Evolutionary game analysis of three parties in logistics platforms and freight transportation companies’ behavioral strategies for horizontal collaboration considering vehicle capacity utilization

In China, logistics platforms are an effective way to solve vehicle capacity utilization using information sharing. However, most logistics platforms do not possess operational sustainability due to excessive profit-seeking. To address this problem, conflicts of interest among freight transportation participants are discussed using a stakeholder approach. A three-player evolutionary game model (TEGM) is developed to analyze the interactions among freight carriers, freight shippers, and logistics platforms. Then, the asymptotic equilibrium and evolutionary stability strategies of the three-player game are analyzed. The results indicate that a high-level positive network externality is the driving force behind the logistics platform’s “high-level service”. A fairness payment incentive guarantees a “sharing” strategy for freight carriers and shippers. When the high-level positive network externality is limited and lower than a threshold value, there is no stable equilibrium point in the TEGM. A government tax incentive cannot change the freight carriers’ and shippers’ strategy to participate in this horizontal collaboration system, except for the logistics platform’s probability of providing “high-level service”. However, the behavioral strategies of the freight transportation participants can be changed to achieve the sustainability of freight transportation by reducing the value-added tax rate through the logistics platform and increasing the high-level positive network externality of the logistics platform and other participants’ perceived fairness through a payment incentive. Finally, suggestions for regulating the behaviors of freight transportation participants and promoting the sustainability of freight transportation are discussed.


Introduction
The low-capacity utilization of vehicles and empty mileage leads to a high freight transportation cost [1]. Inefficient transportation has a negative impact on the environment and society, which has attracted increasing attention, and many B Guohua Wu guohuawu@csu.edu.cn 1 School of Safety and Management Engineering, Hunan Institute of Technology, Hengyang 421001, China scholars have studied ways to improve vehicle capacity utilization [2]. The level of empty running and the capacity utilization of freight vehicles have hardly changed. EU statistics show that in most member states, empty vehicle running ranges between 15% and 30%, and capacity utilization by weight ranges from 54% to 57% over a 5-year period (Eurostat, 2019) [3]. Considering the vehicle capacity utilization problem, since freight transportation is a primary component of supply chains, horizontal collaboration is considered a crucial strategy to optimize the overall cost and the related environmental and social impacts [4]. A lack of information exchange and the absence of social trust deter horizontal collaboration [5]. A logistics platform is presented to solve the information exchange problem, as in Yunmanman, Huolala et al. In present-day China, the sustainability of such a platform is strategically important, because it can optimize vehicle capacity utilization and reduce empty mileage [6]. That is, the sustainability issue of horizontal collaboration is becoming a challenge for freight transportation in China. In this context, it is significant to understand the interests and interactions of freight transportation stakeholders. In practice, most freight transportation platforms cannot coordinate stakeholders' interests to ensure the sustainable operation of horizontal collaboration. Therefore, the behaviors and interactions of freight transportation stakeholders from a sustainable operation perspective represent an important and interesting topic, which is our research's focus.
Specifically, vehicle capacity utilization includes many stakeholders, freight carriers, freight shippers, and logistics platforms, which are considered to be the three critical capacity utilization participants. The three participants often face a conflict of interest when maximizing their respective interests. For example, in the case of weak mutual trust, logistics platforms can often obtain some extra benefits through non-compliant operations. Moreover, the total return of the logistics platform will decrease, which is not aligned with the expected revenue of freight transportation and retards horizontal collaboration. According to Garc´ıa-Perez et al. [7], sustainability can be seen as the result of the coordination of interests among multiple stakeholders. It is almost impossible to achieve the sustainable operation of logistics platforms if the conflicts of interest among logistics platform participants are not balanced [8]. In addition, due to the lack of information exchange, a lack of regulatory systems for logistics platforms, and high privacy security concerns, the regulation of the logistics platform market is typically subject to considerable uncertainty. Therefore, achieving sustainable vehicle capacity utilization depends on the strategic regulatory game that addresses the behaviors of freight carriers, freight shippers, and logistics platforms.
In recent years, issues related to the behavior of actors involved in vehicle capacity utilization have received increasing attention, but this research remains in its early stages. First, most researchers are keen to elaborate on the importance of the issue through case studies [9,10]. To quantify the economic and environmental benefits of collaboration by companies, Palmer et al. [11] reported a 23% reduction in cost with 58% fewer road kilometers traveled and a 46% reduction in CO2 emissions in an actual strategy examination. Second, research on the improvement of optimization algorithms remains limited in the literature [6,12,13]. To reduce the overall cost and related environmental and social impacts, Muñoz-Villamizar et al. [14] proposed a biased randomization-based algorithm to solve the problem with a multiobjective function to explore the relationships between delivery and environmental costs. The optimal selection of vehicle types depends considerably on the time horizon under evaluation and demand variation. Third, from the perspective of sustainable operations, research has focused on mechanisms to coordinate interests using game theory [15]. Hernández et al. [16] indicated that a higher degree of collaboration and capacity utilization improves the tradeoff between collaborative capacity and holding costs. To analyze conflicts of interest, a three-player evolutionary game model (TEGM) emphasizing bounded rationality and dynamic decision-making processes was formulated to study the interest-coordination mechanism among freight transportation participants. On the one hand, due to incomplete information and information asymmetry [17], freight carriers, freight shippers, and logistics platforms fail to acknowledge one another's decisions (e.g., willingness to cooperate, trust, or privacy security concerns), and they show bounded rationality in their decision making based on their previous interactions. On the other hand, the development of cooperation is hindered, because the model is widely applied in internal rather than external networks. With the profit space continuously narrowed and the pressure from the competitive environment of the logistics industry, it is significant to construct an effective mechanism to facilitate the logistics platforms and the freight transportation companies to collaborate to improve the vehicle capacity utilization, reduce freight costs, and promote the development of freight industry. Thus, the behavioral system among freight carriers, freight shippers, and logistics platforms should be captured by dynamic decision-making processes using the TEGM. It is important to apply a TEGM to study logistics platforms and user companies' behavioral strategies.
According to an overview of the studies on the behavior of freight transportation participants, the research questions and motivations of this paper are summarized as follows.
Our study intends to answer the following questions: (1) To coordinate logistics platform and freight transportation companies in vehicle capacity utilization problems by analyzing the positive externalities, which aims to build an effective mechanism to increase the logistics platform's social value. (2) To promote the logistics platform to provide high-level services according to the logistics platform's collaboration trajectory changes over time, which aims to enhance the freight shippers and the freight carriers attending the logistics platform, then the vehicle capacity utilization will be increased.
To address the aforementioned issues, by adopting a stakeholder approach, the conflicts of interest among freight carriers, freight shippers, and logistics platforms are analyzed in this paper. In addition, due to asymmetric information, short-sightedness, and self-interest, freight transportation participants may exhibit bounded rationality in multistage games. A TEGM is developed to analyze the equilibrium and evolutionary stability strategies, which imply the interactions and interest-coordination mechanisms among freight transportation participants.
The purpose of our study is to increase the motivation of freight transportation participants in the logistics platform.
Our contributions are summarized in the following points: (1) An efficient mechanism formulated by TEGM with three players is developed to explore interactions among freight carriers, freight shippers, and logistics platforms, which overcomes the limitations of the two-player game mechanism applied in previous studies. (2) The interest-coordination mechanism among freight transportation participants is designed to guide each participant to choose the behavioral strategy, which is beneficial to the sustainability of freight transportation. The behavioral strategies of freight transportation participants are theoretically and numerically analyzed, and conclusions contributing to the sustainability of freight transportation are obtained. (3) We systematically investigate the factors influencing the behaviors and interactions of freight transportation participants and analyze the impact of rewards and penalties imposed by positive network externality, tax incentives, and freight shippers/carriers' incentives on evolutionary stability strategies. We propose suggestions for the sustainable development of the freight transportation industry.
The remainder of the study is organized as follows. "Related work" presents a literature review on dual supply chains. Section "Model formulation" describes the TEGM mathematical model used in this study and the assumptions and notations applied in this paper. Section "Model analysis" introduces the interactions among freight carriers, freight shippers, and logistics platforms. Section "Numerical analysis" performs a numerical analysis to gain additional management insights. Finally, "Conclusions and implications for future research" provides conclusions and directions for future research.

