prompt brands to prefer resale over direct sales through self-operated channels [32]. The impact of online appointments and direct sales by manufacturers in a multi-channel retail environment has shown that while opening online channels increases profits, the coexistence of direct sales and resale does not always benefit offline retailers [33]. Moreover, studies on green supply chains operating under both offline and online channels have found that accurate information benefits both channels, while value and profit information sharing causes double marginal effects, which can be mitigated by price competition [34]. Research on channel equilibrium under decentralized control and horizontal cost sharing indicates that the lowest points exchange rate is set by retailers in the horizontal cost-sharing model, and when cost spillover and double marginalization are minimal, decentralized control achieves a higher conversion rate than centralized control [35]. Furthermore, game theory analysis of competitive relationships between manufacturers and retailers or e-commerce platforms concludes that when e-commerce platforms set appropriate commission fees, the agency sales model is the best choice for supply chain members [36].

The above studies primarily address the choice between different channel modes in supply chains with a single manufacturer. This study, however, focuses on the channel mode choice for self-operated platforms in the context of competition between platforms and the resulting market share erosion. This aspect, involving multiple competing manufacturers (suppliers) in the supply chain, has been explored by several scholars. Research on optimal channel and logistics strategies for platform brands indicates that a well-chosen channel or logistics mode can benefit brands, platforms, and consumers. For instance, optimal strategies have been shown to significantly enhance performance and market presence [37]. Moreover, the proposal of mixed-integer nonlinear programming models has revealed that the optimal sourcing strategy often involves considering multiple suppliers rather than relying on a single dominant one [38]. Further investigations into marketplace channels have demonstrated that manufacturers’ adoption of these channels increases with the level of spillovers. In contrast, e-commerce platforms show decreased willingness to engage as spillovers intensify [39]. Game theory has also been applied to analyze how commission rates, product differentiation, and production costs affect platform decisions in mixed channel structures and product quality distribution, highlighting the complex interplay between these factors [40]. When examining direct and platform channel strategies, it has been found that suppliers with the same product quality may adopt different strategies. Specifically, one supplier might sell exclusively through direct channels, while the other uses both direct and platform channels via a wholesale contract [41]. Additionally, dual-channel retailers’ strategies are influenced by various factors, such as commission rates and offline costs. High commission rates drive a preference for agent channels, whereas high offline costs diminish this preference [42]. Although the above literature considers the existence of two competing manufacturers (suppliers) in the supply chain, they both belong to the same type.

Finally, the optimal pricing research of on-demand service platforms is related to this study. Consumers frequently encounter price surges in ride-sharing services due to dynamic supply and demand conditions. This study considers C2C platforms like DiDi, which operate as two-sided platforms for on-demand services with dynamic supply and demand connecting consumers and drivers. Ideally, the platform should update prices and driver wages at any time. Several studies have explored how to optimize driver wages and prices for on-demand service platforms. Treating this as an optimal matching problem, research suggests that proportional commission contracts can effectively optimize prices and wages [43]. Dynamic optimization strategies in ride-sourcing markets indicate that broader surge pricing and commission rate ranges, coupled with incentives, yield better results [44]. Observations of Uber’s dynamic pricing system highlight its effectiveness in maximizing profits by adjusting customer prices while maintaining fixed driver commissions, which increases profits during peak demand [45]. The impact of demand patterns on platform prices, profits, and consumer surplus has also been emphasized. When demand patterns across various locations reach equilibrium, both profits and consumer surplus can be optimized [46]. Additionally, constructing a dynamic non-equilibrium ride-sharing model reveals that while dynamic wages and prices might reduce short-term profits due to increased demand and decreased supply, overall profits can rise over time [47].

This study builds upon previous literature by considering uncertainty in customer demands during off-peak periods where supply exceeds demand while also addressing peak periods where there is insufficient supply to meet demand. This study takes the minimum of the established price and supply–demand levels as the platform transaction volume while considering a proportional commission contract between the C2C platform and drivers and a fixed commission contract between B2C platforms and drivers.

3. The Model

3.1. Model Description

Consider the following background: in the ride-sharing industry, a supply unit represents a driver, and a demand unit represents a consumer. Self-operated platforms connect drivers and consumers, set prices for consumers, and pay commissions or wages to drivers who complete travel services. There are multiple self-operated platforms in the ride-sharing market, as well as an aggregation platform. These self-operated platforms provide alternative travel services to consumers through their own software channels, known as independent channels. Additionally, some of these ride-sharing platforms enter the aggregation platform to obtain orders, which is referred to as public channel acquisition. Ride-sharing platforms can be divided into two categories: C2C platforms and B2C platforms. The C2C platform establishes commission contracts with drivers where they must give up part of their earnings to the C2C platform, while B2C platforms prepay salaries (r) at the beginning of each month so that salaries are sunk costs that do not affect the choice of entering a particular market; therefore, when constructing profit functions for B2C platforms, drivers’ wages are not given consideration. In addition, in order to take into account the traffic conditions in different cities, that is, the differences between peak and off-peak periods, this article generally analyzes the differences between peak and off-peak periods in cities and analyzes the strategic choices of traditional ride-sharing platforms in different periods.

The competition among stakeholders has an impact on their strategy for choosing to enter the aggregation platform [45]. The model assumes that the ride-sharing market only contains one C2C platform ($i=1$) and one B2C platform ($i=2$) as well as an aggregation platform. When the aggregation platform has not yet launched its taxi service, the price set by ride-sharing platforms $i$ is $P_i$, which is the fee that drivers charge to consumers after completing a unit of travel service. The demand function and supply function of self-operated platforms $i$ are, respectively:

$$D_i=A_i-P_i+\theta P_j;0<\theta <1,i=\left\{\begin{array}{c}\mathrm{1,2}\end{array}\right\},j=3-i$$

(1)

$$S_i=-B_i+P_i-\beta P;0<\beta <1,i=\left\{\begin{array}{c}\mathrm{1,2}\end{array}\right\},j=3-i$$

(2)

Formulas (1) and (2) consider the differentiation and substitutability of travel services provided by different self-operated platforms. The cross-price sensitivity parameters $\theta$ and $\beta$, respectively, represent the impact of the price of one self-operated platform on the demand and supply of another self-operated platform. $A_i$ represents the demand base of ride-sharing platforms $i$, that is, potential market share. $-B_i$ represents the supply quantity when the price is 0 for ride-sharing platforms, while $i$, $\theta$, $\beta$, $A_i$, and $-B_i$ are all exogenous variables.

The game sequence of the model is as follows. In the first stage, the aggregation platform chooses the promotion commission rate $\rho \left(0<\rho <1\right)$. Based on this, each self-operated platform decides whether to enter Amap.

In the second stage, the C2C platform determines the price and commission rate for providing unit travel services, namely $P_1$ and $\alpha \left(0<\alpha <1\right)$. The B2C platform decides on the price $P_2$ for completing unit travel services. Finally, consumers choose their preferred ordering channel to meet their needs.

This study focuses on exploring the intensity of competition among self-operated platforms as well as the impact of the awareness of the aggregation platform on the entry strategy of self-operated platforms. In order to clarify the model, both $\alpha$ and $\rho$ are considered exogenous variables, while self-operated platforms only need to consider decision variables $T_i$ and $P_i$.

If the C2C platform chooses to enter the aggregation platform, then the C2C platform can obtain orders and provide travel services from both independent channels and public channels. If consumers choose the former to meet their travel needs, then the revenue of the C2C platform is $P_1\alpha$, and the driver’s revenue is $P_1\left(1-\alpha \right)$. If consumers choose the latter to meet their travel needs, then the revenue of the C2C platform is $P_1\left(\alpha -\rho \right)$, the driver’s revenue is $P_1\left(1-\alpha \right)$, and the aggregation platform’s revenue is $P_1\rho$. If B2C platforms choose to enter an aggregation platform, then they can also obtain orders from both independent channels and public channels. Therefore, if consumers choose to use a B2C platform for their travel needs through independent channels, then that platform’s income will be $P_2$. If consumers choose to use the public channel instead, then the B2C platform’s income will be $P_2\left(1-\rho \right)$, while that of the aggregation platform will be $P_2\rho$. The income of each relevant participant can be seen in

Table 1. Revenue of relevant participants.

	C2C Platform			B2C Platform
	Drivers	C2C Platform	Aggregation Platform	Drivers	B2C Platform	Aggregation Platform
Independent channels	$P_1\left(1-\alpha \right)$	$P_1\alpha$	——	r	$P_2$	——
Public channels	$P_1\left(1-\alpha \right)$	$P_1\left(\alpha -\rho \right)$	$P_1\rho$	r	$P_2\left(1-\rho \right)$	$P_2\rho$

.

The solution to the model adopts the reverse induction method, starting from the strategy and price competition of whether self-operated platforms in the final stage choose to enter the aggregation platform. Based on whether the two types of platforms enter the aggregation platform, their strategy sets ($T_1,T_2$) can be divided into four categories: both types of platforms choose the no-entry strategy (R, R); the C2C platform chooses the entry strategy, while the B2C platform chooses the no-entry strategy (E, R); the C2C platform chooses the no-entry strategy, while the B2C platform chooses the entry strategy (R, E); and both types of platforms choose the entry strategy (E, E). In Section 3, different strategies, demand, supply, and profit functions for both types of platforms are established. Based on optimization methods and game theory via the Cournot equilibrium analysis approach, this study investigates under what circumstances each platform will choose to enter the aggregation platform.

3.2. Notation and Assumptions

We make the following assumptions as the basis of this paper:

Assumption 1.

The marginal cost of the order is zero. It describes a situation in which additional units can be produced without increasing total production costs. The marginal cost of supplying another order unit can be zero when the order is noncompetitive.

Assumption 2.

Due to the fact that C2C and B2C platforms typically offer high-end, mid-range, and low-end vehicle models and services, price-sensitive consumers tend to choose lower-priced and lower-quality services regardless of the platform, while consumers seeking high-quality services behave similarly [48]. Therefore, we assume that orders from the ride-hailing platform are homogeneous. This indicates that C2C platforms provide the same orders as those offered by B2C platforms and aggregation platforms.

Assumption 3.

Same as Assumption 2, there is no difference in the drivers’ service level. This indicates that, regardless of whether it is a traditional travel platform or an integrated travel platform, the services provided by its drivers are indistinguishable.

Assumption 4.

Suppose the ride-sharing market only consists of one C2C platform, one B2C platform, and one aggregation platform. In the analysis below, we found that the equilibrium results after adding multiple platforms are similar to the results of only one C2C platform and only one B2C platform. For specific explanations, please see Appendix A.

Assumption 5.

The model is a static rather than a dynamic game. This means that we model the ride-hailing market at a stationary equilibrium state without considering the system dynamics. At this equilibrium, passengers choose between platforms and the integrator based on the equilibrium price of these traditional platforms and the aggregation platforms.

Assumption 6.

When traditional platforms choose entry strategies, the prices of travel services set on the two channels are equal. This is because the model assumes that consumers are purely rational. If the prices on the two channels are not equal, then all consumers will choose channels with lower prices.

The following notations were used to develop the proposed model (

Table 2. Description of variables. (* indicates that the variable is in equilibrium).

