The Evolution of Government–Enterprise Strategies of “Expressway + Logistics Distribution”

Abstract

Currently, China’s expressway revenue and expenditure imbalance problem is serious. The development of an “Expressway Derivative Economy” (EDE) helps address expressway deficits, ensuring the expressway’s sustainable operation. The “Expressway + Logistics Distribution” (ELD) mode is a crucial form of the EDE and enhances expressway traffic flow and asset income. However, the cooperation mechanism among stakeholders remains unclear, hindering the widespread promotion of this mode. This study designs two ELD modes and elaborates on their respective advantages. Therefore, a three-party evolutionary game model involving the government, expressway groups, and logistics enterprises is established. Government “land-use-right” grant and tax incentive policies are formulated to explore the cooperation mechanism among stakeholders. The results indicate that both government “land-use-right” grant and tax incentive policies positively influence the positive evolution of the system. However, when the government “land-use-right” grants reach a high level, the willingness of logistics enterprises to choose entry will decrease due to resource crowding. Comparatively, a higher-level “land-use-right” grant policy significantly enhances the role of government tax incentive policy in promoting the positive development of the system. During tight government funding, it is a feasible policy to prioritize expressway groups by providing more tax incentives. The findings provide theoretical guidance for promoting the ELD mode.

1. Introduction

In recent years, China has seen steady growth in the total mileage of its expressways and road network coverage. By the end of 2022, China’s expressways spanned 177,000 km, with 10,800 toll stations and approximately 4800 service areas, showcasing abundant road assets. However, as the expressway network improves, several issues have become increasingly apparent. New expressway projects now face more complex topographical and geological conditions, leading to an increase in the proportion of bridges and tunnels. Rising costs for land acquisition, demolition compensation, construction materials, and labor wages drive up expressway construction costs. Conversely, the number of new expressway construction projects has decreased, and the benefits of densification and double-track lines are limited during operation. This imbalance between revenue and expenditure is particularly pronounced, reducing the appeal to private investors. According to the 2023 National Toll Road Statistics Bulletin from the Ministry of Transport, the total vehicle toll revenue for national toll roads in 2023 was CNY 663.05 billion, whereas expenditures reached CNY 1.29 trillion, creating a gap of about CNY 620 billion. The cancellation of provincial toll stations has left many abandoned toll stations and idle lands along the expressways. The utilization of these abandoned toll stations and idle lands, the improvement of road asset efficiency, the increase in expressway operating income, the stimulation of the expressway investment market, and the promotion of sustainable regional economic development are urgent issues that need to be addressed. The conflict between economic development and environmental protection remains a key issue for sustainability. Abandoned tailings ponds from mining operations have been restored to agricultural land [1]. Dartford and Sungai Lembing, as resource-based communities, demonstrated the potential to balance economic growth with ecological management by developing abandoned mining areas and preserving mining heritage to seek economic recovery [2,3]. These efforts provide inspiration for repurposing abandoned toll booths and idle lands along expressways to develop new business models that drive economic growth.

The development of the Expressway Derivative Economy (EDE) can help address China’s expressway operating losses. EDE refers to industries or business clusters that rely on expressway route resources. ELD is a new EDE model designed to lower regional logistics costs and maximize overall regional benefits. This model utilizes existing or newly built expressway service areas and idle lands along expressways for logistics distribution activities. Its core objective is to use expressway resources to expand into neighboring areas and related industries, forming business clusters through comprehensive strategies and resource utilization [4]. Developing ELD can boost expressway traffic, enhance operations, and facilitate debt repayment through asset returns [5]. Currently, some expressway service areas have pioneered the implementation of the ELD model. For instance, Shandong Expressway Group has extensively utilized idle lands around toll stations and service areas to construct logistics facilities such as sorting stations, distribution centers, and distributed warehouses. They have also created unified storage and distribution centers around cities by integrating urban logistics routes to form a “fast distribution + distributed warehousing” logistics backbone network [6]. Nevertheless, the promotion of the ELD mode faces several challenges, including inadequate land policies, a lack of incentives for stakeholders, poor coordination between local governments and enterprises, and weak industry connections [7]. These factors have significantly hindered the broader adoption of this model.

The main contributions of this study are as follows: (1) Two ELD modes are designed. (2) The game model of ELD stakeholders is constructed, and the evolutionary stability of each stakeholder is analyzed. (3) The impact of government “land-use-right” grant policy and tax incentive policy on ELD stakeholder strategy selection is revealed.

