Abstract
The online freight platform, also called freight resource sharing platform or freight O2O platform, developed rapidly lately, has gradually become the leaders in China’s road freight market in recent years, especially in the intracity freight market. The platform’s revenue mainly comes from the registration fee and commission, of which the commission is extracted from the freight rate. Therefore, how to determine the registration fee and freight rate becomes a key issue for the platform. Our research focuses on analyzing the pricing strategy by considering the charging mode, game model, and affecting factors. Based on the two-sided market theory and the classic Hotelling model, a tripartite game model of online freight platform-carrier-consignor is constructed. Furthermore, a game model of consignor and alternative carriers is built by introducing the platform user’s psychological pressure and satisfaction priority into the model. Finally, through mathematical derivation and numerical experiment, we analyze the effects of various factors on platform profits, platform registration fees, and freight rate, and propose some suggestions to promote the orderly development of online freight platforms for the intracity freight market.
1. Introduction
In recent years, road freight transportation bears more than 75% of China’s freight volume. A number of online freight platforms have been developing rapidly since the rise of Internet economy and mobile business. The online freight platform reduces the information asymmetry between the consignor and the carrier, and improves the efficiency of vehicle-cargo matching. China’s emerging leaders of online freight platforms such as Lalamove, GOGOX, and Full Truck Alliance have won numerous venture capitals through advanced entrepreneurial ideas and acquired a large number of users through free applications, free use, and subsidies in the early stage. They quickly seized the market share and formed a duopoly market in their own business areas.
The main operation process of the online freight platform can be described as follows: consignors and carriers register as the platform users after they recognize the registration fee and commission of the platform; the consignors upload the shipping demand and their special preferences, and the carriers upload the vehicle information and their special preferences; the platform matches the two-sided users’ attributes based on a number of objective indicators and subjective preferences. Usually, there are more vehicles and less shipping demands, so the consignors are the scarce users of the platform, and the platform pushes a certain number of alternative carriers to them according to the priority of matching degree; under the supervision of the platform, the consignor and the alternative carriers conduct an orderly bidding game to reach a match. The platform makes a profit by charging the registration fee, and drawing commission from freight rate. Therefore, pricing plays an important role in the operation process of the online freight platform, which includes the following two stages: the first is to determine the platform registration fee and the second is to determine the freight rate.
The contributions of this paper are as follows: (i) being the first study on the pricing problem of the online freight platforms in duopoly market that analyzes the different attribution characteristics of two-side users, (ii) establishing a two-stage price game model in which typical variables describing the above-mentioned problem are introduced such as user externality benefits, platform matching capabilities, user conversion costs, and user correction costs, (iii) clarifying the influence of various factors on the pricing problem by conducting mathematical derivation and numerical experiment, and (iv) proposing suggestions for promoting the development of the online freight platform.
The rest of this paper is organized as follows: In Section 2, we review the literature on platform pricing, game theory, and its models. In Section 3, we analyze the platform pricing mechanism of intracity freight market. In Section 4,atwo-stage pricing game model of the platform in the duopoly intracity freight market is established. In Section 5, we use mathematical derivation to carry out the strategy analysis of the platform. In Section 6, we conduct numerical experiments to verify the propositions of Section 5. In Section 7,the main conclusions of this study and future research are proposed.
2. Literature Review
Market competition can be divided into the following four types: perfect competition market, monopolistic competition market, oligopoly market, and complete monopoly market. Among them, an oligopolistic market refers to a situation in which a few firms dominate the vast majority of the entire market [1]. Lalamove and GOGOX are currently the two leading platform companies in China’s intracity online freight market, which has obvious characteristics of duopoly. To solve the pricing problem in duopoly market, Ding et al. [2] study service competition in a price- and service-time-sensitive market in the context of inventory and environmental constraints. Nie et al. [3] developed a patent price theory through a duopoly competition model of patent prices. The research focuses on the pricing of online freight platform in the duopoly market. It should be noted that the duopoly model established in this paper can apply to single oligopoly market and multioligopoly market with a slight modification.
The revenue that the platform obtains directly from two-side users which are registration fee and freight transaction commission. Therefore, the platform pricing game can be divided into two stages: game for registration fee between platform, consignor and carrier and game for freight rate between consignor and alternative carriers. The authors reviewed the relevant research literature on platform pricing and game models.
2.1. Platform Pricing
The charging strategies have a certain impact on platform pricing. Dietl et al. [4] analyzed the impact of one-time full payment and pay per click on platform advertising pricing, which showed that one-time full payment would result in greater profits. Zhao and Wang [5] conducted a research study on the platform charging strategies by adopting two-part tariff. Mccabe et al. [6] considered that pricing rules should be formulated from the perspective of platform diversification in order to ensure pricing strategies suitable for the platform development in different environments.