Variable Type	Variable Name	Variable Definition
Exogenous variable	$\alpha$	Commission rate of the C2C platform
	$\beta$	Cross-price sensitivity parameter in the supply function
	$\theta$	Cross-price sensitivity parameter in the demand function
	$\rho$	Promotion commission rate of the aggregation platform
	$\phi$	When the aggregation platform has a capacity source, its awareness in the field of ride-sharing
	$A_i$	When the aggregation platform has no taxi-hailing business, the market basis of the self-operated platforms i
	$-B_i$	When the integrated travel platform has no taxi service and the price is zero, the supply of the self-operated platforms i
	r	Fixed salary for B2C platform drivers
	m	When both types of platforms are stationed, the proportion of consumers who choose the C2C platform on the aggregation platform
Decision variable	$T_i$	Whether the self-operated platforms i take the decision to enter the aggregation platform
	$P_i$	Prices set by self-operated platforms i
	$P_i^{\left(T_1,T_2\right)\ast }$	The equilibrium price of the traditional travel-sharing platforms i under the strategy set $(T_1,T_2)$
Dependent variable	$D_i$	When the aggregation platform has no taxi service, the demand of the traditional travel-sharing platforms i
	$S_i$	When the aggregation platform has no taxi service, the supply of the traditional travel-sharing platforms i
	$D_i^j$	The demand of ride-sharing platforms i in channel j
	${\pi }_i^{\left(T_1,T_2\right)}/{\pi }_i^{\left(T_1,T_2\right)\ast }$	Profit/balanced profit of the self-operated platforms i under the strategy collection $(T_1,T_2)$
	$D_i^{\left(T_1,T_2\right)}/D_i^{\left(T_1,T_2\right)\ast }$	Demand/balanced demand of the self-operated platforms i under the strategy collection $(T_1,T_2)$
	$S_i^{\left(T_1,T_2\right)}/S_i^{\left(T_1,T_2\right)\ast }$	Supply/balanced supply of self-operated platforms i under strategy collection $(T_1,T_2)$
	${CS}_i^{\left(T_1,T_2\right)\ast }$	Equilibrium consumer surplus of self-operated platforms under strategy collection $(T_1,T_2)$
	${SW}_i^{\left(T_1,T_2\right)\ast }$	Equilibrium social welfare when the policy set is $(T_1,T_2)$

).

4. Balanced Analysis

The transaction volume is determined by the minimum of demand and supply at a given price. For example, during a certain period, if there are M drivers and N consumers in a certain region on the C2C platform, and any driver can only serve one consumer during that period, then the transaction volume will be min {M, N}. If M < N, it means that the C2C platform is in short supply; if N < M, it means that the C2C platform is oversupplied. If both the C2C platform and B2C platforms are in short supply, then the ride-sharing market is in the peak period; if both platforms are oversupplied, then the ride-sharing market is in the off-peak period.

In this section, we establish the demand, supply, and profit functions of two types of self-operated platforms under different strategies. Based on optimization methods and game theory, we derive the equilibrium prices, equilibrium profits, consumer surplus, and social welfare of the two platforms when the ride-sharing market is in different periods.

4.1. Both Types of Platforms Are Not Stationed in (R, R)

When both types of self-operated platforms choose the no-entry strategy, that is, the strategy set is (R, R), then the travel service prices set by the two types of platforms are $P_1$ and $P_2$, respectively. The facing corresponding demand functions are:

$$\left\{\begin{array}{c}{D}_1^{\left(R,R\right)}=D_1=A_1-P_1+\theta P_2\\ D_2^{\left(R,R\right)}=D_2=A_2-P_2+\theta P_1\end{array}\right.$$

(3)

The facing supply functions are, respectively:

$$\left\{\begin{array}{c}{S}_1^{\left(R,R\right)}=S_1=-B_1+P_1-\beta P_2\\ S_2^{\left(R,R\right)}=S_2=-B_2+P_2-\beta P_1\end{array}\right.$$

(4)

The profit functions of the two types of platforms are, respectively:

$$\left\{\begin{array}{c}{\pi }_1^{\left(R,R\right)}=\alpha P_1{D}_1^{\left(R,R\right)}\\ {\pi }_2^{\left(R,R\right)}=P_2{D}_2^{\left(R,R\right)}\end{array}\right.$$

(5)

Lemma 1.

When the market is in the off-peak period, that is, when supply exceeds demand, the equilibrium prices for the two types of self-operated platforms are:

$$\begin{array}{c}{P}_1^{(R,R{)}^{*}}=\left\{\begin{array}{ccc}{P}_1^{\left(R,R\right)M},& \underset{\_}{P_1^{\left(R,R\right)}}\le P_1^{\left(R,R\right)M}\le {\displaystyle \frac{A_1+\theta A_2}{1-{\theta }^2}}& \\ \underset{\_}{P_1^{\left(R,R\right)}},& \mathrm{if} \mathrm{not}& \end{array}\right.\\ P_2^{(R,R{)}^{*}}=\left\{\begin{array}{ccc}{P}_2^{\left(R,R\right)M},& \underset{\_}{P_2^{\left(R,R\right)}}\le P_2^{\left(R,R\right)M}\le {\displaystyle \frac{\theta A_1+A_2}{1-{\theta }^2}}& \\ \underset{\_}{P_2^{\left(R,R\right)}},& \mathrm{if} \mathrm{not}& \end{array}\right.\end{array}$$

(6)

where  $\left\{\begin{array}{c}{P}_1^{\left(R,R\right)M}={\displaystyle \frac{2A_1+\theta A_2}{4-{\theta }^2}},\\ P_2^{\left(R,R\right)M}={\displaystyle \frac{\theta A_1+2A_2}{4-{\theta }^2}}\end{array}\right.;\left\{\begin{array}{c}\underset{\_}{P_1^{\left(R,R\right)}}={\displaystyle \frac{2\left(A_1+B_1\right)+\left(\beta +\theta \right)\left(A_2+B_2\right)}{4-{\left(\beta +\theta \right)}^2}}\\ \underset{\_}{P_2^{\left(R,R\right)}}={\displaystyle \frac{\left(\beta +\theta \right)\left(A_1+B_1\right)+2\left(A_2+B_2\right)}{4-{\left(\beta +\theta \right)}^2}}\end{array}\right.$.

When the market is in its peak period, that is, when demand exceeds supply, the equilibrium prices for the two types of platforms are:

$$P_1^{\left(R,R\right)\mathrm{\ast }}=\underset{\_}{P_1^{\left(R,R\right)}},P_2^{\left(R,R\right)\mathrm{\ast }}=\underset{\_}{P_2^{\left(R,R\right)}}$$

(7)

Proof of Lemma 1.

When the ride-sharing market is in its off-peak period, according to the negative values of ${\displaystyle \frac{{\partial }^2{\pi }_1^{\left(R,R\right)}}{\partial P_1^2}}=-2\alpha$ and ${\displaystyle \frac{{\partial }^2{\pi }_2^{\left(R,R\right)}}{\partial P_2^2}}=-2$, it can be known that ${\pi }_i^{\left(R,R\right)}$ is a concave function with a unique maximum value of approximately $P_i$. According to the first-order optimality condition, we can obtain:

$$\left\{\begin{array}{c}{\displaystyle \frac{\partial {\pi }_1^{\left(R,R\right)}}{\partial P_1}}=\alpha \left(A_1-2P_1+\theta P_2\right)=0\hfill \\ {\displaystyle \frac{\partial {\pi }_2^{\left(R,R\right)}}{\partial P_2}}=A_2-2P_2+\theta P_1=0\hfill \end{array}\right.$$

Therefore, by combining the above two equations, we can determine that the maximum value of the profit function is at point $P_1^{\left(R,R\right)M}={\displaystyle \frac{2A_1+\theta A_2}{4-{\theta }^2}}$, $P_2^{\left(R,R\right)M}={\displaystyle \frac{\theta A_1+2A_2}{4-{\theta }^2}}$. Furthermore, the prices of both platforms during the off-peak period need to satisfy certain conditions:

$$\left\{\begin{array}{c}0\le D_1^{\left(R,R\right)}\le S_1^{\left(R,R\right)}\\ 0\le D_2^{\left(R,R\right)}\le S_2^{\left(R,R\right)}\end{array}\right.\iff \left\{\begin{array}{c}\underset{\_}{P_1^{\left(R,R\right)}}\le P_1\le {\displaystyle \frac{A_1+\theta A_2}{1-{\theta }^2}}\\ \underset{\_}{P_2^{\left(R,R\right)}}\le P_2\le {\displaystyle \frac{\theta A_1+A_2}{1-{\theta }^2}}\end{array}\right.$$

where

$$\begin{array}{c}\underset{\_}{P_1^{\left(R,R\right)}}={\displaystyle \frac{2\left(A_1+B_1\right)+\left(\beta +\theta \right)\left(A_2+B_2\right)}{4-{\left(\beta +\theta \right)}^2}}\\ \underset{\_}{P_2^{\left(R,R\right)}}={\displaystyle \frac{\left(\beta +\theta \right)\left(A_1+B_1\right)+2\left(A_2+B_2\right)}{4-{\left(\beta +\theta \right)}^2}}\end{array}$$

Thus, during the off-peak period, the equilibrium price for both types of platforms is:

$$\begin{array}{c}{P}_1^{(R,R{)}^{*}}=\left\{\begin{array}{ccc}{P}_1^{\left(R,R\right)M},& \underset{\_}{P_1^{\left(R,R\right)}}\le P_1^{\left(R,R\right)M}\le {\displaystyle \frac{A_1+\theta A_2}{1-{\theta }^2}}& \\ \underset{\_}{P_1^{\left(R,R\right)}},& \mathrm{if} \mathrm{not}& \end{array}\right.\\ P_2^{(R,R{)}^{*}}=\left\{\begin{array}{ccc}{P}_2^{\left(R,R\right)M},& \underset{\_}{P_2^{\left(R,R\right)}}\le P_2^{\left(R,R\right)M}\le {\displaystyle \frac{\theta A_1+A_2}{1-{\theta }^2}}& \\ \underset{\_}{P_2^{\left(R,R\right)}},& \mathrm{if} \mathrm{not}& \end{array}\right.\end{array}$$

Similarly, we can deduce the equilibrium price when the market is at its peak period, and thus we can draw the conclusion of Lemma 1.

According to Lemma 1, when the market is in the off-peak period, substituting Formula (6) into Formulas (3) and (5), respectively, can make it possible to obtain equilibrium demand quantity $D_1^{\left(R,R\right)\ast }$, $D_2^{\left(R,R\right)\ast }$ and equilibrium profit ${\pi }_1^{\left(R,R\right)\ast }$, ${\pi }_2^{\left(R,R\right)\ast }$ during the off-peak period. The consumer surplus of the platform is:

$$C{S}_i^{\left(R,R\right)\ast }={\displaystyle \frac{1}{2}}\left(P_i^{\left(R,R\right)max}-P_i^{\left(R,R\right)\ast }\right)D_i^{\left(R,R\right)\ast }$$

(8)

where $A_i-P_i^{\left(R,R\right)\max }+\theta P_j^{\left(R,R\right)\mathrm{\ast }}=0,i=\left\{\begin{array}{c}\mathrm{1,2}\end{array}\right\},j=3-i$.