2. Literature Review

2.1. Sustainable Development of Expressways

During the initial phases of expressway construction, conflicts over sustainable development inevitably arise, especially when developers and environmentalists have opposing views on environmental protection and economic growth, leading to environmental disputes. The decision support system GMCR II offers a graphical methodology for resolving such conflicts, facilitating a strategic balance between economic growth and environmental conservation [8]. Continuous evaluation is needed from the early design and construction phases to project completion. F.C. Santos and A.B. Rohden [9] evaluated expressway pavement technology with a focus on sustainability, quantified the environmental impact of HMA and PCC technologies and linked the life cycle impact on population health and well-being to assess the social aspects of sustainability. Once expressways are completed and operational, they enter a phase of pursuing sustainable traffic control goals, addressing various issues from environmental protection to social and economic development. Traffic emissions and road safety are frequently discussed within the context of sustainable expressway development. Scholars have explored and addressed various challenges in sustainable expressway traffic control using tools like traffic flow models, emission models, energy consumption models, dispersion models, and safety models [10]. Additionally, the construction of expressways can also drive the sustainable development of regional economies. The development of expressway infrastructure not only improves regional accessibility but also promotes economic growth and regional integration [11]. Many scholars have extensively researched the sustainable development of expressways from the initial construction phase to their operational phase. More comprehensively, the research on sustainability covers the environment, society, safety, economy, and other aspects. Based on the previous research, this study focuses on the sustainable development of expressways during their operational phase at the level of sustainable economic development.

2.2. Expressway Logistics Distribution (ELD)

Research by Adelheid Holl and Ilaria Mariotti [12] showed that expressways significantly impact the performance of logistics enterprises. For urban logistics enterprises, tax incentives and shortening the distance to the nearest expressway can improve productivity, further demonstrating the advantages of the ELD model. Currently, research on ELD mainly focuses on the location and route optimization of expressway logistics distribution centers, the selection of expressway logistics distribution models, and the optimization of expressway logistics networks.

Firstly, regarding the location and route optimization of logistics distribution centers, scholars have developed mathematical models that consider factors like time windows, traffic flow predictions, regional characteristics, and multimodal transport to optimize distribution routes [13,14,15,16]. Secondly, based on the existing expressway passenger transport network, scholars have explored the feasibility of converting it into a logistics transport corridor and established corresponding mathematical models to solve optimal route and location problems [17]. Based on actual needs, taking service areas of expressways in provinces like Shandong and Henan as examples, this study uses qualitative and quantitative analysis methods to scientifically and reasonably select locations for logistics distribution centers [18,19,20]. In addition, some scholars established the ELD distribution model by combining demand forecasting and logistics distribution status analysis [21,22]. With expressway service areas in Shaanxi Province as a case study, this specialized logistics distribution model was explored and studied. The corresponding logistics distribution system was designed to expand the new value of the expressway service industry and promote the full integration and development of corporate resources [23]. Furthermore, scholars have identified issues within this logistics distribution model and proposed corresponding frameworks [24]. From a macro perspective, some researchers have proposed the development of new logistics networks based on expressway networks and their associated land and road assets, integrating expressway networks into logistics services systems to construct regional expressway logistics networks [25,26]. Additionally, according to the characteristics of service objects and types of delivered goods, some scholars have proposed fuzzy processing methods based on factors such as consumer demand and logistics vehicle arrival time, optimizing the logistics distribution network model [27,28]. Other scholars have optimized the expressway logistics network through innovative algorithms. The transportation route planning model and algorithm based on Internet of Things technology and particle swarm optimization have effectively reduced distribution costs and improved satisfaction [29].