Related work
In recent years, to solve the vehicle capacity utilization problem, there has been much-related work is reviewed in terms of the selection of vehicles, the optimization algorithm, the horizontal cooperation mechanism, and the logistics platform for freight sharing.
First, the selection of vehicles is one of the main focuses of this work. Leach et al. [18] increased the maximum length of vehicles to 25.25 m to expand the volumetric carrying capacity. They also contend that high-capacity vehicles will yield valuable environmental and financial benefits but are unlikely to have the same impact on road safety. Liimatainen et al. [19] reported that the use of longer and heavier vehicles (LHVs) for various commodities in road freight transport can ensure considerable savings in traffic volume and emissions. Isler et al. [20] designed a visualized geostrategic railway network for freight services to solve multiple freight type transport problems. Carrone et al. [21] found that the use of autonomous vehicles (AVs) in regular vehicle (RV) operation areas will reshape the transport system and greatly improve capacity utilization. Sun et al. [22] raised a road-rail combined transport form to minimize the total costs and carbon dioxide emissions of the routes. The costs and carbon dioxide emissions problem can be minimized through the selection of vehicles to a certain extent; however, the high-capacity vehicles also mean greater investment in fixed assets.
Second, some scholars have improved optimization algorithms to solve the less-than-truckload (LTL) carrier problem without the investment in fixed assets. Barcos et al. [23] developed an ant colony optimization algorithm to solve real-life less-than-truckload carriers serving many-to-many distribution network problems and solve it for a real case in Spain. To increase truck payload utilization and mitigate externalities, Mesa-Arango and Ukkusuri [24] proposed a branch-and-price algorithm to solve a multicommodity oneto-one pickup-and-delivery vehicle routing problem, which implies that nonconsolidated bids are dominated by consolidated bids. Maknoon et al. [13] proposed a sequential priority-based heuristic algorithm to address the scheduling truck problem in a less-than-truckload logistics network. Estrada-Romeu and Robuste [25] proposed an improved tabu search algorithm to identify when freight consolidation strategies are cost-efficient in less-than-truckload carriers' operations, which reduces the transportation costs by 20%. Based on the historical data of a freight transport company, Sicilia-Montalvo et al. [26] developed an intuitive application to optimize long-distance freight transport in an improved ant colony algorithm. Wu et al. [27] modeled a vehicle routing problem with a time window supply chain to study the selection between a private trucker and an outside carrier. They also developed a heuristic algorithm to minimize the total cost of the selection. Wang et al. [28] presented a fuzzy mixed-integer linear programming model to optimize imprecise total costs with uncertain data in intermodal freight transportation and took node capacity, detour, and vehicle utilization into account to estimate its performance. Shao et al. [29] proposed an auction-based waste collection synchronization mechanism with a two-layered algorithm to optimize less-than-truckload transportation service procurement in the waste collection industry. Hernández and Peeta [30] insisted that a higher degree of collaboration always leads to a win-win situation in a single-carrier collaboration problem when a less-than-truckload carrier seeks to acquire other carriers' capacity to service excess demand. Karam and Reinau [31] proposed a double combination to improve the eco-efficiency of road freight transport in empty tractor-semitrailer trips, but it is less effective for just-intime deliveries. Obviously, the algorithm optimization has achieved great benefits for enterprises, but with the development of the supply chain, the limitation of the enterprise's internal operation optimization becomes more obvious.
Third, other scholars have searched for an effective horizontal cooperation mechanism. Through a case study of the inventory routing problem (IRP) with multiple suppliers and customers, Soysal et al. [32] found that horizontal collaboration among suppliers plays a major role in decreasing total costs and emissions. Based on an incremental perspective, Pomponi et al. [5] found that mutual trust among partners and the extent of cooperation are two main dimensions for companies to achieve horizontal collaborations. Sitadewi et al. [9], using Indonesian case study data, reported that trust is a key enabler of horizontal collaboration in their section on freight trucking transportation. Lotfi et al. [33] used qualitative research methods to understand horizontal collaboration in micro-and small companies, and the results show that relational rents, relational capital, and relational governance mechanisms have important effects on collaboration. To balance the distribution of interests among participants, Vanovermeire et al. [34] insisted that the total cost can be further decreased by applying a Shapley value method, and when the partners adopt a flexible attitude, horizontal logistics alliances can increase both collaborative and individual gains with the Shapley value. Seok and Nof [35] found that bids among manufacturers/coalitions are effective in dealing with collaborative capacity sharing (CCS) problems among manufacturers. Chakravarty et al. [17] studied the optimal contracting problem with a newsvendor model, and the results show that the optimal contract may approach the first-best capacity level and benefit both firms. Padilla Tinoco et al. [36] reported that co-loading is the type of horizontal collaboration that can reduce transportation costs and CO2 emissions; they argued that a cost-sharing agreement might lead to a stable situation for the partnership. More literature on horizontal collaboration is summarized in Serrano-Hernández et al. [37]. De Vos et al. [38] developed a heuristic solution method to solve the cyclic inventory routing problem by considering horizontal collaboration through a third-party logistics service provider. Padmanabhan et al. [39] proposed a solution method based on a large neighborhood search to solve a centralized collaborative planning scheme model, which benefits collaboration among lessthan-truckload carriers. Palhazi Cuervo et al. [40] conducted a simulation study to prove that different partner characteristics perform differently in horizontal logistics collaboration.
Hacardiaux et al. [41] accounted for partners' preferences regarding the decrease in logistical costs versus reduced CO2 emissions to formulate a multi-partner multiobjective location-inventory model that ensures fair and efficient horizontal cooperation in logistics.
It is known that horizontal collaboration in logistics would reduce costs, increase fulfillment rates, and decrease CO2 emissions, but it remains rare, because it is not usually sustainable [42]. Buijs et al. [43] investigated the important role of available information technology applications for collaborating freight carriers in the less-than-truckload industry in a case study. Pan et al. [2] provided a literature review on horizontal collaborative transport and reported that the physical internet is a horizontal collaborative transport solution that has been developed since 2010. Although enterprises realize the importance of horizontal cooperation, the lack of effective information exchange and weak mutual trust leads that the horizontal cooperation only occurring in the original close cooperation between enterprises.
To realize efficient information exchange and build mutual trust relationships, logistics platforms for freight sharing have attracted considerable interest. Arnäs et al. [44] developed a platform for transporters' hybrid shipment control of less-than-truckload (LTL) transport networks to reduce resource requirements and carbon emissions. Royo et al. [12] proposed a mixed delivery system for pallet and package delivery companies to improve the use of resources, which is preferable to a pure system. Atasoy et al. [45] proposed a mixed-integer programming formulation for pickup and delivery problems with time windows to trade off the interests of platform providers, shippers, and carriers and used a dynamic pricing approach to ensure that carriers are better off collaborating. Rodríguez Cornejo et al. [46] presented lean thinking in the physical internet (PI), a value stream map method to minimize waste that is resilient to change, which can easily identify empty transport and unnecessary CO2 emissions. Based on localization data, travel time and timewindow constraints, Montecinos et al. [6] proposed a sharing logistics platform with a matching algorithm for less-thantruckload systems to reduce the number of trucks, operational costs, traveling distances, and gas emissions. To maximize the utility of logistics resources utilization, Cai et al. [47] proposed a subsidy strategy to solve the problems in the transaction orders of drivers and consignors on the sharing logistics platform. Logistics platforms are established, but there is a less effective mechanism to make them work effectively.
In summary, although the aforementioned literature has discussed either the behavior of freight transportation participants or horizontal collaboration, there are still limitations that need to be addressed.
(1) According to the aforementioned literature, a logistics platform is introduced to provide information services and freight sharing strategies based on the internet [2]. However, the operational effect of existing logistics platforms is unsatisfactory. Thus, we propose an effective mechanism by formulating a TEGM consisting of three players, including freight carriers, freight shippers, and a logistics platform, to achieve sustainability in freight transportation. (2) An empirical approach [9,10], or a qualitative approach [33], to investigate the freight transportation company's optimal strategy is popular in the existing literature. However, although cooperation brings many benefits, there is still a lack of enthusiasm for it among participants. Our work aims to study the interaction and interest-cooperation mechanisms among freight transportation participants to achieve sustainability in freight transportation. (3) There are conflicts of interest among the major freight transportation participants [5]. Thus, it is necessary to understand the interests and interactions of freight transportation participants to coordinate them to achieve sustainable development in the freight transportation industry.