Social welfare is the sum of the total profits and total consumer surplus for two types of platforms as well as the surplus for drivers and the profit of the aggregation platform. The specific formula is as follows:

$$S{W}^{\left(R,R\right)\mathrm{\ast }}=\sum _{i=1}^2{\displaystyle \frac{1}{2}}\left(P_i^{\left(R,R\right)max}-P_i^{\left(R,R\right)min}+p_i^{\left(R,R\right)\mathrm{\ast }}-p_i^{\left(R,R\right)l}\right)D_i^{\left(R,R\right)\mathrm{\ast }}+\alpha P_1^{\left(R,R\right)\mathrm{\ast }}{D}_1^{\left(R,R\right)\mathrm{\ast }}+P_2^{\left(R,R\right)\mathrm{\ast }}{D}_2^{\left(R,R\right)\mathrm{\ast }}$$

(9)

where $-{\mathrm{B}}_i+{\mathrm{P}}_i^{\left(R,R\right)min}-\beta P_j^{\left(R,R\right)\mathrm{\ast }}=0,-{\mathrm{B}}_i+P_i^{\left(R,R\right)l}-\beta P_j^{\left(R,R\right)\mathrm{\ast }}=D_i^{\left(R,R\right)\mathrm{\ast }},i=\left\{\begin{array}{c}\mathrm{1,2}\end{array}\right\},j=3-i$.

When the market is in its peak period, substituting Formula (7) into Formulas (3) and (4), respectively, can reveal that the equilibrium supply and demand of ride-sharing platforms are equal. Therefore, substituting Formula (7) into Formulas (5), (8) and (9) can make it possible to obtain the equilibrium profit, consumer surplus, and social welfare of both types of platforms during the peak period.

4.2. Only C2C Platforms Are Stationed in (E, R)

The C2C platform selects an entry strategy and sets the travel service price at $P_1$ for both channels. The B2C platform chooses a no-entry strategy and only obtains orders from its own channels, setting the travel service price at $P_2$. The supply functions faced by these two self-operated platforms are $S_1^{\left(E,R\right)}=S_1$ and $S_2^{\left(E,R\right)}=S_2$, respectively.

Due to the certain level of awareness of the aggregation platform in the ride-sharing industry, several consumers ($\phi D_1$) from the C2C platform will transfer to the aggregation platform at an established price level. Simultaneously, several consumers ($\phi D_2$) from the B2C platform will also transfer to the aggregation platform, with $\phi \in \left(\mathrm{0,1}\right)$. Therefore, on the aggregation platform, these consumers choose the C2C platform to meet their needs. The demand function faced by the C2C platform on its own channel is $D_1^o=\left(1-\phi \right)D_1$, while that faced on public channels is $D_1^c=\phi \left(D_1+D_2\right)$. The demand function faced by B2C platforms on their own channels is $D_2^o=\left(1-\phi \right)D_2$. The total demand functions for both types of platforms are:

$$\left\{\begin{array}{c}{D}_1^{\left(E,R\right)}=D_1^o+D_1^c=D_1+\phi D_2\hfill \\ D_2^{\left(E,R\right)}=D_2^o=(1-\phi )D_2\hfill \end{array}\right.$$

(10)

The profit functions of the two types of platforms are, respectively:

$$\left\{\begin{array}{c}{\pi }_1^{\left(E,R\right)}=\alpha P_1{D}_1^o+\left(\alpha -\rho \right)P_1{D}_1^c\hfill \\ {\pi }_2^{\left(E,R\right)}=P_2{D}_2^o\hfill \end{array}\right.$$

(11)

Lemma 2.

When the market is in the off-peak period, that is, when supply exceeds demand, the equilibrium prices for the two types of self-operated platforms are:

$$\begin{array}{c}{P}_1^{(E,R{)}^{*}}=\left\{\begin{array}{ccc}{P}_1^{\left(E,R\right)M},& \underset{\_}{P_1^{\left(E,R\right)}}\le P_1^{\left(E,R\right)M}\le {\displaystyle \frac{A_1+\theta A_2}{1-{\theta }^2}}& \\ \underset{\_}{P_1^{\left(E,R\right)}},& \mathrm{if} \mathrm{not}& \end{array}\right.\\ P_2^{(E,R{)}^{*}}=\left\{\begin{array}{ccc}{P}_2^{\left(E,R\right)M},& \underset{\_}{P_2^{\left(E,R\right)}}\le P_2^{\left(E,R\right)M}\le {\displaystyle \frac{\theta A_1+A_2}{1-{\theta }^2}}& \\ \underset{\_}{P_2^{\left(E,R\right)}},& \mathrm{if} \mathrm{not}& \end{array}\right.\end{array}$$

where

$$\left\{\begin{array}{c}{P}_1^{\left(E,R\right)M}={\displaystyle \frac{2\left(\alpha -\rho \phi \right)A_1+\left[\theta \left(\alpha -\rho \phi \right)+\phi \left(\alpha -\rho \right)\right]A_2}{\left(4-{\theta }^2\right)\left(\alpha -\rho \phi \right)-3\theta \phi \left(\alpha -\rho \right)}}\\ P_2^{\left(E,R\right)M}={\displaystyle \frac{\theta \left(\alpha -\rho \phi \right)A_1+\left[2\left(\alpha -\rho \phi \right)-\theta \phi \left(\alpha -\rho \right)\right]A_2}{\left(4-{\theta }^2\right)\left(\alpha -\rho \phi \right)-3\theta \phi \left(\alpha -\rho \right)}}\end{array}\right.$$

$$\left\{\begin{array}{c}{P}_1^{\left(E,R\right)}={\displaystyle \frac{\left(-2+\phi \right)\left(A_1+\phi A_2+B_1\right)-\left(\beta +\theta -\phi \right)\left(\left(1-\phi \right)A_2+B_2\right)}{\left(\beta +\theta \left(1-\phi \right)\right)\left(\beta +\theta -\phi \right)-\left(-2+\phi \right)\left(-2+\phi \theta \right)}}\\ P_2^{\left(E,R\right)}=-{\displaystyle \frac{\left(\beta +\theta -\theta \phi \right)\left(A_1+B_1\right)+\left(2-2\phi +\beta \phi \right)A_2+\left(2-\theta \phi \right)B_2}{\left(-2+\beta +\theta \right)\left(2+\beta +\theta -\phi -\theta \phi \right)}}\end{array}\right.$$

When the market is in its peak period, that is, when demand exceeds supply, the equilibrium prices for the two platforms are $P_1^{\left(E,R\right)\ast }=\underset{\_}{P_1^{\left(E,R\right)}}$ and  $P_2^{\left(E,R\right)\ast }=\underset{\_}{P_2^{\left(E,R\right)}}$, respectively.

Proof of Lemma 2.

According to the negative values of ${\displaystyle \frac{{\partial }^2{\pi }_1^{\left(E,R\right)}}{\partial P_1^2}}=-2\alpha \left(1-\phi \right)+2\left(\theta -1\right)\left(\alpha -\rho \right)\phi$ and ${\displaystyle \frac{{\partial }^2{\pi }_2^{\left(E,R\right)}}{\partial P_2^2}}=-2\left(1-\phi \right)$, it can be known that ${\pi }_i^{\left(E,R\right)}$ is a concave function with a unique maximum value about $P_i$. According to the first-order optimality condition, we can obtain:

$$\left\{\begin{array}{c}{\displaystyle \frac{\partial {\pi }_1^{\left(E,R\right)}}{\partial {\mathrm{P}}_1}}=(\alpha -\rho \phi )(A_1-2{\mathrm{P}}_1+\theta {\mathrm{P}}_2)+(\alpha -\rho )\phi (A_2-{\mathrm{p}}_2+2\theta {\mathrm{P}}_1)=0\hfill \\ {\displaystyle \frac{\partial {\pi }_2^{\left(E,R\right)}}{\partial {\mathrm{P}}_2}}=(1-\phi )(A_2-2{\mathrm{P}}_2+\theta {\mathrm{P}}_1)=0\hfill \end{array}\right.$$

Therefore, the maximum point of the possible profit function is

$$\left\{\begin{array}{c}{P}_1^{\left(E,R\right)M}={\displaystyle \frac{2\left(\alpha -\rho \phi \right)A_1+\left[\theta \left(\alpha -\rho \phi \right)+\phi \left(\alpha -\rho \right)\right]A_2}{\left(4-{\theta }^2\right)\left(\alpha -\rho \phi \right)-3\theta \phi \left(\alpha -\rho \right)}}\\ P_2^{\left(E,R\right)M}={\displaystyle \frac{\theta \left(\alpha -\rho \phi \right)A_1+\left[2\left(\alpha -\rho \phi \right)-\theta \phi \left(\alpha -\rho \right)\right]A_2}{\left(4-{\theta }^2\right)\left(\alpha -\rho \phi \right)-3\theta \phi \left(\alpha -\rho \right)}}\end{array}\right.$$

When the ride-sharing market is in its off-peak period, there are conditions that need to be met for the prices of both platforms:

$$\left\{\begin{array}{c}0\le D_1^{\left(E,R\right)}\le S_1^{\left(E,R\right)}\\ 0\le D_2^{\left(E,R\right)}\le S_2^{\left(E,R\right)}\end{array}\right.\iff \left\{\begin{array}{c}\underset{\_}{P_1^{\left(E,R\right)}}\le P_1\le {\displaystyle \frac{A_1+\theta A_2}{1-{\theta }^2}}\\ \underset{\_}{P_2^{\left(E,R\right)}}\le P_2\le {\displaystyle \frac{\theta A_1+A_2}{1-{\theta }^2}}\end{array}\right.$$

where

$$\left\{\begin{array}{c}\underset{\_}{P_1^{\left(E,R\right)}}={\displaystyle \frac{\left(-2+\phi \right)\left(A_1+\phi A_2+B_1\right)-\left(\beta +\theta -\phi \right)\left(\left(1-\phi \right)A_2+B_2\right)}{\left(\beta +\theta \left(1-\phi \right)\right)\left(\beta +\theta -\phi \right)-\left(-2+\phi \right)\left(-2+\phi \theta \right)}}\\ \underset{\_}{P_2^{\left(E,R\right)}}=-{\displaystyle \frac{\left(\beta +\theta -\theta \phi \right)\left(A_1+B_1\right)+\left(2-2\phi +\beta \phi \right)A_2+\left(2-\theta \phi \right)B_2}{\left(-2+\beta +\theta \right)\left(2+\beta +\theta -\phi -\theta \phi \right)}}\end{array}\right.$$

Therefore, the equilibrium price of the two types of platforms is as follows:

$$\begin{array}{c}{P}_1^{(E,R{)}^{*}}=\left\{\begin{array}{ccc}{P}_1^{\left(E,R\right)M},& \underset{\_}{P_1^{\left(E,R\right)}}\le P_1^{\left(E,R\right)M}\le {\displaystyle \frac{A_1+\theta A_2}{1-{\theta }^2}}& \\ \underset{\_}{P_1^{\left(E,R\right)}},& \mathrm{if} \mathrm{not}& \end{array}\right.\\ P_2^{(E,R{)}^{*}}=\left\{\begin{array}{ccc}{P}_2^{\left(E,R\right)M},& \underset{\_}{P_2^{\left(E,R\right)}}\le P_2^{\left(E,R\right)M}\le {\displaystyle \frac{\theta A_1+A_2}{1-{\theta }^2}}& \\ \underset{\_}{P_2^{\left(E,R\right)}},& \mathrm{if} \mathrm{not}& \end{array}\right.\end{array}$$

Similarly, we can deduce the equilibrium price when the market is at its peak period, and thus we can draw the conclusion of Lemma 2.