2.3. Evolutionary Game

Game theory has become a useful mathematical tool for addressing the challenge of strategy selection in multi-agent scenarios [30]. Evolutionary game analysis has been widely used to study the impact of policy mechanisms on the behavioral decisions of various stakeholders [31,32]. For instance, Feng and Ge [33] used evolutionary game theory to analyze how government fiscal policies influence enterprises to transition toward green and low-carbon practices. Li, J., Gao, L., and Tu, J. [34] introduced a peer-incentive mechanism and constructed an evolutionary game model between the government and enterprises under a reward and punishment mechanism. This revealed the evolutionary mechanism behind stakeholders’ behavioral decisions, offering important guidance for government regulatory strategies and enterprise emission reduction strategies. Tianshan, M., Rehman, S.A., et al. [35] explored how different regulatory policies affect the benefits of illegal and legal recycling groups. Moreover, they tested the impact of government policies on scrapped car recycling strategies using numerical simulations. Zheng and Yu [36] built a three-party evolutionary game model involving fishermen, consumers, and the government to examine the impact of government subsidies on strategic choices and system stability. In addition, Mohammad-Ali Eghbali et al. [37] created a three-party evolutionary game model of technology companies, start-ups, and accelerators to explore the impact of static and dynamic government intervention on the behavioral decision-making of the participants in the green innovation chain. Liu, C., Wang, H., and Dai, Y. [38] developed a three-party evolutionary game model involving schools, enterprises, and the government, analyzing the impact of government reward–punishment mechanisms on cooperation and providing suggestions for sustainable collaboration among these entities. Wang, Man, and Wang [39] analyzed the interaction between local governments and shipping companies under fixed and dynamic subsidies by constructing an evolutionary game model, offering insights for optimizing low-sulfur fuel subsidy policies and SO_x emission reduction methods for shipping companies. Xu, J., Cao, J., Wang, Y., et al. [40] explored the long-term dynamic relationship between government environmental regulations and corporate green behavior using evolutionary games. Zhang and Kong [41] investigated the joint reserve model for emergency supplies by developing a three-party evolutionary game model involving the government, enterprises, and society. This research focused on identifying specific conditions and influencing factors for achieving public–private cooperation.

These studies offer valuable references for promoting the ELD model. Currently, the research on the ELD primarily focuses on analyzing the shortcomings of its development and exploring the industrial model. However, there is a significant oversight regarding the cooperation among system stakeholders in implementing these operational modes. The lack of clarity regarding the cooperation mechanism of the ELD hinders the smooth development of the ELD in China. However, the cooperation mechanism among expressway groups, logistics enterprises, and the government within this model remains insufficiently defined. Therefore, this paper proposes two ELD models and explains their operational processes and advantages. On this basis, an evolutionary game model involving the government, expressway groups, and logistics enterprises is constructed to analyze the stability of the evolutionary game of each stakeholder and reveal the behavior selection mechanism and influencing factors. The research results can provide theoretical support for the strategic decisions of ELD stakeholders, thus promoting the adoption and application of this model and contributing to the sustainable development of expressways.

3. Methodology

In the present study, before constructing the evolutionary game model, the operation process and characteristics of the traditional distribution models and two “expressway + logistics distribution” models are briefly described. On this basis, the stakeholders within the “expressway + logistics distribution” framework are abstracted, namely, the expressway group, logistics enterprises, and the government. The above three parties need to choose strategies based on their own interests, and game theory offers a rigorous mathematical approach to analyze the strategic choices and interaction mechanisms of relevant stakeholders [42]. Classic game theory assumes that participants are fully rational and possess complete information. However, this assumption is often infeasible in practical scenarios [43]. Conversely, in evolutionary game theory, participants with limited rationality can adjust their strategy choices through observation and learning [44]. This study conducts an in-depth discussion on the strategic choices of the government, expressway groups, and logistics enterprises, revealing how various influencing factors contribute to the adjustments and changes in their decision-making processes.

Evolutionary game theory is applicable to this study for the following reasons: (1) In real-life contexts, the government, expressway groups, and logistics enterprises typically cannot fully grasp all information or completely understand each other’s intentions. Evolutionary game theory aptly provides a comprehensive mathematical analysis framework for participants with bounded rationality under conditions of incomplete information. (2) The “expressway + logistics distribution” model is in the developmental phase, requiring the different stakeholders to continuously adjust their strategic choices over time. Evolutionary game theory clearly illustrates the evolutionary trajectory of these stakeholders’ strategy choices.

In order to more clearly present the analysis results, this paper uses numerical simulation to simulate and analyze the strategic choices of each stakeholder. The following section delineates the assignment of simulation parameters: part of the values is derived from actual data in the annual financial reports of logistics enterprises and expressway groups (specifically sourced from the full 2023 annual reports of Shenzhen Expressway Group Co., Ltd., Shenzhen, China (A shares) and SF (ShunFeng, a logistics enterprise in China) Holding Co., Ltd., Shenzhen, China), while other values are assigned based on parameter assumptions and the stability conditions of equilibrium points. The following is a detailed description of the actual data:

In the financial report section of SF Holding Co., Ltd.’s 2023 annual report, its operating income composition table and operating cost composition table can be found. The data show that the income of the logistics and freight forwarding part is CNY 251,127,665 thousand, the transportation cost is CNY 44,578,173 thousand, and the value-added tax rate for transportation services and real estate leasing is 9%. After scaling, these data correspond to the R_bb, V_bs + V_bb, and Q₁ parameters in this article.