The factors affecting platform pricing include platform differentiation, user externalities, and user attributes [7]. Alexander and Tobias [8] focused on the influence of copyright in platform pricing, and analyzed the impact of pirated software on the app store platform. Sun and Wu [9] analyzed the impact of factors such as platform matching capabilities and indirect network externalities on pricing strategies. Comparing different user attributes, Ji [10] concluded that the platform can obtain higher profits when the user attributes are partially multihomed. Ji and Wang [11] studied the impact of pricing time series on platform pricing and competition strategies. Zhan and Qiao [12] analyzed the impact of product differentiation and user attributes on the pricing of mobile near-field payment platforms. Li et al. [13] explored the impact of customer segmentation on pricing strategy selection, and suggested high starting fare and low extra charge rate strategy for high-end cities and step toll strategy for low-end cities.
The research on online freight platforms for vehicle-cargo matching mainly focuses on the platform construction and design, operation and optimization, platform profit models, platform evolution analysis, and a few pricing analyses. Chen et al. [14] analyzed the optimal market structure and pricing strategy of the regional logistics information platform based on the two-sided market theory and network externalities. Wang and Fu [15] analyzed the pricing strategy choices of freight sharing platforms under the different ownership behavior of two-sided users considering the characteristics of two-sided markets. Xing et al. [16] gave the optimal pricing decision of logistics information platform by considering two-sided pricing and unilateral pricing of platform in the monopoly market, and extended it to platform pricing decision in competitive market through comparative analysis and sensitivity analysis. Pan et al. [17] found the optimal product price to maximize profit by analyzing the application and the pricing behavior of green technology in the duopoly market. Wang et al. [18] studied a two-way matching model and the impact of suppliers and demanders’ loss aversion on matching results and put forward some suggestions to improve the efficiency of platform matching.
2.2. Game Theory and Models
The current game theory research on oligopoly is mainly based on the Cournot model, the Sweezy model, the Cartel model, and the Stackelberg model. Nie et al. [19] used the Stackelberg model to analyze the impact of the secondary market on durable goods, they found in the patent pricing problem that companies with higher marginal costs have higher patent prices in the Stackelberg case than in the Cournot case. The Hotelling model is frequently used to study pricing problems in duopoly markets. Yao et al. [20] explored the complex effects of consumer preference uncertainty in optimal strategies in duopoly markets based on an improved Hotelling model. The Hotelling price competition model is an application of Nash equilibrium under the static game of complete information, which means that the products are the same in material properties, but different in spatial position. In this paper, we use the Hotelling model to study the pricing game between the two oligarchs.
Liu et al. [21] proposed an optimized distributed robust formula for the stochastic continuous Nash equilibrium problem, and they established a numerical scheme for calculating the Nash equilibrium value. Based on that, they proposed a distributed robust formula for the stochastic Stackelberg game. Qu et al. [22] were the earliest scholars to consider constructing a distributed robust formula for stochastic finite games. The principle of the game is to require each participant to use the worst probability distribution instead of directly using the worst results as in reference [23] for handling incomplete external random information.
There are many research progresses and achievements on the equilibrium game model. Ahipaşaoğlu et al. [24] studied the dynamic stochastic user equilibrium models, assuming that participants know only the first and second moment information of random variables. Singh et al. [25] considered a distributed game with restricted opportunities and studied the existence of mixed strategy Nash equilibrium. Loizou [26] proposed a robust distribution Nash equilibrium model. The goal of each participant is an equilibrium value based on risk conditions (CVaR for short). When the CVaR threshold is zero, the model is consistent with the model studied by authors in reference [22]. In other words, a distributed robust game is equivalent to a Nash equilibrium game that does not consider hidden information. When the structure of an ambiguity set is changed, the distributed stable game state can be redefined as a deterministic Nash equilibrium game. Peng et al. [27] imitated the bidding of weak participants in the process of matching preference objects, established the matching equilibrium and price equilibrium between shippers and carriers, and proposed a gale Shapley algorithm based on the price game mechanism. To sum up, most of the existing research studies on online freight platforms do not address pricing issues. Therefore, this study focuses on the pricing problem of online freight platform in the intracity freight market. A two-stage game model is established based on the two-sided market theory and game theory, followed by the analysis of the influence of various factors on the platform profit and user utility. Finally, the authors put forward suggestions for promoting the development of the online freight platform in the intracity freight market, and maintain the interests of the three parties (platform, consignor, and carrier) and cooperation relations.
3. Pricing Problem Analysis
3.1. Charging Mode and Two-Stages Game
In order to attract users, online freight platforms are generally free for users in the early days. When the number of users reaches a certain scale, the normal operation of the platform adopts a two-part tariff, that is, registration fee and commission. On the basis of a certain number of users, online freight platform charges a registration fee to ensure its profit. Based on the principle of “the more you use the platform’s services, the more you pay,” the platform charges a commission from the user (usually the carrier), who makes a deal with other-side user (the consignor). It can be seen that determining the amount of registration fees and commissions is one of the key issues in the operation of online freight platform. Therefore, the authors use the two-stage pricing game model to analyze the two-part tariff process which determines the registration fee and the commission.