Problem description
The Chinese government offers numerous supports for network logistics platform enterprises, including offering subsidies to logistics platforms for their R&D, building supporting facilities and infrastructures, imposing a value-added tax, and tax incentives. In this study, we consider the three most influential stakeholders, including freight carriers, freight shippers, and logistics platforms, to achieve sustainability in the freight transportation industry. As shown in Fig. 1, the behavior of investors is significantly affected by both logistics platforms and freight transportation companies. In detail, a good reputation can attract more freight transportation companies to share their demand/transportation information on a logistics platform [46]. Moreover, the lack of regulation, the non-compliant operation of logistics platforms and the default behavior of freight transportation companies are the main causes of chaos in the freight transportation industry. Thus, research on the sustainability of freight transportation can also simplify the discussion of the behavioral strategies chosen by freight carriers, freight shippers, and logistics platforms regarding their conflicts of interest. Specifically, the logistics platform needs to follow the competitive rules of the market, regulate its behavior according to local policies and regulations, and ensure the security of logistics platform transactions. Specifically, through high-level services, the logistics platform can transfer tax incentives to freight transport participants through tax planning and improve user matching between freight carriers and shippers. Freight shippers are freight transportation companies that send freight transportation demand information to a freight carrier through the logistics platform. The freight carriers are companies or individuals that deliver the goods to the agreed location following the freight shippers' requests on the logistics platform. These three participants often have conflicts of interest when pursuing their respective interests, and such conflicts will prevent horizontal collaboration among freight transportation companies from solving the vehicle capacity utilization problem.
In addition, in the presence of information asymmetry, it is difficult for logistics platforms to encourage more freight transportation companies to share their capacity due to incomplete information sharing. Furthermore, freight shippers do not know whether the carrier will adopt a "share" strategy or whether the platform will offer "high-level service". Similarly, freight carriers also do not know any information about the other participants. Thus, a dynamic game exists in the interaction among freight carriers, freight shippers, and logistics platforms. In other words, since the three participants exhibit bounded rationality, the behavioral choices are closely related to their previous behaviors. Therefore, a TEGM that determines how to balance the interests among the three participants is developed in the presence of information asymmetry is the focus of the following work.

Assumptions and parameter settings
Assumption 1. To simplify the problem and limit the scope of the research, the TEGM has only three participants, where the logistics platform enjoys government tax preference and supplies information-sharing services for freight carriers and shippers; freight carriers receive transportation orders through the logistics platform, and freight shippers release demand information through the logistics platform.

Assumption 2.
Considering human beings' ability to calculate and recognize the environment is limited. The three participants in the freight transportation system are subject to bounded rationality which leads them to choose their strategy by the duplicate dynamic equation, as this is more aligned with reality, and we choose evolutionary game theory as the main research method. [48], to model the objection of three freight transportation participants, they are all assumed to be risk-neutral, so they aim to maximize their interests. As a horizontal collaboration intermediary, the logistics platform aims to maximize its profit. Freight carriers, as actual carriers, maximize their vehicle capacity utilization and attempt to maximize their income. Freight shippers, as demand information supporters, also seek to maximize their profits.