According to Lemma 2, substituting the equilibrium prices of the two types of self-operated platforms into Formulas (10) and (11), respectively, can make it possible to obtain the equilibrium demand $D_1^{\left(E,R\right)\ast }$, $D_2^{\left(E,R\right)\ast }$ and equilibrium profit ${\pi }_1^{\left(E,R\right)\ast }$, ${\pi }_2^{\left(E,R\right)\ast }$.

The remaining consumers and social welfare of platform are, respectively:

$$C{S}_i^{\left(E,R\right)\ast }={\displaystyle \frac{1}{2}}\left(P_i^{\left(E,R\right)max}-P_i^{\left(E,R\right)\ast }\right)D_i^{\left(E,R\right)\ast }$$

$$S{W}^{(E,R{)}^{*}}=\sum _1^2{\displaystyle \frac{1}{2}}\left(P_i^{\left(E,R\right)\mathrm{m}\mathrm{a}\mathrm{x}}-P_i^{\left(E,R\right)\mathrm{m}\mathrm{i}\mathrm{n}}+P_i^{(E,R{)}^{*}}-P_i^{\left(E,R\right)l}\right)D_i^{(E,R{)}^{*}}+\alpha P_1^{(E,R{)}^{*}}{D}_1^{(E,R{)}^{*}}+P_2^{(E,R{)}^{*}}{D}_2^{(E,R{)}^{*}}$$

where

$$A_i-{\mathrm{P}}_i^{\left(E,R\right)\mathrm{m}\mathrm{a}\mathrm{x}}+\theta {\mathrm{P}}_j^{\left(E,R\right)\ast }=0,-{\mathrm{B}}_i+{\mathrm{P}}_i^{\left(E,R\right)\mathrm{m}\mathrm{i}\mathrm{n}}-\beta {\mathrm{P}}_j^{\left(E,R\right)\ast }=0,$$

$$-{\mathrm{B}}_i+{\mathrm{P}}_i^{\left(E,R\right)l}-\beta {\mathrm{P}}_j^{\left(E,R\right)\ast }=D_i^{\left(E,R\right)\ast }, i=\left\{\begin{array}{c}\mathrm{1,2}\end{array}\right\},j=3-i$$

4.3. Only B2C Platforms Are Stationed in (R, E)

The C2C platform chooses the no-entry strategy and sets the travel service price to $P_1$. The B2C platform chooses the entry strategy and sets the travel service prices on both channels to $P_2$. The supply functions faced by the two self-operated platforms are $S_1^{\left(R,E\right)}=S_1$ and $S_2^{\left(R,E\right)}=S_2$, respectively. In this case, there will be $\phi D_1$ consumers originally belonging to the C2C platform who will transfer to the aggregation platform, while $\phi D_2$ consumers originally belonging to the B2C platform will also transfer to the aggregation platform so as to choose the B2C platform to meet their travel needs in the aggregation platform where $\phi \in \left(\mathrm{0,1}\right)$. Thus, the demand function faced by the C2C platform on its own channel is $D_1^o=\left(1-\phi \right)D_1$, the demand function faced by the B2C platform on its own channel is $D_2^o=\left(1-\phi \right)D_2$, and the demand function faced on public channels is $D_2^c=\phi \left(D_1+D_2\right)$. The total demand functions faced by these two platforms are, respectively:

$$\left\{\begin{array}{c}{D}_1^{\left(R,E\right)}=D_1^o=(1-\phi )D_1\hfill \\ D_2^{\left(R,E\right)}=D_2^o+D_2^c=D_2+\phi D_1\hfill \end{array}\right.$$

(12)

The profit functions of the two types of platforms are, respectively:

$$\left\{\begin{array}{c}{\pi }_1^{\left(R,E\right)}=\alpha P_1{D}_1^o\hfill \\ {\pi }_2^{\left(R,E\right)}=P_2{D}_2^o+P_2(1-\rho )D_2^c\hfill \end{array}\right.$$

(13)

Lemma 3.

When the ride-sharing market is in the off-peak period, that is, when supply exceeds demand, the equilibrium prices for the two types of self-operated platforms are:

$$\begin{array}{c}{P}_1^{(R,E{)}^{*}}=\left\{\begin{array}{ccc}{P}_1^{\left(R,E\right)M},& \underset{\_}{P_1^{\left(R,E\right)}}\le P_1^{\left(R,E\right)M}\le {\displaystyle \frac{A_1+\theta A_2}{1-{\theta }^2}}& \\ \underset{\_}{P_1^{\left(R,E\right)}},& \mathrm{if} \mathrm{not}& \end{array}\right.\\ P_2^{(R,E{)}^{*}}=\left\{\begin{array}{ccc}{P}_2^{\left(R,E\right)M},& \underset{\_}{P_2^{\left(R,E\right)}}\le P_2^{\left(R,E\right)M}\le {\displaystyle \frac{\theta A_1+A_2}{1-{\theta }^2}}& \\ \underset{\_}{P_2^{\left(R,E\right)}},& \mathrm{if} \mathrm{not}& \end{array}\right.\end{array}$$

where

$$\left\{\begin{array}{c}{P}_1^{\left(R,E\right)M}={\displaystyle \frac{\theta \left(1-\rho \phi \right)A_2+\left[2\left(1-\rho \phi \right)-\theta \phi \left(1-\rho \right)\right]A_1}{\left(4-{\theta }^2\right)\left(1-\rho \phi \right)-3\theta \phi \left(1-\rho \right)}}\hfill \\ P_2^{\left(R,E\right)M}={\displaystyle \frac{\left[\theta \left(1-\rho \phi \right)+\phi \left(1-\rho \right)\right]A_1+2\left(1-\rho \phi \right)A_2}{\left(4-{\theta }^2\right)\left(1-\rho \phi \right)-3\theta \phi \left(1-\rho \right)}}\hfill \end{array}\right.;$$

$$\left\{\begin{array}{c}\underset{\_}{P_1^{\left(R,E\right)}}={\displaystyle \frac{\left(-2+\theta \phi \right)\left(\left(1-\phi \right)A_1+B_1\right)-\left(\beta +\theta \left(1-\phi \right)\right)\left(\phi A_1+A_2+B_2\right)}{\left(\beta +\theta \left(1-\phi \right)\right)\left(\beta +\theta -\phi \right)-\left(-2+\phi \right)\left(-2+\phi \theta \right)}}\hfill \\ \underset{\_}{P_2^{\left(R,E\right)}}={\displaystyle \frac{-\left(\beta +\theta \right)\left(A_1+B_1\right)+\left(\phi -2\right)\left(A_2+B_2\right)+\phi \left(B_1+\left(\beta +\theta -1\right)A_1\right)}{\left(-2+\beta +\theta \right)\left(2+\beta +\theta -\phi -\theta \phi \right)}}\hfill \end{array}\right.$$

When the market is in its peak period, that is, when demand exceeds supply, the equilibrium prices for the two types of platforms are $P_1^{\left(R,E\right)\ast }=\underset{\_}{P_1^{\left(R,E\right)}}$ and $P_2^{\left(R,E\right)\ast }=\underset{\_}{P_2^{\left(R,E\right)}}$, respectively.

Proof of Lemma 3.

Since both ${\displaystyle \frac{{\partial }^2{\pi }_1^{\left(R,E\right)}}{\partial P_1^2}}=-2\alpha \left(1-\phi \right)$ and ${\displaystyle \frac{{\partial }^2{\pi }_2^{\left(R,E\right)}}{\partial {\mathrm{P}}_2^2}}=-2\left(1-\phi \right)+2\left(1-\rho \right)\phi \left(\theta -1\right)$ are negative, it can be inferred that ${\pi }_i^{\left(R,E\right)}$ is a concave function with a unique maximum value with respect to $P_i$. According to the first-order optimal condition, we can obtain:

$$\left\{\begin{array}{c}{\displaystyle \frac{\partial {\pi }_1^{\left(R,E\right)}}{\partial P_1}}=\alpha \left(1-\phi \right)\left(A_1-2P_1+\theta P_2\right)=0\hfill \\ {\displaystyle \frac{\partial {\pi }_2^{\left(R,E\right)}}{\partial P_2}}=\left(1-\rho \phi \right)\left(A_2-2P_2+\theta P_1\right)+\left(1-\rho \right)\phi \left(A_1-P_1+2\theta P_2\right)=0\hfill \end{array}\right.$$

Therefore, the maximum point of the profit function in this case is:

$$\left\{\begin{array}{c}{P}_1^{\left(R,E\right)M}={\displaystyle \frac{\theta \left(1-\rho \phi \right)A_2+\left[2\left(1-\rho \phi \right)-\theta \phi \left(1-\rho \right)\right]A_1}{\left(4-{\theta }^2\right)\left(1-\rho \phi \right)-3\theta \phi \left(1-\rho \right)}}\hfill \\ P_2^{\left(R,E\right)M}={\displaystyle \frac{\left[\theta \left(1-\rho \phi \right)+\phi \left(1-\rho \right)\right]A_1+2\left(1-\rho \phi \right)A_2}{\left(4-{\theta }^2\right)\left(1-\rho \phi \right)-3\theta \phi \left(1-\rho \right)}}\hfill \end{array}\right.$$

When the ride-sharing market is in its off-peak period, there are conditions that must be met for the prices of both platforms:

$$\left\{\begin{array}{c}0\le D_1^{\left(R,E\right)}\le S_1^{\left(R,E\right)}\\ 0\le D_2^{\left(R,E\right)}\le S_2^{\left(R,E\right)}\end{array}\right.\iff \left\{\begin{array}{c}\underset{\_}{P_1^{\left(R,E\right)}}\le P_1\le {\displaystyle \frac{A_1+\theta A_2}{1-{\theta }^2}}\\ \underset{\_}{P_2^{\left(R,E\right)}}\le P_2\le {\displaystyle \frac{\theta A_1+A_2}{1-{\theta }^2}}\end{array}\right.$$

where

$$\left\{\begin{array}{c}\underset{\_}{P_1^{\left(R,E\right)}}={\displaystyle \frac{\left(-2+\theta \phi \right)\left(\left(1-\phi \right)A_1+B_1\right)-\left(\beta +\theta \left(1-\phi \right)\right)\left(\phi A_1+A_2+B_2\right)}{\left(\beta +\theta \left(1-\phi \right)\right)\left(\beta +\theta -\phi \right)-\left(-2+\phi \right)\left(-2+\phi \theta \right)}}\hfill \\ \underset{\_}{P_2^{\left(R,E\right)}}={\displaystyle \frac{-\left(\beta +\theta \right)\left(A_1+B_1\right)+\left(\phi -2\right)\left(A_2+B_2\right)+\phi \left(B_1+\left(\beta +\theta -1\right)A_1\right)}{\left(-2+\beta +\theta \right)\left(2+\beta +\theta -\phi -\theta \phi \right)}}\hfill \end{array}\right.$$

Therefore, the equilibrium prices of the two types of platforms are as follows:

$$\begin{array}{c}{P}_1^{(R,E{)}^{*}}=\left\{\begin{array}{ccc}{P}_1^{\left(R,E\right)M},& \underset{\_}{P_1^{\left(R,E\right)}}\le P_1^{\left(R,E\right)M}\le {\displaystyle \frac{A_1+\theta A_2}{1-{\theta }^2}}& \\ \underset{\_}{P_1^{\left(R,E\right)}},& \mathrm{if} \mathrm{not}& \end{array}\right.\\ P_2^{(R,E{)}^{*}}=\left\{\begin{array}{ccc}{P}_2^{\left(R,E\right)M},& \underset{\_}{P_2^{\left(R,E\right)}}\le P_2^{\left(R,E\right)M}\le {\displaystyle \frac{\theta A_1+A_2}{1-{\theta }^2}}& \\ \underset{\_}{P_1^{\left(R,E\right)}},& \mathrm{if} \mathrm{not}& \end{array}\right.\end{array}$$

Similarly, we can deduce the equilibrium price when the market is at its peak period, and thus we can draw the conclusion of Lemma 3.