In duopoly market, the first stage is the game between two platforms, consignors, and carriers. In order to get more users, there is a game between the two platforms. Simultaneously, two platforms and their users play a game which results in determining the registration fee. If the platform scale’s similar information is transparent, and pricing time series is not considered, the pricing will be consistent, and the market will eventually be divided equally by two platforms when the game is in equilibrium. If the platform scale is different and the unit service cost of the platform is different too, the platform with larger scale will finally get more users.
In the second stage, the consignor and the candidate carriers play a game to determine the freight rate which is the basis for calculating the commission. The platform supervises the operation of freight transactions between the consignor and the carrier, and reserves the right of two-side users to make their own choices. Considering the situation of the market where supply exceeds demand, the platform provides the consignor with candidate carriers. The game of second stage is subject to the game of first stage and manifested in the freight rate.
3.2. Factors Affecting Platform Pricing
The factors affecting the platform pricing strategy include platform scale, platform differentiation, user attribution, user external benefits, user habits, and government subsidies.
3.2.1. Platform Scale
The platform scale reflects its market position. The unit service cost of the platform decreases as the scale increases, which reflects the scale benefits of the platform. The authors use platform unit service cost to refer to platform scale in the pricing game model in the duopoly market.
3.2.2. Platform Differentiation
Platform differentiation comes from the differences in platform service functions, market reputation, etc., and is reflected in the differences in platform competitiveness. The platform with higher vehicle-cargo matching rate and user service satisfaction will be more competitive and more proactive in pricing and be easier to attract users to switch from another platform to its own. We use platform unit conversion cost to refer to platform differentiation in the pricing game model in the duopoly market.
3.2.3. User Attribution
The attribution of the users to the platform can reflect the market position of the platform and have an important impact on its pricing strategy.
In the intracity freight market, the carrier’s attributions are usually single-homing. There are strict distribution area restrictions in the city, and the platform will tag the carrier’s vehicle. The most common form is to spray on the platform’s logo on the vehicle, which brings advertising revenue and strengthens the relationship between the platform and the carrier.
In the duopoly market, the consignor’s attributions are partially multihoming and partially single-homing. In the intracity freight market, consignors include individual users and company users. Individual users have fewer consignment requirements, less consignment volume, and unstable relationship with the platform, so they are multihoming. On the contrary, company users have more consignment business, larger consignment volume, and stable relationship with the platform, which is manifested as single-homing.
Due to the differences and diversification of user attribution, the platform’s pricing strategy is to maintain users for single-homed users and attract users for multihomed users.
3.2.4. User External Benefits
The user externality benefits refer to the positive external benefit brought by users, which reflect market value of users. For example, the platform logo sprayed on the vehicle attracts more potential users for the online freight platform and increases the platform’s revenue. The platform weighs the pricing strategy according to the positive externality benefits brought by users. Due to bilateral network externalities and demand-supply imbalances, the positive externality benefits of consignors are generally higher than those of carriers.
3.2.5. User Habits
The traditional vehicle-cargo matching mode mainly relies on network of relationships between consignors and carriers, which is called user habits. Due to the low matching efficiency and high communication cost of the traditional mode, a new mode that relies on the online freight platform for vehicle-cargo matching has emerged. In order to change or correct user habit and develop new modes, the platform provides the user certain corrective incentives for each freight transaction according to the user’s market value, that is, user correction costs.
3.2.6. Government Subsidies
Online freight platforms can improve the efficiency of freight operations, reduce the unloaded rate of vehicles, and develop the Internet economy. The government usually gives certain subsidies to the platforms. Therefore, the platform can use government subsidies to set up a reward mechanism to increase platform user income, promote vehicle-cargo matching, and improve the vehicle full load rate.
4. Game Model
4.1. Game Model for Registration Fees between Platforms, Consignor, and Carrier
An improved Hotelling model is constructed to analyze the pricing strategy of leading companies on two-sided platforms under the duopoly market structure. This model analyzes the platform’s different pricing structures for two-sided users and the different attribution characteristics of two-sided users, and it introduces variables such as user externality benefits, platform matching capabilities, user conversion costs, and user correction costs.
Assuming that the duopoly platform is located at both ends of the interval [0, 1], namely, and . The carriers and the consignors are evenly distributed between the two platforms, numbered S and H, respectively, as shown in Figure 1.
The model assumptions are as follows:(1)In this market environment, the players in the game include the online freight platform, carriers, and consignors, and no others.(2)The platform’s charging model is a two-part tariff, and a certain part of the fee is allowed to be 0, that is, it is not charged.(3)The default number of transactions is 1.(4)When considering user externalities, only the positive externality benefits are considered.(5)The carrier’s commissions are levied in proportion to the two platforms.