Assumption 4.
Due to the encouragement of local policies in China, the logistics platform always obtains a certain degree of actual value-added tax preference, which is a main driver for the logistics platform gathering freight participants. Based on the basic value-added tax rate for the transport industry t 1 (t 1 denotes the basic value-added tax rate), the logistics platform will pay taxes at preferential tax rates t 2 (t 2 denotes the value-added tax rate after subsidization by the government's preferential policies). Assumption 5. The participants' decision preferences will determine the evolutionary stability strategy, so based on an incomplete information game: the set of strategies of freight carriers is C {share transportation capacity, do not share transportation capacity}, where x represents the probability of freight carriers choosing the "share transportation capacity" strategy, 1-x represents the probability of freight carriers choosing the "do not share transportation capacity" strategy, and 0 ≤ x ≤ 1. The set of strategies of freight shippers is A {share demand information, do not share demand informa-tion}, where y represents the probability of freight shippers choosing the "share demand information" strategy, 1-y represents the probability of freight shippers choosing the "do not share demand information" strategy, and 0 ≤ y ≤ 1. The set of strategies of the logistics platform is P {high-level service, low-level service}, where z represents the probability of the logistics platform choosing the "high-level service" strategy, 1-z represents the probability of the logistics platform choosing the "low-level service" strategy, and 0 ≤ z ≤ 1.
The superscript "S" is used throughout to denote the sharing strategy for both freight carriers and shippers, and "N" denotes the no-sharing strategy. The combination is denoted M {S, N}. The subscript "H" denotes the "high-level service" strategy and "L" denotes the "low-level service" strategy. The combination is denoted B {H, L}; "C" is for freight carriers, "A" is for freight shippers and "P" is for the logistics platform. obviously, t 1 > t 2 . According to the aforementioned assumptions, the main factors that are considered by freight carriers, freight shippers, and the logistics platform in the behavioral strategies are clarified, and the parameters involved in the model are defined, as shown in Table 1.

Return matrix of a three-player evolutionary game model
Case 1. {share transportation capacity, share demand information, high-level service}. The revenue for carriers in the sharing strategy when the logistics platform chooses the "high-level service" strategy is (1−t 2 )r S C H , and the incentive payments by the logistics platform for sharing the transportation capacity of freight carriers is I C ; therefore, the revenue The total revenue of the logistics platform under the freight carriers/shippers sharing strategy is E C + E A , the external benefits of the logistics platform under the "high-level service" strategy is R H , and the cost is C H ; therefore, the revenue of the logistics platform is Case 2. {share transportation capacity, share demand information, low-level service}. Based on Case 1, when the logistics platform chooses the "low-level service" strategy, it will not share tax breaks or incentive payments with the other participants. Therefore, the revenue for carriers under the sharing strategy is (1 − t 1 )r S C L . Similarly, the revenue of freight shippers is (1 − t 1 )r S AL . The total revenue of the logistics platform under the freight carriers/shippers sharing strategy is E C + E A , the external benefits of the logistics platform under the "low-level service" strategy is R L , and the cost is C L ; therefore, the revenue of the logistics platform is In summary, the return matrix of the TEGM among freight carriers, freight shippers, and the logistics platform can be obtained according to the aforementioned statements. It is shown in Table 2.

Freight carriers
The freight carriers' strategy will be influenced by the probability of the logistics platforms providing the "high-level service", as shown in Fig. 2, when the initial state of the behavioral strategy of the freight carriers is in different spaces, such as V 1 ,and V 2 , the freight carriers will adopt a In the subsections, we are going to discuss these two cases.

Replicator dynamic equation and evolutionary stability analysis
Proposition 1. When the initial state of the behavioral strategy of the freight carriers is in space V 1 , that is z > z C , and x 1 will be the equilibrium point, the freight carriers will adopt the strategy of "share transportation capacity". Therefore, as the tax incentives on the platform encourage freight carriers to choose "share transportation capacity", so the cost of sharing capacity for the freight carriers is less than the benefits obtained thereby, the freight carriers will adopt the strategy of "share transportation capacity".

Proposition 2.
When the initial state of the behavioral strategy of freight carriers is in space V 2 , that is z < z C , and x 0 will be the equilibrium point, the freight carriers will adopt the strategy of "do not share transportation capacity". Therefore, when the cost of sharing capacity for the freight carriers exceeds the benefits obtained thereby, the freight carriers will adopt the "do not share transportation capacity" strategy.
Assume that the freight carriers' expected returns from adopting the "share transportation capacity" strategy are E C1 , the expected returns from adopting the "do not share transportation capacity" strategy are E C2 , and the freight carriers' average expected returns under the mixed strategies are E C . Then, we have the following: The duplicate dynamic equation [48] implies the players imitate the rate of growth dominant strategy per unit of time t. The freight carriers select the duplicate dynamic equation for "share transportation capacity" as For ease of calculation, let z C .
➀ When z z C , then F C ≡ 0, which shows that all levels are stable. ➁ When z z C , set F C 0; then, x 0 and x 1 are two stable points.
Let F C be the derivative of x and derived from F C : According to the requirements of the evolutionary stability strategy (ESS)F C < 0, z C is analyzed, because 0 < x < 1, 0 < y < 1, and 0 < z < 1, ESSs are obtained considering the following two scenarios. Scenario 1. If 0 < z < z C , when x 0, F C < 0; when x 1, F C > 0; therefore, x 0 is an ESS. That is, the freight carriers adopt the "do not share transportation capacity" strategy.

Scenario 2.
If z C < z < 1, when x 0, F C > 0; when x 1, F C < 0; therefore, x 1 is an ESS. That is, the freight carriers adopt the strategy of "share transportation capacity".
According to the analysis, the dynamic evolutionary trend of freight carriers is shown in Fig. 2; therefore, propositions 1 and 2 are proven.

Evolutionary analysis of freight carriers
As shown in Fig. 2, when the other parameters are fixed, z C increases as t 2 increases. When z C increases, the area of V 2 expands. That is, as the tax rate after subsidization through the government's preferential policies increases, the "share transportation capacity" strategy will lead freight carriers to afford higher costs. To maximize their own profits, freight carriers will choose "do not share transportation capacity". Similarly, when t 1 increases and z C decreases, the area of V 1 contracts. In other words, an increase in the basic tax rate will cause the freight carriers to choose "share transportation capacity", which will reduce the real tax rate payment through tax preference for the logistics platform. When I C increases and z C decreases, the area of V 1 expands. This shows that the logistics platform is increasing the incentive payment to enable freight carriers to choose "share transportation capacity" under the provision of high-level services. when (r N C L − r S C L ) is increased and z C increases, and the area of V 2 expands. In other words, when the platform provides "low-level service", freight carriers will tend to choose "do not share transportation capacity" to maximize their profits. When r S C H increases, r N C H decreases, and z C decreases, the area of V 1 expands. This means that when the platform provides "high-level service", the freight carriers will gain more profits by choosing "share transportation capacity".