According to Lemma 3, the equilibrium price of the two types of traditional ride-sharing platforms can be added into Formulas (12) and (13), respectively, to obtain the equilibrium demand $D_1^{(R,E{)}^{*}}$, $D_2^{(R,E{)}^{*}}$ and balanced profit ${\pi }_1^{(R,E{)}^{*}}$, ${\pi }_2^{(R,E{)}^{*}}$.

Platform $i$’s balanced consumer surplus and social welfare are, respectively:

$$C{S}_i^{\left(R,E\right)\ast }={\displaystyle \frac{1}{2}}\left(P_i^{\left(R,E\right)max}-P_i^{\left(R,E\right)\ast }\right)D_i^{\left(R,E\right)\ast },$$

$$S{W}^{(R,E{)}^{*}}=\sum _1^2{\displaystyle \frac{1}{2}}\left(P_i^{\left(R,E\right)max}-P_i^{\left(R,E\right)min}+P_i^{(R,E{)}^{*}}-P_i^{\left(R,E\right)l}\right)D_i^{(R,E{)}^{*}}+\alpha P_1^{(R,E{)}^{*}}{D}_1^{(R,E{)}^{*}}+P_2^{(R,E{)}^{*}}{D}_2^{(R,E{)}^{*}}$$

where

$$A_i-P_i^{\left(R,E\right)max}+\theta P_j^{\left(R,E\right)\ast }=0,-B_i+P_i^{\left(R,E\right)min}-\beta P_j^{\left(R,E\right)\ast }=0,$$

$$-B_i+P_i^{\left(R,E\right)l}-\beta P_j^{\left(R,E\right)\ast }=D_i^{\left(R,E\right)\ast }, i=\left\{\begin{array}{c}\mathrm{1,2}\end{array}\right\},j=3-i$$

4.4. Both Types of Platforms Are Stationed in (E, E)

If both the C2C platform and the B2C platform choose the entry strategy, and the travel service prices set on the two channels are $P_1$ and $P_2$, respectively, then the supply functions faced by the two platforms are $S_1^{\left(E,E\right)}=S_1$ and $S_2^{\left(E,E\right)}=S_2$. In this case, there will be a number of $\phi D_1$ consumers originally belonging to the C2C platform who will transfer to the aggregation platform, while there will also be a number of $\phi D_2$ consumers originally belonging to the B2C platform who will transfer to the aggregation platform. Therefore, the total demand faced by the aggregation platform is $\phi \left(D_1+D_2\right)$. For consumers who choose the aggregation platform to meet their needs, self-operated platforms assigned by the aggregation platform are random. They may be served by drivers from either the C2C platforms or B2C platforms depending on their supply levels. Therefore, in the aggregation platform, m represents the proportion of consumers choosing C2C platforms and $\left(1-m\right)$ represents those choosing B2C platforms with $m\approx S_1^{\left(E,E\right)}/\left(S_1^{\left(E,E\right)}+S_2^{\left(E,E\right)}\right)$ being constant for clarity purposes. To maintain consistency in our research study, we assume m is a constant.

Thus, the demand function faced by the C2C platform in self-operated channels is $D_1^o=\left(1-\phi \right)D_1$ and in public channels is $D_1^c=m\phi \left(D_1+D_2\right)$; the demand function faced by the B2C platform in self-operated channels is $D_2^o=\left(1-\phi \right)D_2$ and in public channels is $D_2^c=\left(1-m\right)\phi \left(D_1+D_2\right)$. Their total demand functions are:

$$\left\{\begin{array}{c}{D}_1^{\left(E,E\right)}=D_1^o+D_1^c=\left(1-\phi \right)D_1+m\phi \left(D_1+D_2\right)\hfill \\ \begin{array}{c}{D}_2^{\left(E,E\right)}=D_2^o+D_2^c=\left(1-\phi \right)D_2+\left(1-m\right)\phi \left(D_1+D_2\right)\hfill \end{array}\end{array}\right.$$

(14)

The profit functions of the two types of platforms are, respectively:

$$\left\{\begin{array}{c}{\pi }_1^{\left(E,E\right)}=\alpha P_1{D}_1^o+(\alpha -\rho )P_1{D}_1^c\\ {\pi }_2^{\left(E,E\right)}=P_2{D}_2^o+P_2(1-\rho )D_2^c\hfill \end{array}\right.$$

(15)

Lemma 4.

When the ride-sharing market is in the off-peak period, that is, when supply exceeds demand, the equilibrium prices for the two types of self-operated platforms are:

$$\begin{array}{c}{P}_1^{(E,E{)}^{*}}=\left\{\begin{array}{ccc}{P}_1^{\left(E,E\right)M},& \underset{\_}{P_1^{\left(E,E\right)}}\le P_1^{\left(E,E\right)M}\le {\displaystyle \frac{A_1+\theta A_2}{1-{\theta }^2}}& \\ \underset{\_}{P_1^{\left(E,E\right)}},& \mathrm{if} \mathrm{not}& \end{array}\right.\\ P_2^{(E,E{)}^{*}}=\left\{\begin{array}{ccc}{P}_2^{\left(E,E\right)M},& \underset{\_}{P_2^{\left(E,E\right)}}\le P_2^{\left(E,E\right)M}\le {\displaystyle \frac{\theta A_1+A_2}{1-{\theta }^2}}& \\ \underset{\_}{P_2^{\left(E,E\right)}},& \mathrm{if} \mathrm{not}& \end{array}\right.\end{array}$$

where

$$\left\{\begin{array}{c}\underset{\_}{P_1^{\left(E,E\right)}}={\displaystyle \frac{\left(-2+m\phi +\left(1-m\right)\theta \phi \right)\left(\left(1-\phi +m\phi \right)A_1+m\phi A_2+B_1\right)-\left(\beta -m\phi +\theta \left(1-\phi +m\phi \right)\right)\left(\left(1-m\right)\phi A_1+\left(1-m\phi \right)A_2+B_2\right)}{-4+{\beta }^2+2\beta \theta +{\theta }^2+2\phi -\beta \phi +\phi \theta -\beta \phi \theta -{\theta }^2\phi }}\hfill \\ \underset{\_}{P_2^{\left(E,E\right)}}=-{\displaystyle \frac{\left(\beta +\theta \right)\left(A_1+B_1\right)+\phi \left(1-m\right)\left(A_1-B_1\right)+\left(2-\phi \right)\left(A_2+B_2\right)-m\phi \left(A_2-B_2\right)+\phi \left(m\beta -\theta -\beta \right)A_1+m\beta \phi A_2-m\theta \phi \left(B_1+B_2\right)}{\left(-2+\beta +\theta \right)\left(2+\beta +\theta -\phi -\theta \phi \right)}}\hfill \end{array}\right.$$

When the market is in its peak period, that is, when demand exceeds supply, the equilibrium prices for the two types of platforms are  $P_1^{(E,E{)}^{*}}=\underset{\_}{P_1^{\left(E,E\right)}}$ and $P_2^{(E,E{)}^{*}}=\underset{\_}{P_2^{\left(E,E\right)}}$, respectively.

Proof of Lemma 4.

Since both ${\displaystyle \frac{{\partial }^2{\pi }_1^{\left(E,E\right)}}{\partial P_1^2}}=-2\alpha \left(1-\phi \right)+2\left(\alpha -\rho \right)m\phi \left(\theta -1\right)$ and ${\displaystyle \frac{{\partial }^2{\pi }_2^{\left(E,E\right)}}{\partial P_2^2}}=-2\left(1-\phi \right)+2\left(1-\rho \right)\left(1-m\right)\phi \left(\theta -1\right)$ are negative, it can be inferred that ${\pi }_i^{\left(E,E\right)}$ is a concave function with a unique maximum value with respect to $P_i$.

According to the first-order optimal condition, we can obtain:

$$\left\{\begin{array}{c}{\displaystyle \frac{\partial {\pi }_1^{\left(E,E\right)}}{\partial P_1}}=\alpha \left(1-\phi \right)\left(A_1-2P_1+\theta P_2\right)+\left(\alpha -\rho \right)m\phi \left(A_1-2P_1+\theta P_2+A_2-P_2+2\theta P_1\right)=0\hfill \\ {\displaystyle \frac{\partial {\pi }_2^{\left(E,E\right)}}{\partial P_2}}=\left(1-\phi \right)\left(A_2-2P_2+\theta P_1\right)+\left(1-\rho \right)\left(1-m\right)\phi \left(A_1-P_1+2\theta P_2+A_2-2P_2+\theta P_1\right)=0\hfill \end{array}\right.$$

By combining the two equations, we can obtain the maximum value points of the profit function for two types of platforms as $P_1^{\left(E,E\right)M}$ and $P_2^{\left(E,E\right)M}$.

When the ride-sharing market is in its off-peak period, there are conditions that must be met for the prices of both platforms:

$$\left\{\begin{array}{c}0\le D_1^{\left(E,E\right)}\le S_1^{\left(E,E\right)}\\ 0\le D_2^{\left(E,E\right)}\le S_2^{\left(E,E\right)}\end{array}\right.\iff \left\{\begin{array}{c}\underset{\_}{P_1^{\left(E,E\right)}}\le P_1\le {\displaystyle \frac{A_1+\theta A_2}{1-{\theta }^2}}\\ \underset{\_}{P_2^{\left(E,E\right)}}\le P_2\le {\displaystyle \frac{\theta A_1+A_2}{1-{\theta }^2}}\end{array}\right.$$

Therefore, the equilibrium prices of the two types of platforms are:

$$\begin{array}{c}{P}_1^{(E,E{)}^{*}}=\left\{\begin{array}{ccc}{P}_1^{\left(E,E\right)M},& \underset{\_}{P_1^{\left(E,E\right)}}\le P_1^{\left(E,E\right)M}\le {\displaystyle \frac{A_1+\theta A_2}{1-{\theta }^2}}& \\ \underset{\_}{P_1^{\left(E,E\right)}},& \mathrm{if} \mathrm{not}& \end{array}\right.\\ P_2^{(E,E{)}^{*}}=\left\{\begin{array}{ccc}{P}_2^{\left(E,E\right)M},& \underset{\_}{P_2^{\left(E,E\right)}}\le P_2^{\left(E,E\right)M}\le {\displaystyle \frac{\theta A_1+A_2}{1-{\theta }^2}}& \\ \underset{\_}{P_2^{\left(E,E\right)}},& \mathrm{if} \mathrm{not}& \end{array}\right.\end{array}$$

where

$$\left\{\begin{array}{c}{P}_1^{\left(E,E\right)}={\displaystyle \frac{\left(-2+m\phi +\left(1-m\right)\theta \phi \right)\left(\left(1-\phi +m\phi \right)A_1+m\phi A_2+B_1\right)-\left(\beta -m\phi +\theta \left(1-\phi +m\phi \right)\right)\left(\left(1-m\right)\phi A_1+\left(1-m\phi \right)A_2+B_2\right)}{-4+{\beta }^2+2\beta \theta +{\theta }^2+2\phi -\beta \phi +\phi \theta -\beta \phi \theta -{\theta }^2\phi }}\hfill \\ P_2^{\left(E,E\right)}=-{\displaystyle \frac{\left(\beta +\theta \right)\left(A_1+B_1\right)+\phi \left(1-m\right)\left(A_1-B_1\right)+\left(2-\phi \right)\left(A_2+B_2\right)-m\phi \left(A_2-B_2\right)+\phi \left(m\beta -\theta -\beta \right)A_1+m\beta \phi A_2-m\theta \phi \left(B_1+B_2\right)}{\left(-2+\beta +\theta \right)\left(2+\beta +\theta -\phi -\theta \phi \right)}}\hfill \end{array}\right.$$

Similarly, we can deduce the equilibrium price when the market is at its peak period, and thus, we can draw the conclusion of Lemma 4.