The model parameters are as follows: and represent the number of carriers that are solely attributed to and , respectively, and normalize them to satisfy ; , , : , and represent the number of consignors that are solely attributed to and , respectively, indicates the number of consignors belonging to and , and normalize them so that ; and unit service costs for and , respectively; and : represent the unit conversion cost of the consignor that is solely attributable to the platform and represents the unit conversion cost of the carrier that is solely attributable to the platform; and represent the positive externality benefits of the consignor and carrier, respectively; and denote the expected vehicle rewards paid by and to the carrier, respectively; , represent the opportunity benefits (government subsidies) received by and , respectively; represents the platform’s charge of commission rate to the carrier, ; represents the probability of successful two-sided user transactions, ; and represent the basic utility of carrier and consignor, respectively; and denote habitual correction costs paid by and to the carrier, respectively; and represent habitual correction costs paid by and to the consignor, respectively; and represent the registration fees paid by the carrier to and , respectively; and represent the registration fees paid by the consignor to and , respectively; represents the final freight between carrier and consignor; this indicator is the decision result of the second stage game; and indicate the utility obtained by the carrier from and ; and represent the utility obtained by the consignor that are solely attributed to and , respectively; represents the utility obtained by the consignor belonging to and ; and represent the profit functions of and , respectively.
The utility of the carrier belonging to platform 1 alone on platform 1 is
Similarly, the utility of the carriers who belong to platform 2 alone on platform 2 is
The consignors are partially multihoming. The utility obtained by the single-homed consignor and the multihomed consignor can be expressed as follows:
Let be the undifferentiated points for the utility of the carriers. Since users are evenly distributed between and , indicates the number of carriers belonging to , that is . On the other hand, indicates the number of carriers belonging to , that is, . Similarly, and are the undifferentiated points for the utility of the consignors, and satisfy , , and . indicates the number of consignors belonging to , whereas indicates the number of consignors belonging to .
At point , the carriers have the same utility, that is . By combining equations (1) and (2), the undifferentiated point for the utility of the carriers is
In the above-mentioned formula, , , and .
Similarly, the undifferentiated points for the utility of the consignors are shown in the following equations
By combining equations (6)–(8), is shown in equation (7):
Considering , and combining equations (5) and (6), the number of carriers and consignors available for the above-mentioned various types is
The profit function of the online freight platform in a duopoly environment is
According to the equation set (9), and can be regarded as a multivariate function on . When considering , it is assumed that is a constant. Similarly, when considering , it is assumed that is a constant. At this time, the aforementioned equations can be converted into a binary function for processing. For the convenience of calculation, the case of symmetric equilibrium is considered, that is , , , and . Referring to the extreme value discriminant formula of the binary function, and can take the maximum value only when the conditions of the following equation are satisfied:
Let the first-order partial derivative of be 0, and the registration fee of for two-sided users in equilibrium state can be obtained according to the first-order conditions of profit maximization, as
Similarly, the registration fee of for two-sided users in equilibrium state can be obtained and we can know and . The equation set (12) can be further obtained:
The aforementioned formulas show that when there is no difference between the service and functions provided by the platform in the duopoly market, the result of the game between the two parties is to divide the market equally.
4.2. Game Model for Freight Rate between Consignor and Carrier
Let the set of consignors on the online freight platform be and , where represents the consignor, . Similarly, let the set of carriers on the online freight platform be and , where represents the consignor, . In this paper, each consignor plays a game with a number of candidate carriers at the same time. All the parameters in this paper are defined in Table 1.