Freight shippers
The freight shippers' strategy will be influenced by the probability of the logistics platforms providing the "high-level service", as shown in Fig. 3, when the initial state of the behavioral strategy of the freight shippers is in different spaces, such as V 3 ,and V 4 , the freight shippers will adopt a different strategy. In the subsections, we are going to discuss these two cases. 3 , that is z > z A , and y 1 is the equilibrium point, the freight shippers will adopt the strategy of "share demand information". Therefore, considering that the tax incentives of the platform encourage freight shippers to choose "share demand information", when the cost of sharing traffic for the freight shippers is less than the benefits obtained thereby, the freight shippers will adopt the strategy of "do not share demand information". 4 , that is z < z A , and y 0 is the equilibrium point, the freight shippers will adopt the strategy of "do not share demand information". Therefore, when the cost of sharing capacity for the freight shippers exceeds the benefits obtained thereby, the freight shippers will adopt the strategy of "do not share demand information".

Proposition 4. When the initial state of the behavioral strategy of freight shippers is in space V
Assume that the freight shippers' expected returns from adopting the "share demand information" strategy are E A1 , the expected returns from adopting the "do not share demand information" strategy are E A2 , and the freight shippers' average expected returns under the mixed strategies are E A . Then, we have the following: The freight shippers select the duplicate dynamic equation for "share demand information" as For ease of calculation, let z A .
➀ When z z A , then F A ≡ 0, which shows that all levels are stable. ➁ When z z A set F A 0; then, y 0 and y 1 are two stable points.
Let F A be the derivative of y and derived from F A : According to the requirements of the evolutionary stability strategy F C < 0, z A is analyzed, because the ESSs of 0 < x < 1, 0 < y < 1, and 0 < z < 1 are obtained considering the following two scenarios. Scenario 3. If 0 < z < z A , when y 0, F A < 0; when y 1, F A > 0; therefore, y 0 is an ESS. That is, freight shippers adopt the strategy of "do not share demand information". Scenario 4. If z A < z < 1, when y 0, F A > 0; when y 1, F A < 0; therefore, y 1 is an ESS. That is, freight shippers adopt the strategy of "share demand information".
According to the analysis, the dynamic evolutionary trend of freight shippers is shown in Fig. 3; therefore, propositions 3 and 4 are proven.

Evolutionary analysis of freight shippers
As shown in Fig. 3, when the other parameters are fixed, if t 2 increases, and z A increases. When z A increases, the area of V 4 expands. That is, when the logistics platform increases tax incentives, freight shippers will choose to "share demand information" to reduce costs. The tax benefits raised by the logistics platform will not enable freight shippers to choose "share demand information" but will lead them to choose the "do not share demand information" strategy. Similarly, when t 1 increases and z A decreases, the space of V 3 becomes larger; in other words, the increase in the basic tax rate amount of the freight shippers will enable them to share demand information and reduce their real tax rate by the logistics platform's tax preference. When I A increases and z A decreases, the area of V 3 expands, which shows that the logistics platform has increased the incentives for freight shippers under the provision of high-level services, and freight shippers will tend to choose to "share demand information"; when (r N AL − r S AL ) is increased and z A increases, the area of V 4 expands. In other words, when the logistics platform provides a lower of level service, freight shippers will prefer to choose the "do not share demand information" strategy, and then r S AH increases, r N AH decreases, and z A decreases, the area of V 3 contracts. This means that when the logistics platform provides a high level of service, freight shippers will prefer to choose the "share demand information" strategy.

Logistics platform
The logistics platforms' strategy will be influenced by the positive network externality and freight transportation companies' sharing strategy, as shown in Fig. 4, when the initial state of the behavioral strategy of the logistics platform is in different spaces, such as V 5 ,and V 6 , the logistics platform will adopt different strategies. In the subsections, we are going to discuss these two cases.

Replicator dynamic equation and evolutionary stability analysis
Proposition 5. When the initial state of the behavioral strategy of the logistics platform is in space V 5 , that is x I C +y I A < R H − C H − R L + C L , and z 1 is the equilibrium point, the logistics platform will adopt the strategy of "high-level service". Therefore, considering that the freight carriers and Fig. 4 Dynamic trend diagram for the logistics platform freight shippers choose their "sharing" strategy to benefit the logistics platform, when the benefits of providing highlevel services are greater than those of providing low-level services, the logistics platform will choose the "high-level service" strategy.

Proposition 6. When the initial state of the behavioral strategy of the logistics platform is in space V
and z 0 is the equilibrium point, the logistics platform will adopt the strategy of "low-level service".
Assume that the logistics platform's expected returns from adopting the "high-level service" strategy are E P1 , the expected returns from adopting the "low-level service" strategy are E P2 , and the logistics platform's average expected returns under the mixed strategies are E P . Then, we have the following: The logistics platform selects the duplicate dynamic equation for "high-level service" as For ease of calculation, let w x I C + y I A , w 1 ➀ When w w 1 , then F P ≡ 0, which shows that all levels are stable. ➁ When w w 1 , set F P 0; then, z 0 and z 1 are two stable points.
Let F P be the derivative of z and derived from F P : According to the requirements of the evolutionary stability strategy F P < 0, w, w 1 , and w 2 are analyzed, and because 0 < x < 1, 0 < y < 1, and 0 < z < 1, ESSs are obtained considering the following two scenarios.

Scenario 5.
When w > w 1 , that is x > w 2, when z 0, F P < 0; when z 1, F P > 0; therefore, z 0 is an ESS. That is, the logistics platform adopts the strategy of "lowlevel service". Scenario 6. When w < w 1 , that is x < w 2, when z 0, F P > 0; when z 1, F P < 0; therefore, z 1 is an ESS. That is, the logistics platform adopts the strategy of "high-level service".
According to the analysis, the dynamic evolutionary trend of the platform is shown in Fig. 4; therefore, propositions 5 and 6 are proven.