By substituting the equilibrium prices into Formulas (14) and (15), we can obtain the equilibrium demand $D_1^{(E,E{)}^{*}}$ and $D_2^{(E,E{)}^{*}}$ as well as the equilibrium profit ${\pi }_1^{(E,E{)}^{*}}$ and ${\pi }_2^{(E,E{)}^{*}}$.

Platform $i$’s balanced consumer surplus and social welfare are, respectively:

$$C{S}_i^{\left(E,E\right)\ast }={\displaystyle \frac{1}{2}}\left(P_i^{\left(E,E\right)max}-P_i^{\left(E,E\right)\ast }\right)D_i^{\left(E,E\right)\ast },$$

$$S{W}^{(E,E{)}^{*}}=\sum _1^2{\displaystyle \frac{1}{2}}\left(P_i^{\left(E,E\right)max}-P_i^{\left(E,E\right)min}+P_i^{(E,E{)}^{*}}-P_i^{\left(E,E\right)l}\right)D_i^{(E,E{)}^{*}}+\alpha P_1^{(E,E{)}^{*}}{D}_1^{(E,E{)}^{*}}+P_2^{(E,E{)}^{*}}{D}_2^{(E,E{)}^{*}}$$

where

$$A_i-P_i^{\left(E,E\right)max}+\theta P_j^{\left(E,E\right)\ast }=0_{,}-B_i+P_i^{\left(E,E\right)min}-\beta P_j^{\left(E,E\right)\ast }=0_{,}$$

$$-B_i+P_i^{\left(E,E\right)l}-\beta P_j^{\left(E,E\right)\ast }=D_i^{\left(E,E\right)\ast }, i=\left\{\begin{array}{c}\mathrm{1,2}\end{array}\right\}, j=3-i.$$

5. Decision for the Ride–Sharing Platform

The game between the two types of self-operated platforms is played based on the payment matrix shown in

Table 3. Payoff matrix.

		B2C Platform
		R	E
C2C platform	R	${\pi }_1^{\left(R,R\right)\ast },{\pi }_2^{\left(R,R\right)\ast }$	${\pi }_1^{\left(R,E\right)\ast },{\pi }_2^{\left(R,E\right)\ast }$
	E	${\pi }_1^{\left(E,R\right)\ast },{\pi }_2^{\left(E,R\right)\ast }$	${\pi }_1^{\left(E,E\right)\ast },{\pi }_2^{\left(E,E\right)\ast }$

. When making decisions, the C2C platform’s reasoning process is as follows. If the B2C platform adopts the no-entry strategy (R), then whether to adopt the no-entry strategy (R) or the entry strategy (E) depends on how much profit the C2C platform can obtain under the equilibrium strategies (R, R) and (E, R), respectively. If the former is less than the latter, that is, adopting the entry strategy (E) can improve its own profits, then the C2C platform will adopt the entry strategy (E); otherwise, it will adopt the no-entry strategy (R).

At the same time, we must also consider the situation where the B2C platform adopts the entry strategy (E). In this case, whether the C2C platform adopts the no-entry strategy (R) or the entry strategy (E) depends on their equilibrium profits under the strategy sets of (R, E) and (E, E), respectively. If the former is less than the latter, then the C2C platform will adopt the entry strategy (E); otherwise, it will adopt the no-entry strategy (R). In short, for the C2C platform to adopt the entry strategy (E), it must be able to improve its own profit regardless of what strategies are adopted by the B2C platform. Only when both inequalities ${\pi }_1^{\left(E,R\right)\ast }\ge {\pi }_1^{\left(R,R\right)\ast }$ and ${\pi }_1^{\left(E,E\right)\ast }\ge {\pi }_1^{\left(R,E\right)\ast }$ are satisfied at the same time will the platform adopt the entry strategy (E). Similarly, for B2C platforms to enter the aggregation platform, both inequalities, namely ${\pi }_2^{\left(R,E\right)\ast }\ge {\pi }_2^{\left(R,R\right)\ast }$ and ${\pi }_2^{\left(E,E\right)\ast }\ge {\pi }_2^{\left(E,R\right)\ast }$, must be satisfied.

The analytical expression derived from the previous section’s formula is quite complex, making it difficult to intuitively analyze the management and practical significance of the equilibrium solution of the model. This section explores platform decision making through numerical experiments. The focus of this study lies in analyzing the impact of competition intensity ($\theta$) between self-operated platforms and the awareness ($\phi$) of the aggregation platform on the ride-sharing platform entry strategy. To ensure the accuracy and feasibility of the model, we referenced the research conducted by Li et al. [18] and Doğan et al. [49]. In addition, we integrated it with real-world conditions, assigning numerical values to the model accordingly. Let $A_1=600$, $A_2=500$, $B_1=100$, $B_2=200$, $\alpha =0.25$, $\rho =0.2$, $\beta =0.1$ be defined. Let $m=0.5$ satisfy the condition $m\approx S_1^{\left(E,E\right)}/\left(S_1^{\left(E,E\right)}+S_2^{\left(E,E\right)}\right)$.

5.1. Entry Strategy of the C2C Platform

With the emergence of the aggregation platform, whether to join has become a core decision for self-operated platforms. Combining supply and demand relationships, Propositions 1 and 2 analyze the entry conditions of two types of self-operated platforms.

Proposition 1.

When the market is in the off-peak period, that is, when supply exceeds demand, if both parameter $\theta$ and parameter $\phi$ are large and satisfy certain conditions:

$$\begin{array}{c}\alpha {\displaystyle \frac{2\left(A_1+B_1\right)+\left(\beta +\theta \right)\left(A_2+B_2\right)\left[4-{\left(\beta +\theta \right)}^2\right]A_1+\left[\theta \left(\beta +\theta \right)-2\right]\left(A_1+B_1\right)+\left(\theta -\beta \right)\left(A_2+B_2\right)}{4-{\left(\beta +\theta \right)}^2}}\le \hfill \\ {\displaystyle \frac{2\left(\alpha -\rho \phi \right)A_1+\left[\theta \left(\alpha -\rho \phi \right)+\left(\alpha -\rho \right)\phi \right]A_2}{\left(4-{\theta }^2\right)\left(\alpha -\rho \phi \right)-3\theta \phi \left(\alpha -\rho \right)}}\{(\alpha -\rho \phi ){\displaystyle \frac{\left[2\left(\alpha -\rho \phi \right)-3\theta \phi \left(\alpha -\rho \right)\right]A_1}{\left(4-{\theta }^2\right)\left(\alpha -\rho \phi \right)-3\theta \phi \left(\alpha -\rho \right)}}+\hfill \\ (\alpha -\rho \phi ){\displaystyle \frac{\left[\theta \left(\alpha -\rho \phi \right)-\left({\theta }^2+1\right)\left(\alpha -\rho \right)\phi \right]A_2}{\left(4-{\theta }^2\right)\left(\alpha -\rho \phi \right)-3\theta \phi \left(\alpha -\rho \right)}}+(\alpha -\rho )\phi {\displaystyle \frac{\theta \left(\alpha -\rho \phi \right)A_1+\left[2\left(\alpha -\rho \phi \right)-\theta \phi \left(\alpha -\rho \right)\right]A_2}{\left(4-{\theta }^2\right)\left(\alpha -\rho \phi \right)-3\theta \phi \left(\alpha -\rho \right)}}\}\hfill \end{array}$$

Then, the C2C platform will adopt the entry strategy (E); otherwise, it will adopt the no-entry strategy (R). When the market is in its peak period, that is, when supply cannot meet demand, the C2C platform will always adopt the no-entry strategy (R).

Figure 4a shows the decision diagram of the C2C platform when the ride-sharing market is in the off-peak period and the B2C platform adopts the no-entry strategy (R). If the C2C platform adopts the entry strategy (E), then its equilibrium price will gradually increase with increasing values of $\theta$ and $\phi$. In regions I, II, and III, where the aggregation platform’s awareness is relatively low, adopting the entry strategy (E) would not only be disadvantageous in eroding the B2C platform’s market share but would also result in lower prices and a loss of promotion commission. Overall, this would not be conducive to profit growth for itself; therefore, it will adopt the no-entry strategy (R). In region IV, where the aggregation platform has higher awareness, adopting the entry strategy (E) would help to erode the B2C platform’s market share while also allowing for higher prices that can lead to increased profits for itself.

Figure 4b shows the decision diagram of the C2C platform when the market is in the off-peak period and the B2C platform adopts the entry strategy (E). In both region V and region VI, regardless of the strategy adopted by the C2C platform, its equilibrium price will continue to fall with a decrease in $\theta$ and exhibit a slight increasing trend with a decrease in $\phi$. Therefore, in region V, the C2C platform adopts a no-entry strategy (R). On the one hand, the low awareness of the aggregation platform helps reduce the erosion of its market share. On the other hand, higher prices are advantageous for ensuring profit growth. In region VI, the C2C platform adopts the entry strategy (E). Although its prices are lower than others, it can erode the market share of B2C platforms through the aggregation platform to achieve small profits but a quick turnover and thus benefit its own profit growth.

In regions VII to IX, regardless of the strategy adopted by the C2C platform, its equilibrium price will continue to fall with a decrease in $\theta$ and exhibit a slight increasing trend with a decrease in $\phi$. Therefore, in region VIII, although the aggregation platform has moderate awareness and relatively low prices, adopting the entry strategy (E) can help stabilize or even increase its market share for the C2C platform and contribute to profit growth. In regions VII and IX, where the aggregation platform is relatively less well-known, even if the C2C platform adopts the no-entry strategy (R), it will not experience too much erosion of its market share. Moreover, its higher prices are conducive to profit growth.