The model assumptions are given as follows:(1)Factors such as vehicle type, transportation mileage, and reachable time of each carrier have met the requirements of consignor and will not affect the outcome of the game. The game information environment has complete information. The platform monitors the entire game process. The information between the consignor and the carrier is relatively transparent, but there is an information exchange barrier between carriers to prevent cooperation between alternative carriers.(2)Both sides of the game remain rational, the carrier will not accept low-price transactions, and the consignor will not accept high-price transactions. The quotation ranges of carrier and consignor are and , respectively. As a party that sells shipping capacity, the carrier’s psychological highest freight rate will be higher than the highest price of the consignor, and the lowest price it can accept is higher than the lowest price of the consignor. A transaction can only be concluded if the intersection of the quotation ranges of the two parties is not empty. With the help of the online freight platform, both parties can learn the lowest price that the other party is willing to continue trading, and the higher lowest price will become the common knowledge of both parties. In order to ensure the fairness of transaction, the online freight platform refers to historical transaction data and determines the highest freight rate of the corresponding transportation mileage and service time for each model, denoted as . The price generally does not exceed the highest price the consignor can afford. To sum up, the relational relationship of each price indicator is shown in equation (15): That is, the final negotiation interval for two-sided users is , which is also the common knowledge of both parties.(3)With the continuous bargaining between the two-sided users, the value of transactions is not static. The discount rates and represent changes in value, satisfying and . represents the static discount rate under no pressure, . As the dominant party, the consignor makes the first bid during the game. As the process progresses, the transaction value of the consignor will gradually decrease, and the transaction value of the carrier will increase.(4)The change in the discount rate is mainly due to the unequal status of the two parties, which results in different psychological pressures during the pricing game. The psychological pressure on the carrier, namely, , as the weak party in the transaction, is higher than the psychological pressure on the consignor, namely, , that is, . The psychological principle states that the party with the most stress will get much less than the counterpart. Hence, the psychological pressure is inversely proportional to changes in the transaction value. When the psychological pressure is 0, . When one party is under too much psychological pressure, the transaction will be concluded no matter how much the other party bids, that is, . The mathematical relationship between and is , in which represents psychological pressure and represents discount rate. In summary, and . To determine the specific relationship between psychological stress and discount rate requires a lot of behavioral analysis and data fitting, and the mathematical relationship is often different in different situations. After the analysis, a relational expression is developed as follows:
Other supplementary model parameters are described as follows.
: represents the freight rate determined by the consignor and the alternative carrier . Only when does the bidding process make sense. In order to calculate the one-to-one game equilibrium solution, it is assumed that the determined price conforms to a uniform distribution. If the negotiation interval is mapped to the unit interval [0, 1], then is transformed to , and the relationship is expressed as equation (17).
A three-round bargaining game is introduced to analyze this process, and the unique Nash equilibrium solution can be obtained. For detailed proofs, see [28, 29]. The three-round steps are shown in Figure 2. Considering that when the game reaches the equilibrium conditions, the two-sided users will agree on the equilibrium solution. Therefore, no matter which round the leading consignor starts quoting, the equilibrium solution stays the same.
In the following, it is shown how to solve the problem according to the idea of the reverse induction method. Assuming that the third round is the turn of the consignor’s offer, the carrier must accept the consignor’s offer at this time. The consignor’s price is , and the benefit of both parties is . In the second round, the carrier’s offer is , which should satisfy , that is, , and the benefit of both parties is . Finally, back to the first round, the consignor’s offer is , which should satisfy , that is, . At this time, the benefit of both parties is . From the perspective of game equilibrium, we can determine , and further obtain the equilibrium solution as
Based on equations (14)–(16), the one-to-one game equilibrium solution can be obtained as
Obviously, .
: indicates the lowest matching satisfaction that the consignor is willing to continue trading. Only when , the consignor is willing to bid.
: represents the psychological freight rate of the consignor. This indicator takes the consignor’s satisfaction with the carrier, the minimum satisfaction, and the equilibrium solution with the one-to-one game into account. The calculation formula is
The bidding game between the consignor and the candidate carrier is a one-to-many game. However, considering that the candidate carriers will not cooperate privately among themselves during the game and both parties have more common understanding, the one-to-many game can be split into multiple one-to-one games. , , , and need to be considered comprehensively when determining the transaction fee. The calculation formula is
In summary, in the bidding game model between the consignor and the alternative carrier, if and are satisfied for , then there exists a set of the following equations:t
5. Proposition Analysis
In this section we focus on the platform profit, registration fee, transaction fee, and consignor attributes. Based on the relevant information presented in the previous sections, the relationship between each dependent variable and influencing factors can be obtained as follows:
From , , , , , , , , , , Proposition 1 is obtained.
Proposition 1. Under the equilibrium conditions, an increase in positive externality benefits of two-sided users will reduce the platform’s viscosity to consignors, and an increase in consignor’s conversion costs will help the platform gather consignor resources. The platform’s ability to serve two-sided users is directly proportional to the unit service cost. Good service quality can increase the viscosity of the platform to consignors.
When the positive externality benefits are large enough, the market will transform into a pure multihomed freight market. When the unit conversion cost is large enough, there will be no multihoming users. If the platform service quality is improved to the highest theoretical level, there may still be multihomed users. As the number of increases, the unit service cost will continue to decrease. Hence, expanding the scale of the platform will become the platform’s top operating concern when the service quality cannot be improved.
Turning the attention to the impact of and on the platform profits and two-sided user registration fees, from , ; , ; , , and , Proposition 2 is obtained.
Proposition 2. Under the equilibrium conditions, an increase in two-sided external users’ positive external income is not conducive to increasing platform profits, and the positive external income of carriers will have a greater impact on the amount of platform profits. For carriers, the positive externality gains of two-sided users will reduce their registration fees and show a periodical characteristic.