Evolutionary analysis of logistics platform
As shown in Fig. 4, the initial state of the platform's behavior strategy is related to the size of x and y in spaces V 5 and V 6 , and when y remains unchanged, I C decreases, and x becomes larger. When x increases, the area of V 6 expands. That is, when the logistics platform provides "high-level services", the incentives for freight carriers to choose "share transportation capacity" increase, so that the benefits obtained by the platform from providing low-level services are greater than those obtained by providing high-level services. Thus, the platform provides "low-level service". Similarly, when (R H -R L ) decreases and x decreases, s the area of V 5 expands; in other words, the net positive network externality of highlevel service being provided by the platform exceeds that of low-level service, which will lead to the platform to provide "high-level service". When (C L -C H ) decreases, and x decreases, s the area of V 5 expands. This means that the cost for the platform to provide a low level of service is lower than the cost of providing a high level of service, and the platform benefits when the freight carriers choose to share. To obtain more benefits, the platform will encourage the freight carriers to choose to share to be able to provide high-level services.
In this case, the benefits gained by the platform from providing high-level services are greater than those from providing low-level services; therefore, the logistics platform will be more inclined to provide high-level services.

Evolutionary stability analysis of the three participants
The purpose of the evolutionary analysis is to determine the evolutionary stability strategy of the two sides of the game, that is, the dynamic balance formed by the two sides of the game with limited rationality when they pursue the maximization of their immediate interests. The replicated dynamic equations reflect the dynamic decision trajectories of the three parties in the game on the time axis. It is clear that when F C 0, F A 0 and F P 0 are extremum necessary conditions, the equilibrium points of the pure strategy include E 0 (0,0,0), E 1 (0,0,1), E 2 (0,1,0), E 3 (0,1,1), E 4 (1,0,0), E 5 (1,0,1), E 6 (1,1,0), and E 7 (1,1,1). In an asymmetric game, if evolutionary game equilibrium E is an evolutionary stable equilibrium, then E must be a strict Nash equilibrium, and the strict Nash equilibrium is a pure strategy equilibrium, that is, the mixed equilibrium must not be an evolutionarily stable equilibrium in an asymmetric game, so it is only necessary to study the asymptotic stability of the pure strategy equilibrium. Therefore, this paper only analyzes E 0 (0,0,0), E 1 (0,0,1), E 2 (0,1,0), E 3 (0,1,1), E 4 (1,0,0), E 5 (1,0,1), E 6 (1,1,0), and E 7 (1,1,1).
The asymptotic stability of the equilibrium points is determined by the Lyapunov discriminant method, so the Jacobian matrix and its eigenvalues are solved first. The Jacobian matrix is as follows: Thus, the following formulas are acquired.
According to the Lyapunov discriminant method, the evaluation criteria of its evolutionary stability are as follows: if all eigenvalues λ < 0, the equilibrium point is an evolutionary stable point (ESS), which is the confluence; if all eigenvalues λ > 0, the equilibrium point is an unstable point, which is the source; if all eigenvalues λ have positive and negative real numbers, the equilibrium point is a saddle point; and if λ is a conjugate imaginary number, the equilibrium point is the center point. The stability of each equilibrium point is analyzed, as shown in Table 3.
In this scenario, the freight carriers adopt the strategy of "do not share transportation capacity", the freight shippers adopt the strategy of "do not share demand information", and the logistics platform provides "high-level service". In this state, even if the logistics platform is willing to provide a high level of service and the freight carriers and freight shippers will be rewarded by choosing a sharing strategy, since the tax incentives are not high enough, the cost of choosing to share is higher than that of choosing not to share, so both freight carriers and freight shippers prefer to choose a nonsharing strategy. That is, (1−t 2 )r S C H + I C < (1−t 1 )r N C H , (1− t 2 )r S AH + I A < (1−t 1 )r N AH ; therefore, the freight carriers will choose "do not share transportation capacity", and the freight shippers will choose "do not share demand information". This reduces the logistics platform's profit. However, when the logistics platform provides high-level services and lower tax incentives, the benefits gained by the logistics platform exceed its losses, so the logistics platform can also benefit more by providing high-rather than low-level services. That is, if R H − R L > C H − C L , the logistics platform is willing to adopt a "high-level service" strategy.
In this scenario, the freight carriers adopt the strategy of "do not share transportation capacity", the freight shippers adopt the strategy of "share demand information", and the logistics platform provides "high-level service". In this case, when the logistics platform provides a high level of service, the freight shippers will be rewarded for choosing a sharing strategy and a tax incentive. As the freight carriers' strategy is "do not share transportation capacity", the freight shippers will suffer a loss, but their gain is far greater than their loss. Therefore, the freight shippers can obtain more benefits by choosing the "share demand information" strategy. Since (1−t 2 )r S AH +I A > (1−t 1 )r N AH , the freight shippers are willing to choose a sharing strategy to promote the development of sharing. For the freight carriers, even if the logistics platform is willing to provide high-level services and they will obtain incentive payments from the logistics platform by choosing to share transportation capacity, the tax preference enjoyed through the platform is still low. This is why the freight carriers prefer to choose "do not share transportation capacity". That is, (1 − t 2 )r S C H + I C < (1 − t 1 )r N C H ; therefore, freight carriers will not share transportation capacity. The freight shippers' choice of the "share demand information" strategy will benefit the logistics platform. Even if the freight carriers' choice of "do not share transportation capacity" will cause some economic loss, the logistics platform will also choose a high level of service, because its gain far exceeds its losses. That is.R H − R L > I A + C H − C L . As a result, the platform will provide a high level of service.
In this scenario, the freight carriers adopt the strategy of "share transportation capacity", the freight shippers adopt the strategy of "do not share demand information", and the logistics platform adopts the strategy of "high-level service". In this case, when the logistics platform provides a high level of service, the freight carriers will gain a satisfactory incentive payment from the logistics platform for choosing the "share transportation capacity" strategy and can also enjoy a tax incentive. Even if the freight shippers' choice of the "do not share demand information" strategy will cause some economic loss, their gain far exceeds their loss. Therefore, the freight carriers can obtain more benefits when choosing to share transportation capacity. That is, (1 − t 2 )r S C H + I C > (1 − t 1 )r N C H . Therefore, freight carriers are willing to choose the "share transportation capacity" strategy to promote the development of sharing. For the freight shippers, even if the logistics platform is willing to provide high-level services and provide an incentive payment if they choose the "share demand information" strategy, the freight shippers can obtain more benefits by choosing the "do not share demand information" strategy. That is, (1−t 2 )r S AH +I A < (1−t 1 )r N AH . Therefore, the freight shippers If λ 11 < 0 and λ 12 < 0, E 1 (0,0,1) is ESS If λ 11 < 0, λ 12 > 0, and λ 23 > 0, E 3 (0,1,1) is ESS If λ 11 > 0, λ 12 < 0 and λ 43 > 0, E 5 (1,0,1) is ESS is the saddle point If λ 11 > 0, λ 12 > 0 and λ 63 > 0, E 7 (1,1,1) is ESS will choose the "do not share demand information" strategy. However, the gains of the logistics platform exceed its losses, so the logistics platform can obtain more benefits by providing high-level services than by providing low-level services, that is, R H − R L > I C +C H − C L . As a result, the platform will provide a high level of service.
In this scenario, both the freight carriers and freight shippers choose a sharing strategy, and the logistics platform provides a high level of service. In this case, when the logistics platform provides a high level of service, the freight carriers and the freight shippers choose to share to obtain the rewards given by the platform and can also enjoy relatively high tax preferences. The freight carriers and freight shippers can obtain more profits by choosing a sharing strategy. That is, (1 − t 2 )r S C H + I C > (1 − t 1 )r N C H and (1 − t 2 )r S AH + I A > (1 − t 1 )r N AH ; therefore, the freight carriers and freight shippers are willing to choose to share. This will benefit the logistics platform. Even if the logistics platform provides rewards to the freight carriers and shippers, it can also gain excess profits. Thus, the logistics platform will benefit more from a high-level service than a low one, that is to say R H − R L > I C + I A + C H − C L , and the logistics platform is willing to provide a high level of service.