In regions X to XIV, regardless of the strategy adopted by the C2C platform, its equilibrium price will rise with an increase in $\theta$ and $\phi$. Therefore, in regions XII and XIII, where the aggregation platform is highly recognized, adopting the entry strategy (E) helps to increase market share and raise prices significantly for the C2C platform, leading to increased total profits. In regions X and XIV, where the aggregation platform is not particularly well-known, if the C2C platform adopts the entry strategy (E), it not only fails to erode B2C platforms’ market share but also experiences lower prices than when adopting the no-entry strategy (R), thus leading to losses from promotion commissions, which overall hinder profit growth. This is indeed why the C2C platform adopts the no-entry strategy (R). In region XI, regardless of what strategy is adopted by the C2C platforms, there is not much difference between their equilibrium prices. Although adopting the entry strategy (E) can help grow market share, losing the promotional commission overall hinders profit growth, hence why these platforms adopt the no-entry strategy (R).

When the ride-sharing market is in its peak period, no matter what strategy the B2C platform adopts, the C2C platform will always adopt the no-entry strategy (R). This is because during the peak period, if the C2C platform adopts the entry strategy (E), even if it can gain more market share, it cannot meet this type of new demand well due to insufficient supply. Additionally, it would need to pay extra promotion commissions for the aggregation platform, which makes it harder for it to maintain its growth and profits. Therefore, during the peak period, the C2C platform will always adopt the no-entry strategy (R).

5.2. Entry Strategy of the B2C Platform

Proposition 2.

Regardless of whether the market is in the off-peak or peak period, the B2C platform will always adopt the entry strategy (E).

Irrespective of whether the ride-sharing market is in the off-peak or peak period, and regardless of what strategy the C2C platform adopts, if the B2C platform adopts the entry strategy (E), then its prices will rise with the increase of $\theta$ and $\phi$. If there is high competition intensity between the two types of platforms and the aggregation platform has higher visibility, then the B2C platform’s price will be relatively high. Adopting the entry strategy (E) can help erode the C2C platform’s market share and increase total profits. In other cases, although the B2C platform’s price is relatively low, adopting the entry strategy (E) can achieve small profits but a quick turnover. Therefore, in any case, it is always best for the B2C platform to adopt the entry strategy (E).

Based on comprehensive Propositions 1 and 2, during the off-peak period when competition between the two types of ride-sharing platforms is intense and the visibility of the aggregation platform is high, both types of platforms will adopt a strategy of entering the aggregation platform. Therefore, (E, E) is the equilibrium strategy set; otherwise, (R, E) is the equilibrium strategy set. The boundary line between these two sets of strategies satisfies Formula (16). During the peak period, the C2C platform will always adopt the no-entry strategy (R), while the B2C platform will always adopt the entry strategy (E), that is, (R, E) is an equilibrium strategy set.

$$\begin{array}{c}\alpha {\displaystyle \frac{2\left(A_1+B_1\right)+\left(\beta +\theta \right)\left(A_2+B_2\right)}{4-{\left(\beta +\theta \right)}^2}}{\displaystyle \frac{\left[4-{\left(\beta +\theta \right)}^2\right]A_1+\left[\theta \left(\beta +\theta \right)-2\right]\left(A_1+B_1\right)+\left(\theta -\beta \right)\left(A_2+B_2\right)}{4-{\left(\beta +\theta \right)}^2}}=\\ {\displaystyle \frac{2\left(\alpha -\rho \phi \right)A_1+\left[\theta \left(\alpha -\rho \phi \right)+\left(\alpha -\rho \right)\phi \right]A_2}{\left(4-{\theta }^2\right)\left(\alpha -\rho \phi \right)-3\theta \phi \left(\alpha -\rho \right)}}\{\left(\alpha -\rho \phi \right){\displaystyle \frac{\left[2\left(\alpha -\rho \phi \right)-3\theta \phi \left(\alpha -\rho \right)\right]A_1+\left[\theta \left(\alpha -\rho \phi \right)-\left({\theta }^2+1\right)\left(\alpha -\rho \right)\phi \right]A_2}{\left(4-{\theta }^2\right)\left(\alpha -\rho \phi \right)-3\theta \phi \left(\alpha -\rho \right)}}\\ +(\alpha -\rho )\phi {\displaystyle \frac{\theta \left(\alpha -\rho \phi \right)A_1+\left[\begin{array}{c}2\left(\alpha -\rho \phi \right)-\theta \phi \left(\alpha -\rho \right)\end{array}\right]A_2}{\left(4-{\theta }^2\right)\left(\alpha -\rho \phi \right)-3\theta \phi \left(\alpha -\rho \right)}}\}\end{array}$$

(16)

5.3. Price Competition Situation

Before the emergence of the aggregation platform, the two types of self-operated platforms could only adopt the no-entry strategy (R), where (R, R) was the optimal decision. Following the emergence of the aggregation platform, both types of platforms can choose their optimal decisions based on Propositions 1 and 2. By comparing the equilibrium price difference between the two types of platforms before and after the emergence of the aggregation platform, Proposition 3 can be obtained. This proposition reflects the impact of the aggregation platform’s emergence on the price competition situation between these two types of platforms.

Proposition 3.

Irrespective of whether the ride-sharing market is in the off-peak or peak period, after the two types of self-operated platforms adopt optimal entry and pricing decisions, the price competition between them will be less intense than before the emergence of the aggregation platform.

Figure 5 shows the price competition situation between the two traditional platforms when the ride-sharing market is in the off-peak period. We know that the greater the price difference, the less intense the competition. This is because, in a market, if the prices of products from different companies vary greatly, consumers will be more likely to find low-priced products and purchase those products. This results in the market share of higher priced products being squeezed as consumers tend to purchase cheaper alternatives. Therefore, markets with larger price differences tend to imply lower levels of competition. In contrast, if the price difference between products on the market is small, consumers may consider other factors more when making purchase decisions, such as quality, brand reputation, service, etc. In this case, consumers may be more willing to buy the product they believe has a higher value, even if the product prices are not much different. In this case, the level of competition in the market becomes more intense because companies need to provide higher quality products and better services to attract consumers.

The shaded part in the figure represents the intensity of price competition between the two types of traditional platforms when the cross-price sensitivity parameter in the demand function ($\theta$) is different, and the smaller area of the shaded part indicates the more intense competition. When the market is in the off-peak period, as shown in Figure 5a, if both types of platforms adopt the no-entry strategy (R, R), the price competition between the two sides will be very intense and intensify with the increase in ($\theta$). This is because in the case of other factors, such as the service not being much different, consumers will be more inclined toward the party with the lower price, and therefore, both parties will set the price based on the other party’s price to seize the market share.

Figure 5b represents the price competition situation when both platforms choose the entry strategy (E, E) when the market is in the off-peak period. Intuitively speaking, direct competition will occur between self-operated platforms that enter the aggregation platform, and price competition will become more intense, which is more beneficial to consumers. However, according to Proposition 3, it can be found that after the appearance of the aggregation platform, the equilibrium price difference between the two types of self-operated platforms rises and continues to rise with the increase in $\theta$ and $\phi$. This indicates that price competition between the two types of platforms will weaken as competition intensifies between them and as awareness of the aggregation platform increases, which is not in favor of consumers. The reason for this difference from intuition is that an aggregation platform can lead to a situation where price competition among self-operated platforms does not completely follow market rules because it can randomly allocate drivers to consumers who place orders on its platform based on supply levels from self-operated platforms entering its system. This ensures both benefits for self-operated platforms themselves and greatly enhances the convenience and richness of consumer ride choices, thereby maintaining consumer welfare.

Figure 5c,d represent the price competition relationship when only the C2C platform chooses the entry strategy (E, R) and only the B2C platform chooses the entry strategy (R, E), respectively. It can be seen that when the market is in the off-peak period, if the B2C platform adopts the no-entry strategy (R), the equilibrium price will be smaller than that of the entry strategy (E), and the price difference will be more obvious with the increase in $\theta$. When the equilibrium price is smaller than the equilibrium price when adopting the move-in strategy (E), and the price difference will be more obvious with the increase in $\theta$. Therefore, this reinforces the correctness of Proposition 2, i.e., the B2C platform will always adopt the move-in strategy. With regard to Figure 5d, when only the B2C platform chooses the entry strategy, due to the increase in awareness of the aggregation platform, the consumers who originally chose to join the platform will gradually transfer to the aggregation platform stationed on the B2C platform, and the B2C platform’s market share will be increased, which results in the price difference between the C2C platform and the B2C platform decreasing, thus intensifying the competition between the two sides. The next section explores the impact of the aggregation platform on social welfare.

5.4. Consumer Surplus and Social Welfare Analysis

Although whether to join an aggregation platform is a core decision for operated platforms, when making the optimal decision, they also need to consider the impact of their actions on consumers and society. Fundamentally, only decisions that are beneficial to consumers and society can contribute to the long-term development of platform enterprises. In this section, Propositions 4 through 8 conclude regarding the impact of the emergence of the aggregation platform on consumer surplus, while Proposition 9 concludes regarding its impact on social welfare.

Proposition 4.

When the ride-sharing market is in the off-peak period, and both types of self-operated platforms adopt optimal entry and pricing decisions, if the awareness of the aggregation platform is relatively low and there is intense competition between the two platforms, then consumer surplus for the C2C platform will increase. If the awareness of the aggregation platform is relatively high and there is very little competition between the two platforms, then consumer surplus for the C2C platform will also increase. In all other cases, consumer surplus for the C2C platform will decrease.

Figure 6a reflects the change in consumer surplus of the C2C platform when the ride-sharing market is in its off-peak period and both types of self-operated platforms adopt optimal decisions. In regions XV to XIX, when the C2C platform adopts the no-entry strategy (R), its equilibrium price is lower than before the aggregation platform appeared. Therefore, when the aggregation platform’s awareness is relatively low, the C2C platform’s market share will not be eroded too much, which overall helps to increase consumer surplus, specifically in regions XV and X VI. In regions XX and X XI, when the C2C platform adopts the no-entry strategy (R), its equilibrium price is higher than before the aggregation platform appeared, and the fact that the awareness of the latter is high leads to more erosion of the market share for the C2C platform. This gives rise to less improvement in consumer surplus, although in region XXI, where prices are lower than those offered by B2C platforms, it helps maintain market share, leading to an increase in consumer surplus. In region XXII, where competition between both types of platforms is intense, the adoption of the entry strategy (E) by the C2C platform helps maintain a stable market share, resulting in an increased consumer surplus.

Proposition 5.

When the ride-sharing market is in its peak period and both types of ride-sharing platforms make the best decisions regarding entry and pricing, if the awareness of the combined travel platform is relatively low and there is intense competition between the two platforms, then the consumer surplus for the C2C platform will increase. However, in other scenarios, such as when there is less competition or higher awareness for the integrated platform, the consumer surplus for the C2C platform may decrease.

Figure 6b reflects the change in consumer surplus of the C2C platform when the ride-sharing market is in its peak period and both types of self-operated platforms adopt optimal decisions. In all regions, the C2C platform adopts the no-entry strategy (R), while the B2C platform adopts the entry strategy (E). Therefore, in regions XXIII and XXIV, due to the relatively low awareness of the aggregation platform, the market share of the C2C platform will not be eroded much, and its equilibrium price is lower than after the aggregation platform’s appearance, thus meaning that consumer surplus increases. However, in region XV, due to the relatively high awareness of the aggregation platform, the market share of the C2C platform will be eroded more significantly, leading to a decrease in consumer surplus.