In the financial data of the full text of the 2023 annual report of Shenzhen Expressway Group Co., Ltd. (A shares), the detailed table of toll business shows that the toll revenue is CNY 5,374,901 thousand, the operating cost is CNY 2,666,989 thousand, and the income tax expense is CNY 598,865 thousand. After scaling, these data correspond to the S₂, C_b, and S₁ parameters in this article.

Although no actual data were found to support the other parameters directly, they were determined based on assumptions from scholarly articles on evolutionary game theory, strictly adhering to the stability conditions of equilibrium points to ensure the scientific and rational nature of the simulation data.

4. Comparative Analysis of Three “Logistics Distribution” Modes

4.1. Original Distribution Mode

In the original distribution mode, the distribution centers of logistics enterprises are usually located in areas outside expressways and adjacent to demand points. Goods are delivered to these distribution centers via expressways by large trucks and then delivered by small trucks to each demand point, as illustrated in Figure 1. This operating mode exhibits the following characteristics: ① Large trucks need to exit the expressway and enter urban roads, reducing travel speed and negatively impacting urban traffic and the environment. ② This process increases the empty return mileage of large trucks, thereby reducing the effective utilization rate of the vehicles. ③ This mode requires additional land resources beyond the expressway land-use boundary for the construction of logistics distribution centers. ④ The establishment of logistics distribution centers adversely affects surrounding traffic conditions and the living environment. (The distribution center is indicated with “W” on the figure).

4.2. ELD Service Area Closed Mode

In the ELD service area closed mode, the distribution centers of logistics enterprises are usually set up in expressway service areas or idle areas along expressways. Large trucks deliver the goods to these distribution centers via expressways, where they are divided into smaller loads for different small trucks. Small trucks exit the expressway at the nearest off-ramp and enter urban roads to deliver goods to various demand points. Upon returning, these small trucks re-enter the expressway through the nearest on-ramp and return to the distribution center, as shown in Figure 2. This mode eliminates the need for large trucks to enter urban roads, though small trucks must frequently switch between expressways and urban roads.

This mode offers several advantages: ① The logistics distribution center is built in expressway service areas or idle areas along expressways, which optimally utilizes expressway land resources and increases revenue for the expressway group. ② The entry of logistics enterprises not only brings more traffic to small trucks but attracts vehicles of logistics center staff, increasing toll revenue by boosting traffic flow. Additionally, the consumption needs of logistics enterprises and their employees stimulate overall consumption levels within service areas. ③ Since large trucks do not need to enter urban roads, this mode significantly improves the distribution efficiency of logistics enterprises compared to the traditional distribution mode.

4.3. ELD Service Area Open Mode

In the ELD service area open mode, the distribution centers of logistics enterprises are usually set up in expressway service areas or idle areas along expressways. Large trucks transport goods to these distribution centers via expressways, and then the goods are redistributed to various small trucks. These smaller trucks use the internal roads of the expressway service area to exit onto urban roads and deliver the goods to different demand points. Upon return, the small trucks re-enter the expressway directly through the internal road in the service area and head back to the distribution center, as shown in Figure 3. In this mode, large trucks do not need to enter urban roads, and small trucks do not have to re-enter the expressway.

This mode presents the following advantages: ① The logistics distribution center is built in the expressway service areas or idle areas along expressways, which fully utilizes the land resources of the expressway while saving government land quotas. ② The entry of logistics enterprises stimulates consumption demand within service areas, which will be conducive to the development of other business formats in the service area, consequently enhancing overall economic efficiency. ③ This mode significantly improves the efficiency of cargo distribution. ④ It avoids the increased expressway toll fees associated with the closed service area mode.

5. Evolutionary Game Mode of ELD

5.1. Basic Assumptions of the Model

5.1.1. Game Stakeholder

The evolutionary game involves three key participants: the government, the expressway group, and logistics enterprises, each possessing bounded rationality.

5.1.2. Behavioral Strategies of Game Stakeholders

The behavioral strategies of each game stakeholder are shown in Figure 4, with specific explanations as follows:

• The government’s behavioral strategy is to choose whether to provide support policies for the development of ELD to the expressway group and logistics enterprises. Such policies include investment in logistics -related infrastructure, granting land development rights within expressway land-use boundary, and implementing tax incentives. These measures aim to encourage proactive participation from the expressway group and logistics enterprises in the development of ELD. Therefore, the government’s strategy set is defined as W₁ = {Q₁: policy support, Q₂: no policy support};
• The behavioral strategy of the expressway group is to choose whether to collaborate with logistics enterprises in developing ELD, that is, to decide whether to take measures to attract logistics enterprises, such as reducing land and warehouse rental fees and offering toll discounts. Accordingly, the strategy set for the expressway is W₂ = {M₁: cooperation, M₂: no cooperation}.
• The behavioral strategy of the logistics enterprise is to choose whether to enter the expressway to carry out logistics distribution, that is, to choose whether to use the expressway road property resources to carry out logistics and distribution business. These resources include idle land resources in service areas, abandoned toll station land resources, rich road network resources, and expressway platform information resources. Therefore, the behavioral strategy set of logistics enterprises is defined as: W₃ = {N₁: entry, N₂: no entry}.