In Proposition 2, as the user who belongs to the platform alone, the carrier is the main contributor to the profit of the platform. Hence, it appears that has a greater impact on the profit of the platform. For the consignor, the greater the positive externality income, the higher the registration fee will be charged. For the carrier, an increase in the positive externality income of the two-sided user will reduce its registration fee and show a periodical characteristic. The impact of positive externality benefits from both parties on the carrier’s registration fee shows a periodical characteristic. The main reason is that in the intracity freight market, is higher than . Initially has a greater impact. As the number of multiownership continue to decrease, the influence of will continue to weaken. Therefore, has a greater impact on the carrier registration fee later.
Considering the impact of and on the platform profits and two-sided user registration fees, from , , , , and , Proposition 3 is obtained.
Proposition 3. Under the equilibrium conditions, the greater the attractiveness of the platform, the higher the profit of the platform and the registration fee of the carrier. However, the registration fee of the consignor has nothing to do with the attractiveness of the platform.
An attractive platform indicates that its services and scale are leading the industry. At this time, the number of carriers is gradually increasing, and its registration fee will also increase, which in turn will increase the profit of the platform. As far as the consignor is concerned, the conversion cost has little restriction on it, and the platform is more than willing to reach a cooperation deal with it.
Considering the impact of unit conversion cost on the platform profits and two-sided user registration fees, from , , and , Proposition 4 is obtained.
Proposition 4. Under the equilibrium conditions, the higher the unit service cost, the smaller the platform’s profit will be, and the platform’s registration fee for two-sided users will increase.
According to the analysis in 3.2.3, the platform scale is negatively related to the unit service cost. Therefore, the higher the unit service cost, the smaller the platform scale is, leading to smaller profits. Equation (9) can also explain Proposition 4.
Considering the impact of on the platform profits and two-sided user registration fees, since the sign of is unknown, the sign of is unknown and , Proposition 5 is obtained.
Proposition 5. Under the equilibrium conditions, the impact of increased platform service capabilities on the platform profits and consignor registration fees is uncertain. For single-homed carrier users, increased service capabilities will increase the registration fees.
The impact of the improvement in platform service capabilities on the platform profits is negative first and then positive. In the early stage of development, the platform actively improved its service capabilities to attract two-sided users, thereby expanding the platform scale. At this time, the platform needs to sacrifice certain platform profits to pay for service costs. In the later stage, as the platform scale increases and the platform service structure system is completed, the platform will gradually enter a stage of rapid profitability.
Considering the impact of freight rate on the platform profits and two-sided user registration fees, from , , and , Proposition 6 is obtained.
Proposition 6. Under the equilibrium conditions, an increase in freight rate is not conducive to the growth of platform profits, and has a negative impact on the two-sided user registration fees.
For consignors, an increase in freight rates puts added economic pressure on them. The platform needs to reduce the registration fee of the consignor appropriately. The increase in freight rates sends a strong signal to unconnected carriers and will attract more carriers to access the platform. The increase in the number of carriers will encourage the platforms to reduce their registration fees. However, one of the main responsibilities of the platform is to regulate the freight market and to prevent the phenomenon of random price hikes or price cuts. If the platform’s ability to control freight rates declines, the platform’s viscosity to two-sided users will decrease, resulting in a decline in platform profits.
Considering the effect of on the platform profits and two-sided user registration fees, since the sign of is unknown, and , Proposition 7 is obtained.
Proposition 7. Under the equilibrium conditions, in order to ensure carrier benefits, the platform will reduce its registration fee while increasing commissions, but the impact on the platform profits is uncertain.
As the scale of the platform gradually expands and the number of carriers reaches a certain scale, the registration fee will not fluctuate too much. Meanwhile, the unit service cost will continue to decline, and the profit of the platform can be increased by increasing the commissions.
Considering the impact of the customary correction costs, government subsidies, and vehicle reward expectations on the platform profits and two-sided user registration fees, from , , , , and , Proposition 8 is obtained.
Proposition 8. Under the equilibrium conditions, the opportunity income obtained by the platform is positively motivated. The vehicle reward expectations and habits will not reduce the profit of the platform, and it will increase the attractiveness of the platform to two-sided users. Registration fees and correction costs of habits of two-sided users are closely related, and the vehicle reward expectations affect carrier registration fees.
Contrary to common sense, the spending on customary correction costs and vehicle reward expectations will not directly affect the platform profits, because the platform will increase the two-sided user registration fees while spending customary correction costs and vehicle reward expectations. However, looking at these two parameters separately, the impact of registration fees on the platform profits is positive, and the cost of customary corrections is negative.
Since , and the symbols of are unknown, when . Conversely, the sign of cannot be determined. The sign of is unknown, and its sign has a greater correlation with the carrier that eventually matches. This leads to Proposition 9.