Scenario 5:
When λ 11 > 0, λ 12 > 0 and λ 63 < 0, there is no stable equilibrium point. Based on Scenario 4, if λ 63 < 0, all the aforementioned equilibrium points will not be satisfied, and a complex scenario with no stable equilibrium point will be discussed in the next section containing the numerical analysis.

Numerical analysis
To further validate the proposed model, MATLAB R2020b is used to simulate and calculate Scenario 5, which is more complex than the others. To simplify the analysis of the influence of the initial state of the system and related parameters on the development of the final dynamic game, The following conditions need to be imposed on the variables: λ 11 ( This sub-section explores the effectiveness of models by considering the data of the Yunmanman Company's real case. Yunmanman Company is a typical representative of the logistics platform in the field of freight transportation. The website address of Yunmanman Company is https://www. ymm56.com/. The values of parameters are gathered based on the data of both the local government department (http:// hunan.chinatax.gov.cn/) and experts' opinions. Specifically, the values of the basic value-added tax rate t 1 0.11 and the value-added tax rate after subsidization by the government's preferential policies t 2 0.05 are available in the statistics information of the local government department. Nevertheless, other parameters, i.e., the revenue for carriers and shippers under strategy M, the incentive payments of the "high-level service" logistics platform for the carriers and shippers' "share transportation capacity" strategy are difficult to be determined in practice. Accordingly . When x 1, y 1, and z 1, that is, the freight carriers choose "share transportation capacity", the freight shippers choose "share demand information", and the logistics platform chooses "high-level service", which is also the development goal of the freight transportation industry in China. To study the influence of key system parameters on the equilibrium strategies, sensitivity analysis on the equilibrium strategies with respect to (x(0), y(0), z(0)), t 2 , R H , I A , and I C is conducted. In this study, only one parameter varies, and the others are fixed, and the numerical results are shown in Figs. 5, 6, 7, 8, 9. Sensitivity analysis of the initial proportion (x(0),y(0), z(0)) As shown in Fig. 5, the evolution result of the three-player game varies according to the initial proportions of the three participants. When the initial proportions are the same, (x(0), y(0), z(0)) (0.5, 0.5, 0.5), as time passes in Fig. 5a, the freight carriers change their probability: x gradually increases, then slowly decreases and finally converges to 1.
The freight shippers change their probability: y gradually increases, then declines substantially, and finally converges to 0. The logistics platform changes its probability: z increases and then decreases and finally converges to a certain value between 0.4 and 0.6. When the initial proportions are different, (x(0), y(0), z(0)) (0.1, 0.3, 0.2), as time passes in Fig. 5b, the freight carriers change their probability: x increases sharply and then decreases slowly and finally converges to 1. the freight shippers change their probability: y gradually increases, then gradually decreases and the fluctuation amplitude decreases and finally converges to 0. The logistics platform changes its probability: z increases to the threshold 1, then decreases to the threshold 0, and then reaches a certain value between 0.4 and 0.6. This implies that the initial proportion value only affects the process of the evolutionary game, but the final convergence result remains unchanged.

Sensitivity analysis of tax incentives t 2
As shown in Fig. 6, when the tax rate after subsidization by the government's preferential policies t 2 varies among 0.01, 0.08 and 0.1, over time, the probability of the platform actively selecting the "high-level service" strategy increases. However, the final strategy of the freight carriers and the freight shippers remain unchanged. The freight carriers have been very likely to choose the "share transportation capacity" strategy, while the freight shippers choose the "do not share demand information" strategy. This is because freight carriers will gain the tax incentives provided by the logistics platform and obtain more rewards, which will benefit carriers that adopt the "share transportation capacity" strategy. However, the freight shippers will prefer the "do not share demand information" strategy, because despite the worse benefits, the tax incentives and rewards are increased. For the logistics platform, with the improvement of tax incentives and the freight carriers' and shippers' strategies being definite, the probability of choosing the "high-level service" strategy continues to increase. This implies that the tax incentive value affects the process of the evolutionary game through the logistics platform's strategy and has less influence on freight carriers and shippers.

Sensitivity analysis of positive network externality RH
As shown in Fig. 4, the evolutionary result of the three-player game varies according to the positive network externality. When the positive network externality value is low, as time passes in Fig. 7a, the freight carriers, freight shippers and logistics platform's probabilities (x, y, z) will all converge to 0. That is, the freight carriers choose the "do not share transportation capacity" strategy, freight shippers choose the "do not share demand information" strategy and the logistics platform chooses the "low-level service" strategy. However, when the positive network externality value is high, as time passes in Fig. 7b, the freight carriers, freight shippers and logistics platform's probabilities (x, y, z) will all converge to 1. That is, the freight carriers choose the "share transportation capacity" strategy, freight shippers choose the "share demand information" strategy and logistics platform choose the "high-level service" strategy. This implies that when Scenario 5 is in the ascendancy, the positive network externality is the key factor in the evolutionary result of the three-player game, and a high-level R H ultimately leads to a cooperative relationship.

Sensitivity analysis of freight carriers' incentive IC
As shown in Fig. 8, the evolutionary result of the three-player game varies according to the value of the parameter representing freight carriers' incentives I C . When the freight carriers' incentive value is low, as time passes in Fig. 8a I C 1, the freight carriers' probability x will converge to 0, while the freight shippers and logistics platform's probabilities (y, z) will converge to 1. This indicates that the freight carriers choose the "do not share transportation capacity" strategy, the freight shippers choose a "share demand information" strategy and logistics platforms choose the "high-level service" strategy. However, when the freight carriers' incentive value is high, as time passes in Fig. 8b I C 5, the freight shippers' probability y converges to 0, while the freight carriers' and logistics platform's probabilities (x, z) will both change trend. That is, the logistics platform has greater incentives to provide share rewards to the freight carriers, but its revenue cannot cover the cost. Therefore, the probability of the logistics platform choosing a high level of service will decrease, while the probability of the freight carriers choosing the "share transportation capacity" strategy increases. Thus, freight carriers' positive attitude will encourage the logistics platform to choose the "high-level service" strategy. Therefore, both the freight carriers and logistics platform are in a state of fluctuation. In this case, for the freight shippers, the benefit of choosing the "do not share demand information" strategy is greater than that of "share demand information", so the freight shippers tend to choose the "do not share demand information" strategy.