5.1.3. Implementation Probability of Behavior Strategy

At the initial stage of the evolutionary game among the government, expressway group, and logistics enterprises, the probability distribution of each stakeholder implementing its strategy is as follows: the probability that the government implements {Q₁: policy support, Q₂: no policy support} is {x, 1 − x}, the probability that the high-speed group implements {M₁: cooperation, M₂: no cooperation} is {y, 1 − y}, and the probability that the logistics enterprise implements {N₁: entry, N₂: no entry} is {z, 1 − z}.

5.1.4. Related Parameters and Meanings in the Evolutionary Game Model

• When the government provides support policies for the development of ELD, it incurs costs associated with infrastructure construction, such as the construction or reconstruction costs of the service area connecting the municipal roads, involving human resources, materials, and finances (denoted as C₁). At the same time, these policies yield comprehensive benefits, including rewards from higher-level governments and improvements in governmental image (R₁ > C₁). When implementing the support policies, the government grants the expressway groups that choose to cooperate with the “land-use-right” (K₁), allowing them to freely engage in land planning and infrastructure usage within the land-use boundary along the expressway. Furthermore, the government offers tax incentives to these expressway groups, with the incentive level a (0 < a < 1). Under normal circumstances, the tax imposed on expressway groups is represented by S₁. Similarly, for logistics enterprises that choose entry, the government also provides tax incentives with the incentive level b (0 < b < 1). Otherwise, the tax collected by the government from logistics enterprises is Q₁. When expressway groups choose cooperation or logistics enterprises choose entry, the government can gain social benefits. These benefits include the increase in social benefits caused by the reduction in logistics costs and the sustainable development benefits brought by the increase in expressway group income (represented by R₂). Conversely, if expressway groups do not cooperate and logistics enterprises do not enter, the government faces potential penalties, denoted as G₁;
• The income variation for expressway groups before and after cooperation primarily manifests in toll fees. The income other than the tolls is R_a. If logistics enterprises choose entry, the income is R_a + K_b. Before the expressway group chooses cooperation, the toll fee is S₂, the operating cost is C_b, and the tax is S₁. After the expressway group chooses cooperation, the toll fee is S₂. If logistics enterprises choose entry, it is S₃ (S₃ > S₂). The operating cost is C_a. The tax is S₁. If the government provides policy support, it is aS₁. In addition, the rental subsidy given by the expressway group to logistics enterprises is K₂;
• Before logistics enterprises choose entry, the income from the distribution business is R_bb, the toll fee is S₂, tax is Q₁, and site rent is K_b. If the expressway group chooses cooperation, site rent is K_b − K₂. The transportation costs of large and small vehicles are V_bb and V_bs (considering mileage and driving time). After logistics enterprises choose entry, the income from the distribution business is R_aa, the toll fee is S₂. If the expressway group chooses cooperation, the toll fee is S₃. Tax is Q₁. If the government provides policy support, tax is bQ₁). Site rent is K_b. If the expressway group chooses cooperation, site rent is K_b − K₂. The transportation costs of large and small vehicles are V_ab and V_as (considering mileage and driving time).

The aforementioned parameters and their respective meanings are illustrated in

Table 1. Main parameters and meanings.