Proposition 6.

Irrespective of whether the ride-sharing market is in the off-peak or peak period, when two types of self-operated platforms adopt optimal entry and pricing decisions, the consumer surplus of the B2C platform will always increase.

According to Proposition 6, regardless of whether the market is in the off-peak or peak period, the consumer surplus of the B2C platform will always increase. This is because the B2C platform always adopts the entry strategy (E), which helps erode the market share of C2C platforms and thus increases consumer surplus.

Proposition 7.

When the ride-sharing market is in the off-peak period, and both types of self-operated platforms adopt optimal entry and pricing decisions, if the awareness of the aggregation platform is very high and competition between the two types of self-operated platforms is not intense, then total consumer surplus will decrease; otherwise, total consumer surplus will increase under other circumstances.

Figure 7 shows the change in total consumer surplus when the ride-sharing market is in its off-peak period and both types of self-operated platforms make optimal decisions. In region XXVIII, due to the high awareness of the aggregation platform and low competition between the two types of self-operated platforms, the C2C platform loses a significant market share, giving rise to a decrease in consumer surplus and ultimately leading to a decrease in total consumer surplus.

Proposition 8.

When the ride-sharing market is in its peak period and two types of self-operated platforms adopt optimal entry and pricing decisions, the total consumer surplus will increase.

Proposition 9.

Irrespective of whether the ride-sharing market is in the off-peak period or peak period, when two types of self-operated platforms adopt optimal entry and pricing decisions, social welfare will always increase.

According to Propositions 7 to 9, regardless of whether the ride-sharing market is in the off-peak period or peak period, when two types of self-operated platforms make optimal decisions, social welfare will always increase, and in most cases, total consumer surplus will also increase. This indicates that the emergence of the aggregation platform not only largely maintains consumer interests but also creates social welfare.

In addition, incorporating environmental and equity factors into the analysis can further expand the significance of the research. From an environmental perspective, aggregation platforms can effectively reduce carbon emissions by promoting cooperation between platforms and optimizing vehicle scheduling, reducing empty driving rates and repeated operations, especially during peak periods. Resource integration improves vehicle utilization efficiency, reduces idle vehicle operations during off-peak periods, and promotes sustainable development [50]. From a fairness perspective, price competition by self-operated platforms during peak periods may increase the burden on low-income consumers, while drivers may increase income fairness due to large orders. Aggregation platforms help improve service coverage in remote areas during off-peak periods and promote the balance between regional transportation resources. Overall, regardless of whether the shared travel market is in off-peak or peak periods, the optimal decisions of the two types of traditional platforms not only increase consumer and producer surplus but also show positive externalities in environmental protection and social equity and fully support sustainable development.

5.5. Empirical Validation

To further validate the theoretical findings of this study, we conducted an empirical analysis to examine the real-world applicability and robustness of the results. Specifically, to investigate the impact of cross-price sensitivity ($\theta$) on consumer surplus and social welfare, we selected two sets of $\theta$ values: one ranging from 0.85 to 0.95 and the other from 0.45 to 0.55, with increments of 0.01. This analysis aimed to explore how changes in $\theta$ affect the equilibrium profits of ride-sharing platforms (results rounded to two decimal places). Based on Lemmas 1 and 4, we calculated the equilibrium profit trends of both types of platforms, as $\theta$ changes under two scenarios: when neither platform joins the aggregation platform (R, R) and when both join (E, E). The results are presented in

Table 4. Changing trend of equilibrium profit of self–operated platforms.

$\theta$	0.85	0.86	0.87	0.88	0.89	0.90	0.91	0.92	0.93	0.94	0.95
${\pi }_1^{\left(R,R\right)}$	7.06	7.12	7.19	7.25	7.32	7.38	7.44	7.50	7.56	7.62	7.67
${\pi }_2^{\left(R,R\right)}$	14.69	15.25	15.83	16.43	17.05	17.70	18.37	19.07	19.79	20.54	21.32
$\theta$	0.45	0.46	0.47	0.48	0.49	0.5	0.51	0.52	0.53	0.54	0.55
${\pi }_1^{\left(E,E\right)}$	3.75	3.80	3.85	3.90	3.95	4.00	4.06	4.11	4.17	4.23	4.29
${\pi }_2^{\left(E,E\right)}$	4.61	4.80	5.00	5.20	5.41	5.62	5.84	6.07	6.30	6.54	6.79

.

According to Table 4, as the $\theta$ in the demand function increases, the equilibrium profit of the C2C platform shows a slow upward trend under both strategies. In low-sensitivity markets (e.g., $\theta =0.45$), when the C2C platform adopts the stationed strategy, its reliance on individual drivers, coupled with high fixed costs and competition from B2C platforms, limits its profit growth. However, in high-sensitivity markets (e.g., $\theta =0.85$), the C2C platform’s flexible operational model and higher visibility attract more consumers, leading to greater profit growth.

For the B2C platform, its profit changes are more pronounced in high-sensitivity markets, with its growth consistently exceeding that of the C2C platform. This is because, when joining the aggregation platform, the B2C platform benefits from the aggregation platform’s resource integration, brand influence, and enhanced vehicle utilization during off-peak periods, making it better suited to meet the demands of high-sensitivity markets. Notably, when $\theta >0.9$, the B2C platform experiences a significant increase in profits, demonstrating its ability to leverage economies of scale and operational efficiency to gain a competitive advantage in intense market competition.

The aggregation platform, by integrating C2C and B2C services, provides a one-stop solution that enhances consumer convenience. In low-sensitivity markets, joining the aggregation platform significantly expands the range of consumer choices. On the one hand, the diverse services offered by the aggregation platform and the competitive pressure it introduces force self-operated platforms to provide higher-quality services and more competitive pricing, resulting in a notable increase in consumer surplus compared to high-sensitivity markets. The increase in social welfare primarily stems from improved market efficiency (i.e., reduced search costs for consumers in matching services). Therefore, the emergence of the aggregation platform also enhances social welfare [51]. On the other hand, by optimizing resource allocation, reducing carbon emissions, and improving market efficiency, the aggregation platform significantly promotes environmental and social sustainability in the transportation sector.

6. Conclusions

This study explores the factors of aggregation platforms in a scenario with only one C2C platform, one B2C platform, and one aggregation platform in the ride-sharing market and examines the factors influencing the decision of self-operated platforms to choose to enter the ride-sharing platform. In order to further study the differences in the shared travel markets in different regions, this paper generally emphasizes the differences between different regions with different peak and off-peak periods and focuses on the strategic choices of various traditional shared travel platforms during peak and off-peak periods and the corresponding changes in social welfare. Based on game theory’s Cournot model, this study constructs demand, supply, and profit functions for the two types of self-operated platforms under different strategy sets and calculates equilibrium prices and profits considering the commission rate and awareness.

Subsequently, the analysis reveals that during the off-peak period, if there is intense competition between self-operated platforms and high awareness of the aggregation platform, then both types of platforms will enter the aggregation platform; otherwise, the C2C platform will adopt the no-entry strategy while the B2C platforms will opt for entry strategies. A conclusion is drawn regarding the peak period, i.e., C2C platforms always adopt the no-entry strategy because even if they can gain more market share by adopting the entry strategy, due to insufficient supply, they cannot meet this new demand well enough, which makes it difficult to maintain their growing profits while also having to pay additional promotion commissions to the aggregation platform. This shows that in China’s ride-sharing market, during the off-peak period or in some economically underdeveloped areas, if the competition among B2C platforms such as DiDi and T3 is fierce, and at the same time, Amap has a relatively high degree of awareness, then consumers can call for rides from DiDi and B2C platforms through the Amap aggregation platform. If one of these two conditions is not met, or in economically developed areas where the peak period lasts for a long time, then consumers can only take rides from B2C platforms on the Amap aggregation platform; otherwise, they can only use DiDi’s exclusive app to take a taxi online.

To conclude, in both the off-peak period and the peak period when both types of platforms make optimal decisions, ride-sharing social welfare improves. Moreover, this study finds that in big cities, the limited off-peak periods restrict platforms’ ability to adjust their strategies, while in smaller cities, lower consumer awareness of aggregation platforms and differences in vehicle types between C2C and B2C platforms lead to less intense competition. These factors influence platform entry strategies and market dynamics, highlighting the need for future research on how city size and consumer behavior shape the ride-sharing market.

Our results contribute to the sustainable development of the ride-sharing market in three key aspects. First, we extend the application scenarios of the economic model by leveraging the CPS alliance, which represents the shared mobility industry. We investigate the conditions and motivations for traditional shared mobility platforms to join aggregation platforms despite additional commission fees and potential channel conflicts. This research provides a theoretical foundation for achieving platform resource integration and minimizing redundant competition, thereby optimizing market resource allocation. Second, we measure the supply and demand matching efficiency under the coexistence of multiple types of shared mobility platforms and explore the changes in consumer surplus by quantifying the impact of aggregation platform cognition. This efficiency improvement and increase in consumer welfare help promote more efficient and environmentally friendly transportation solutions under the sharing economy model. Finally, by introducing a new business model, we expand the application of welfare economics in the transportation field. The results show that the emergence of aggregation platforms has promoted the overall social welfare improvement of the shared mobility market and provided support for a sustainable urban transportation system. These contributions not only provide theoretical and practical guidance for the development of the shared mobility industry but also provide possibilities for achieving sustainable development of the economy, society, and environment.

We expand on the competitive and cooperative relationships in supply chain management, providing solid theoretical support for the collaboration strategies of ride-sharing platforms and thereby generating a series of managerial insights.

After introducing the aggregation model, the competitive strategies of C2C platforms and B2C platforms are influenced by factors such as the duration of peak and off-peak periods, consumer awareness of aggregation platforms, and commission ratios. First, for platforms, aggregation platforms provide an opportunity to enhance price transparency and service comparability, pushing self-operated platforms to improve service quality and adopt more competitive pricing strategies. This can foster innovation and efficiency in platform operations, ultimately benefiting the platforms themselves through increased consumer engagement. Second, for consumers, aggregation platforms offer more convenient and cost-effective options, enabling better decision making and potentially reducing travel costs. As a result, passengers benefit from higher service quality and greater flexibility in choosing ride-sharing options. Finally, for policymakers, promoting aggregation platforms can serve as an effective strategy to reduce monopolistic behaviors, enhance the efficiency of driver–passenger matching, and improve overall travel efficiency, contributing to sustainable urban transportation systems. Moreover, while the introduction of aggregation platforms generally increases social welfare, policymakers should monitor scenarios, particularly during off-peak periods, where excessive competition might lead to a market share loss for C2C platforms and a potential decrease in overall welfare. Tailored regulations could help mitigate these risks and balance the interests of all stakeholders. In most cases, the adoption of aggregation platforms leads to a win–win scenario for platforms, consumers, and society as a whole, reinforcing their role in advancing sustainable and efficient transportation ecosystems.

There are certain shortcomings in this study, and future research can address the following aspects. First, this study assumes that the ride-sharing market contains two types of self-operated platforms, and in the future, multiple ride-sharing platforms can be studied for entry. Additionally, this study did not consider competition between other transportation tools, such as taxis and ride-sharing platforms, which can be further explored in future research.