Proposition 9. Under the equilibrium conditions, the psychological pressure of the carrier will negatively affect the equilibrium pricing, and the psychological pressure of the consignor is a favorable factor for the carrier to obtain high returns. The impact of static discount rate and matching satisfaction on the final freight rate is unclear.
The uncertainty of the effect of the static discount rate on the freight rate is an interesting phenomenon. Considering and , the different effects of the two-sided user discount rate on the freight rate are the external reasons for this phenomenon. The internal reason is strong psychological pressure, which does not reciprocate the effect of consignor discount rate. The matching satisfaction of the consignor with the carrier is not the prior knowledge of the alternative carrier, and will affect neither the psychological pressure of the carrier, nor the game pricing of the two parties.
6. Numerical Experiment
Based on the two-stage gaming model constructed in the previous section, the M tool is used for the experiment analysis to verify the above-mentioned propositions.
Numerical experiment is carried out around four aspects, specifically the four aspects of the owner’s user attribution characteristics, platform profit, bilateral user registration fee, and transaction fee. Through numerical experiment, the relationship between the parameters can be displayed intuitively, which helps us to obtain operational sexual conclusions or recommendations. Considering the platform’s profit and government subsidies, the two-sided user registration fee has a linear relationship with the customary correction cost and the vehicle reward expectation. Therefore, the parameter values of the three indicators are set as follows: , , and . For the sake of simplicity, taking , , and only the influence of the forward external income of the consignor on the relevant decision indicators are analyzed.(1)Simulating and analyzing the influence of , , and on the attribution characteristics of the consignor. By setting and , and varying , the results obtained are plotted in Figure 3(a). It can be seen that and change in opposite direction with .When is large enough, the consignor tends to be single-homing ( = 0), and eventually the two platforms share the resources of the consignor ( = 0.5). By setting and , and varying , the results are plotted in Figure 3(b). It can be seen from Figure 3(a) that and change in opposite direction with . When is large enough, the consignor’s attribute tends to be multihoming, and eventually the platform’s dominant position in the market is lost. By setting and , and varying , the results are plotted in Figure 3(c). It can be seen from Figure 3(c) that and change in opposite direction with .When is large enough, the consignor tends to be single-homing and eventually the consignor chooses the platform with higher service quality.(2)The experiment analysis of the impact of , , , , , and on the platform’s profit. By setting , , and varying , the results obtained are plotted in Figure 4(a). It can be seen that decreases as increases. By setting , and varying , the results are plotted in Figure 4(b). It can be seen that increases as both and increase. It indicates that setting a higher two-sided user unit conversion cost has a positive effect on maintaining the platform’s profit. By setting and varying , the results are plotted in Figure 4(c). It can be seen that increases as increases. It shows that the construction of a perfect service network system will help to improve the profit of the platform, in consideration of the limitations on the setting of numerical indicators. With the completion of the service system, reducing the unit cost of providing services by the platform will become one of the goals of the platform’s operation. By setting and varying , the results are plotted in Figure 4(d). It reveals that decreases as increases. It shows that controlling the freight rate is the key to ensure the profitability of the platform. By setting for the case of and varying and by setting for the case of , and varying , the results of the two cases are plotted in Figure 4(e). The results reveal that in different environments, it has different characteristics with changing trends. In the initial stage of platform construction, the unit service cost is high, and the platform needs to actively attract two-sided users. At this time, the commission is not the main source of platform profit. With the gradual expansion of the platform scale, the service network system is gradually improved, and the unit service cost is constantly changing. Lowering commissions will become a major tactic for growing platform profits.(3)Simulating and analyzing the impact of , on the two-sided user registration fees and . By setting , and varying , the results obtained are plotted in Figure 5(a) to show the trend of and changes with , relatively minor on and major on in a beneficial way. By setting and varying and , the results are plotted in Figure 5(b), which shows that increases with unit conversion costs for two-sided users. By setting , and varying , the results are plotted in Figure 5(c), which shows that both and increase with . Hence, higher unit conversion cost invites higher user registration fee, more on the carrier than the consignor. By setting , , , , , and varying , the results are plotted in Figure 5(d), which shows that decrease with . Hence, higher freight rate promotes lower registration fees. By setting , , , , , and varying , the results are plotted in Figure 5(e), which Indicates that decreases with . It implies that higher commission would lower carrier’s registration fee.(4)For the second stage of the game, the influence of on the freight rate is simulated and analyzed. By setting , , and varying , the results obtained are plotted in Figure 6(a). It can be seen that the psychological pressure on the consignor has a positive impact on the freight rate. By setting , analysis of the impact of on the transaction of freight might need to consider multiple factors including the number of carriers and each carrier’s psychological pressure. In the process of this research, the psychological pressures on a certain two carriers are considered in order to study the impact of individual carrier psychological pressure on the transaction of freight. The results obtained are plotted in Figure 6(b). It can be seen that the impact of carrier’s psychological stress on freight rate is negative. Considering the impact of static discount rate on the freight rate, it is found in the research process that when , the effect of static discount rate on the freight rate is uncertain. However, when and , by setting for the convenience of numerical calculation, taking the results plotted in Figure 6(c). On the other hand, when , if , then is satisfied, else, . By setting , and , for the respective case, the results are plotted in Figure 6(d). It can be seen that when , the impact on the freight rate is fluctuating (going up first and then down). But regardless of which case, if maintains at a high level, then a considerable freight rate is the result. Proposition 6 is proved.