Parameter	Meaning
$R_1$	Comprehensive benefits when the government provides policy support
$C_1$	The costs of manpower, material resources, and financial resources incurred by the government in providing support policies
$K_1$	The “land-use-right” given to the expressway group that chooses to cooperate when the government provides support policies
$S_1$	The taxes collected by the government to the expressway group
$a$	The tax incentives given to the expressway group that chooses to cooperate when the government provides support policies
$Q_1$	The taxes collected by the government for the logistics enterprise
$b$	The tax incentives given to the logistics enterprise that chooses entry when the government provides support policies
$R_2$	The social benefits obtained by the government when expressway groups choose to cooperate or logistics enterprises choose entry
$G_1$	The potential penalties suffered by the government when expressway groups choose not to cooperate and logistics enterprises choose not to enter
$C_a$	The operating costs of the expressway group after cooperation
$C_b$	The operating costs of the expressway group before cooperation
$K_2$	The rental subsidies given to the logistics enterprise by the expressway group that chooses to cooperate
$S_2$	The tolls collected by the expressway group before cooperation
$S_3$	The tolls collected by the expressway group after cooperation (if the logistics enterprises do not enter, it is still S2)
$R_{aa}$	The income from distribution business after the logistics enterprise chooses entry
$R_{bb}$	The income from distribution business before the logistics enterprise chooses entry
$K_b$	Site rent before logistics enterprises choose entry
$V_{ab}$	Large vehicle transportation cost after logistics enterprises choose entry
$V_{as}$	Small vehicle transportation cost after logistics enterprises choose entry
$V_{bb}$	Large vehicle transportation cost before logistics enterprises choose entry
$V_{bs}$	Small vehicle transportation cost before logistics enterprises choose entry

.

5.2. Payoff Matrix

According to the behavior strategies of the government, the expressway group and the logistics enterprises, it can be concluded that there are eight game combinations among the three, namely, {Q₁: policy support, M₁: cooperation, N₁: entry}, {Q₁: policy support, M₁: cooperation, N₂: no entry}, {Q₁: policy support, M₂: no cooperation, N₁: entry}, {Q₁: policy support, M₂: no cooperation, N₂: no entry}, {Q₂: no policy support, M₁: cooperation, N₁: entry}, {Q₂: no policy support, M₁: cooperation, N₂: no entry}, {Q₂: no policy support, M₂: no cooperation, N₁: entry}, and {Q₂: no policy support, M₂; no cooperation, N₂: no entry}.

Based on the assumptions, the following is the profit and loss matrix of the government, expressway group, and logistics enterprises under different strategic behavior game combinations, as shown in

Table 2. Tripartite game payoff matrix of ELD.