Sensitivity analysis of freight shippers' incentive IA
As shown in Fig. 9, other parameters remain unchanged, and the final evolutionary results of the three participants can be changed by the value of the freight shippers' incentive I A . When the freight shippers' incentive value is low, as time passes in Fig. 9a I A 1, the freight carriers and logistics platform's probabilities (x, z) will converge to 1, while the freight shipper's probability y will converge to 0. This indicates that the freight carriers choose the "share transportation capacity" strategy, freight shippers choose the "do not share demand information" strategy and logistics platform chooses the "high-level service" strategy. However, when the freight shippers' incentive value is high, as time passes in Fig. 9b I A 3, the freight shippers' probability y converges to 1, while the freight carriers' probability x converges to 0, and the logistics platform's probability z will decline and then increase and finally converge to a threshold value (this value ∈ (0.2, 0.4)). Therefore, when the logistics platform provides high-level services, the incentive for freight shippers to share increases, and they have a strong incentive to choose the strategy of "do not share demand information". However, the platform needs to share more revenue, which will reduce its benefits, so it is less motivated to choose the "high-level service" strategy. The result also enables the freight carriers to choose the "do not share transportation capacity" strategy.
From Figs. 8 and 9, we can see that both the freight carriers and shippers will not be attracted to the logistics platform by a low incentive, such as I A 1 and I C 1. This implies that a sense that the incentive is fair guarantees that freight transportation participants will choose a sharing strategy. Perceptions of unfairness can lead to resistance and rejection behavior [49]. In addition, tax incentives and positive external network externalities are the key factors for logistics platforms to choose a high level of service. To perfectly coordinate the supply chain while considering vehicle capacity utilization, a fairness incentive, tax incentives and positive network externality are considered. This implies that the authorities should provide an appropriate tax incentive to the logistics platform to invest in a "high-level service" strategy, which will give the freight carriers and shippers more initiatives to choose a sharing strategy. Consequently, the logistics platform can develop positive network externalities and provide a fair incentive payment to freight carriers and shippers; hence, both freight carriers and shippers are willing to support a sharing strategy, which leads to a win-win situation.

Discussion and managerial insights
1. Considering the freight transportation companies' horizontal collaboration, it is critical to construct an excitation mechanism to coordinate the logistics platform and freight transportation companies to increase the rate of vehicle utilization. The logistics platforms prefer to obtain a higher positive network externality to facilitate horizontal collaboration, they must provide a "high-level service". From Fig. 7, we can conclude that when R H 16, namely, the positive network externality is lower, the horizontal collaboration is not working. However, when R H increases to 25, the positive network externality is located at a higher level, and the logistics platform and freight transportation companies will be coordinated. 2. The logistics platforms that prefer to promote horizontal collaboration should consider four cases: (1) when the positive network externality and tax incentive are both higher, the logistics platforms should provide a "high-level service" to attract the freight transportation companies.
(2) When the positive network externality and tax incentive are both lower, the logistics platforms will provide a "low-level service" to protect their own profits. (3) When the positive network externality is higher and the tax incentive is lower, the logistics platforms should provide a "high-level service" at a low level to attract the freight transportation companies (in Figs. 8a and 9a, I C 1 and I A 1). (4) When the positive network externality is lower and the tax incentive is higher, the logistics platforms should provide a "low-level service", because the tax incentive may not cover its costs (in Fig. 7a, R H 16). 3. Our result indicates the significance of fair incentive quantity between the freight shippers and the freight carriers. From Figs. 8, 9, we can see that both the freight carriers and shippers will not be attracted to the logistics platform by a low incentive, such as I A 1 and I C 1. This implies that a sense that the incentive is fair guarantees that freight transportation participants will choose a sharing strategy. As a result, the logistics platform should take both the fairness between members and a moderate incentive quantity into account when making incentive decisions.

Conclusions and implications for future research
This paper discussed the interaction and cooperation among freight transportation participants from a sustainability perspective. Conflicts of interest among freight carriers, freight shippers and logistics platforms are analyzed. Thereafter, the evolutionary trends of the three participants' behavioral strategies are analyzed using a three-player evolutionary game model. Finally, the impacts of relevant factors on the evolutionary results of the behavioral strategies of the participants are investigated. The conclusions are as follows: (1) Strict fairness of the logistics platform is necessary for the sustainable operation of the platform in the long term. According to the numerical analysis, there are no differences in the results of the three-player game with different initial states. (2) Given the conflict of interest among freight carriers, freight shippers and logistics platforms, the interests of the three participants can be transformed into revenues and costs to formulate a TEGM. The replicator dynamics equation is used to solve for the equilibrium solution of the TEGM. The behavioral strategies of the three participants can be changed to "share transportation capacity", "share demand information" and "high-level service" to balance the interests of the participants by adjusting the parameters (e.g., t 2 , R H , I C , I A ). (3) By reducing the tax on freight transportation on the logistics platform and increasing the positive network externality, the logistics platform will eventually choose the "high-level service" strategy. By increasing the payment incentives and tax incentives for freight carriers and shippers, they will eventually choose the "share transportation capacity" and "share demand information" strategies. Moreover, a fair payment incentive can balance freight carriers' and shippers' enthusiasm to participate in horizontal collaboration on a logistics platform.
This study provides several insights into the behavioral theory of freight transportation participants regarding sustainable operation. First, a theoretical link between sustainable principles and the behavior of freight transportation participants is proposed to balance the interests of the participants. Second, this paper aims to design an interest-coordination mechanism among freight transportation participants to guide each participant to choose the behavioral strategy that benefits the sustainability of freight transportation. Third, meaningful suggestions are provided for authorities' development of freight transportation. In the era of logistics distribution, vehicle capacity utilization has become very common in many areas, such as freight transportation. Therefore, it will be helpful to consider vehicle capacity utilization to study horizontal collaboration on logistics platforms. Furthermore, this study can be extended by introducing the Bayesian network inference mechanism, because the freight demand distribution can be explored over time in a Bayesian manner when it is unavailable. We hope to study these problems in the future.