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7. Conclusions and Recommendations
The road freight market under the participation of the online freight platforms has typical characteristics of a two-sided market. Our research selects the duopoly online freight platform under the intracity freight market as the object, sets the platform service mode as the bidding mode, and establishes a two-stage pricing game model. While focusing on the platform pricing strategy, full attention is also paid to the freight rate. In order to construct a perfect platform pricing mechanism, the main conclusions obtained in this research are listed as follows:(1)The equilibrium solution is stable only when the carrier expects the return, while the user’s forward externality parameter and the unit conversion cost satisfy certain constraints.(2)Setting a higher conversion cost can retain users, increase platform profit and reduce user utility, but also need to consider the effect of user’s positive external income. The greater the user value, the less willing to belong to the platform alone, and the impact of registration fees is also a variable. When charging users for registration fees, a tradeoff between these two factors must be weighted.(3)The excessive user’s positive external income and the carrier’s expected income are unfavorable to the increase of the platform profit, but it is extremely beneficial to increase the user’s utility. The influence of the carrier’s expected income on the consignor’s registration fee is clear. The impact of its own registration fee, however, is uncertain.(4)Constructing a complete service network system and controlling freight rate will help to increase the profit of the platform.(5)In the initial stage of platform construction, the unit service cost is relatively high. With the gradual expansion of the platform scale, the unit service cost will continue to decrease, and the commission will become a major growth point of the platform profit.(6)Government subsidies are positive motivation for the platform. The impact of vehicle transportation incentives on the platform profits is negative. In the actual process, customary cost will not directly affect the platform profit and two-sided user utility, and it is closely related to the platform registration fee.(7)In the consignor-carrier transaction, the consignor is the dominant party of the transaction, the psychological pressure is the main factor affecting the freight rate, and the impact of the static discount rate and matching satisfaction on the freight rate is uncertain.
Based on the aforementioned conclusions, a number of recommendations are made for promoting the development of the online freight platform as described below:(1)Since the increase in conversion cost is beneficial to increase the profit of the platform and the number of users belonging to the platform, and the fundamental reason for increasing conversion cost is triggered by the increasing market influence of the platform. Therefore, increasing the degree of differentiation with similar platforms is an effective operation mode of online freight platform.(2)In the initial stage of platform construction, the unit service cost is relatively high, and the platform needs to actively attract bilateral users. It can appropriately sacrifice due profits and actively invest in the construction of a service network system. After the scale of the platform expands, the platform needs to improve service quality and continue to maintain and consolidate the relationship with bilateral users.(3)Collecting commissions and controlling freight rates are the key means to ensure that the platform can obtain considerable profits. Therefore, the platform needs to grasp the changes in market freight rates in a timely manner, formulate regional transaction charge rules, and reasonably control the freight rates of bilateral users. The platform waives commissions in the early stage to attract more drivers. After the platform expands, it gradually charges commissions, such as Yunmanman’s pricing strategy.(4)The opportunity benefits brought by the policy are positive incentives for the platform, and the vehicle reward expectations and habit correction costs are closely related to bilateral user registration fees. In order to attract users to access the platform, in the freight trading market, the platform can increase the viscosity of the platform to cargo owners by issuing cash coupons and waiving commissions. In addition, charging the carrier registration fee is one of the main sources of income for the platform. The platform can provide services such as free vehicle inspections and vehicle maintenance.(5)Equally important is to ensure that the renegotiation of two-sided users is carried out online, and try to avoid mutual contact between the two parties before the transaction, to ensure that the matching satisfaction does not become the common knowledge of two-sided users, thus ensuring the fairness of the transaction.
This study only considers the pricing of freight information platforms in the same-city logistics industry, and the market environment only studies the duopoly environment, and the game environment is a static and complete information environment that does not consider pricing timing. Follow-up research can focus on freight information platforms in the trunk logistics industry. The market environment can also be extended to the competitive monopoly environment, and the gaming environment can become an incomplete information environment considering the timing of pricing. Adding specific cases for analysis in the research process to fully verify the proposition is also one of the research directions.
Data Availability
The data that support the findings of this study are available on request from the corresponding author upon reasonable request.
Conflicts of Interest
The authors declare that they have no conflicts of interest.
Acknowledgments
This work was supported by the National Key R&D Program of China through Grant no. 2018YFC1407405.