Logistics Enterprise	$\mathbf{Entry}$ z		$\mathbf{No}\mathbf{Entry}$ 1 − z
Expressway Group	$\mathbf{Cooperation}$ y	$\mathbf{No}\mathbf{Cooperation}$ 1 − y	$\mathbf{Cooperation}$ y	$\mathbf{No}\mathbf{Cooperation}$ 1 − y
Government
$\mathrm{Policy}\mathrm{support}$ x	${\mathrm{R}}_1+{\mathrm{R}}_2+\mathrm{a}{\mathrm{S}}_1+\mathrm{b}{\mathrm{Q}}_1-{\mathrm{C}}_1-{\mathrm{K}}_1$ ${\mathrm{K}}_1+{\mathrm{K}}_{\mathrm{b}}+{\mathrm{S}}_3-\mathrm{a}{\mathrm{S}}_1-{\mathrm{C}}_{\mathrm{a}}-{\mathrm{K}}_2$ ${\mathrm{R}}_{\mathrm{a}\mathrm{a}}+{\mathrm{K}}_2-{\mathrm{b}\mathrm{Q}}_1-{\mathrm{S}}_3-{\mathrm{K}}_{\mathrm{b}}-{\mathrm{V}}_{\mathrm{a}\mathrm{b}}-{\mathrm{V}}_{\mathrm{a}\mathrm{s}}$	${\mathrm{R}}_1+{\mathrm{R}}_2+{\mathrm{S}}_1+\mathrm{b}{\mathrm{Q}}_1-{\mathrm{C}}_1$ ${\mathrm{K}}_{\mathrm{b}}+{\mathrm{S}}_2-{\mathrm{S}}_1-{\mathrm{C}}_{\mathrm{b}}$ ${\mathrm{R}}_{\mathrm{a}\mathrm{a}}-{\mathrm{b}\mathrm{Q}}_1-{\mathrm{S}}_2-{\mathrm{K}}_{\mathrm{b}}-{\mathrm{V}}_{\mathrm{a}\mathrm{b}}-{\mathrm{V}}_{\mathrm{a}\mathrm{s}}$	${\mathrm{R}}_1+{\mathrm{R}}_2+{\mathrm{a}\mathrm{S}}_1+{\mathrm{Q}}_1-{\mathrm{C}}_1-{\mathrm{K}}_1$ ${\mathrm{K}}_1+{\mathrm{S}}_2-\mathrm{a}{\mathrm{S}}_1-{\mathrm{C}}_{\mathrm{a}}-{\mathrm{K}}_2$ ${\mathrm{R}}_{\mathrm{b}\mathrm{b}}+{\mathrm{K}}_2-{\mathrm{Q}}_1-{\mathrm{S}}_2-{\mathrm{K}}_{\mathrm{b}}-{\mathrm{V}}_{\mathrm{b}\mathrm{b}}-{\mathrm{V}}_{\mathrm{b}\mathrm{s}}$	${\mathrm{R}}_1+{\mathrm{S}}_1+{\mathrm{Q}}_1-{\mathrm{G}}_1-{\mathrm{C}}_1$ ${\mathrm{S}}_2-{\mathrm{C}}_{\mathrm{b}}-{\mathrm{S}}_1$ ${\mathrm{R}}_{\mathrm{b}\mathrm{b}}-{\mathrm{Q}}_1-{\mathrm{S}}_2-{\mathrm{K}}_{\mathrm{b}}-{\mathrm{V}}_{\mathrm{b}\mathrm{b}}-{\mathrm{V}}_{\mathrm{b}\mathrm{s}}$
$\mathrm{No}\mathrm{policy}\mathrm{support}$ 1 − x	${\mathrm{S}}_1+{\mathrm{Q}}_1+{\mathrm{R}}_2$ ${\mathrm{K}}_{\mathrm{b}}+{\mathrm{S}}_3-{\mathrm{C}}_{\mathrm{a}}-{\mathrm{S}}_1-{\mathrm{K}}_2$ ${\mathrm{R}}_{\mathrm{a}\mathrm{a}}+{\mathrm{K}}_2-{\mathrm{Q}}_1-{\mathrm{S}}_3-{\mathrm{K}}_{\mathrm{b}}-{\mathrm{V}}_{\mathrm{a}\mathrm{b}}-{\mathrm{V}}_{\mathrm{a}\mathrm{s}}$	${\mathrm{S}}_1+{\mathrm{Q}}_1+{\mathrm{R}}_2$ ${{\mathrm{K}}_{\mathrm{b}}+\mathrm{S}}_2-{\mathrm{C}}_{\mathrm{b}}-{\mathrm{S}}_1$ ${\mathrm{R}}_{\mathrm{a}\mathrm{a}}-{\mathrm{Q}}_1-{\mathrm{S}}_2-{\mathrm{K}}_{\mathrm{b}}-{\mathrm{V}}_{\mathrm{a}\mathrm{b}}-{\mathrm{V}}_{\mathrm{a}\mathrm{s}}$	${\mathrm{S}}_1+{\mathrm{Q}}_1+{\mathrm{R}}_2$ ${\mathrm{S}}_2-{\mathrm{C}}_{\mathrm{a}}-{\mathrm{S}}_1-{\mathrm{K}}_2$ ${\mathrm{R}}_{\mathrm{b}\mathrm{b}}+{\mathrm{K}}_2-{\mathrm{Q}}_1-{\mathrm{S}}_2-{\mathrm{K}}_{\mathrm{b}}-{\mathrm{V}}_{\mathrm{b}\mathrm{b}}-{\mathrm{V}}_{\mathrm{b}\mathrm{s}}$	${\mathrm{S}}_1+{\mathrm{Q}}_1-{\mathrm{G}}_1$ ${\mathrm{S}}_2-{\mathrm{C}}_{\mathrm{b}}-{\mathrm{S}}_1$ ${\mathrm{R}}_{\mathrm{b}\mathrm{b}}-{\mathrm{Q}}_1-{\mathrm{S}}_2-{\mathrm{K}}_{\mathrm{b}}-{\mathrm{V}}_{\mathrm{b}\mathrm{b}}-{\mathrm{V}}_{\mathrm{b}\mathrm{s}}$

.

6. Analysis of Evolutionary Stable Strategy

6.1. Evolutionary Stable Strategy of Government

Let V₁₁ be the expected revenue for the government when choosing the “policy support” strategy and V₁₂ be the expected revenue when choosing the “no policy support” strategy. The average expected revenue is denoted as V₁.

$$\begin{array}{cc}\hfill {\mathrm{V}}_{11}=({\mathrm{R}}_1+{\mathrm{R}}_2+& \mathrm{a}{\mathrm{S}}_1+\mathrm{b}{\mathrm{Q}}_1-{\mathrm{C}}_1-{\mathrm{K}}_1)\mathrm{y}\mathrm{z}+\left({\mathrm{R}}_1+{\mathrm{R}}_2+{\mathrm{a}\mathrm{S}}_1+{\mathrm{Q}}_1-{\mathrm{C}}_1-{\mathrm{K}}_1\right)\mathrm{y}\left(1-\mathrm{z}\right)\hfill \\ & +\left({\mathrm{R}}_1+{\mathrm{R}}_2+{\mathrm{S}}_1+\mathrm{b}{\mathrm{Q}}_1-{\mathrm{C}}_1\right)(1-\mathrm{y})\mathrm{z}+({\mathrm{R}}_1+{\mathrm{S}}_1+{\mathrm{Q}}_1-{\mathrm{G}}_1-{\mathrm{C}}_1)(1-\mathrm{y})(1-\mathrm{z})\hfill \end{array}$$

$${\mathrm{V}}_{12}=({\mathrm{S}}_1+{\mathrm{Q}}_1+{\mathrm{R}}_2)\mathrm{y}\mathrm{z}+({\mathrm{S}}_1+{\mathrm{Q}}_1+{\mathrm{R}}_2)\mathrm{y}(1-\mathrm{z})+({\mathrm{S}}_1+{\mathrm{Q}}_1+{\mathrm{R}}_2)(1-\mathrm{y})\mathrm{z}+({\mathrm{S}}_1+{\mathrm{Q}}_1-{\mathrm{G}}_1)(1-\mathrm{y})(1-\mathrm{z})$$

$${\mathrm{V}}_1=\mathrm{x}{\mathrm{V}}_{11}+(1-\mathrm{x}){\mathrm{V}}_{12}$$

The replicator dynamic equation for constructing government behavior strategies is defined as follows:

$${\mathrm{F}}_{\left(\mathrm{x}\right)}={\displaystyle \raisebox{1ex}{$\mathrm{d}\mathrm{x}$}\!\left/ \!\raisebox{-1ex}{$\mathrm{d}\mathrm{t}$}\right.}=\mathrm{x}\ast (\mathrm{x}-1)\ast ({\mathrm{C}}_1-{\mathrm{R}}_1+\mathrm{y}{\mathrm{K}}_1+\mathrm{z}{\mathrm{Q}}_1+\mathrm{y}{\mathrm{S}}_1-\mathrm{z}\mathrm{b}{\mathrm{Q}}_1-\mathrm{y}\mathrm{a}{\mathrm{S}}_1)$$

The first derivative of x and the designated $\mathrm{G}\left(\mathrm{y}\right)$ are as follows:

$${\displaystyle \frac{\mathrm{d}\left(\mathrm{F}\left(\mathrm{X}\right)\right)}{\mathrm{d}\mathrm{x}}}=\left(2\mathrm{x}-1\right)\left({\mathrm{C}}_1-{\mathrm{R}}_1+\mathrm{y}{\mathrm{K}}_1+\mathrm{z}{\mathrm{Q}}_1+\mathrm{y}{\mathrm{S}}_1-\mathrm{z}\mathrm{b}{\mathrm{Q}}_1-\mathrm{y}\mathrm{a}{\mathrm{S}}_1\right)$$

$$\mathrm{G}\left(\mathrm{y}\right)={\mathrm{C}}_1-{\mathrm{R}}_1+\mathrm{y}{\mathrm{K}}_1+\mathrm{z}{\mathrm{Q}}_1+\mathrm{y}{\mathrm{S}}_1-\mathrm{z}\mathrm{b}{\mathrm{Q}}_1-\mathrm{y}\mathrm{a}{\mathrm{S}}_1$$

According to the stability theorem of differential equations, the probability that the government chooses to provide policy support reaches a stable state if it satisfies $\mathrm{F}\left(\mathrm{x}\right)=0$ and ${\displaystyle \raisebox{1ex}{$\mathrm{d}\left(\mathrm{F}\right(\mathrm{x}\left)\right)$}\!\left/ \!\raisebox{-1ex}{$\mathrm{d}\mathrm{x}$}\right.}<0$. Since ${\displaystyle \raisebox{1ex}{$\partial \left(\mathrm{G}\right(\mathrm{y}\left)\right)$}\!\left/ \!\raisebox{-1ex}{$\partial \mathrm{y}$}\right.}>0$, $\mathrm{G}\left(\mathrm{y}\right)$ is an increasing function with respect to y. Therefore, when $\mathrm{y}={\displaystyle \frac{{\mathrm{R}}_1-{\mathrm{C}}_1-\mathrm{z}({\mathrm{Q}}_1-{\mathrm{b}\mathrm{Q}}_1)}{{\mathrm{K}}_1+{\mathrm{S}}_1-\mathrm{a}{\mathrm{S}}_1}}=\mathrm{y}\ast$, $\mathrm{G}\left(\mathrm{y}\right)=0$. At this point, ${\displaystyle \raisebox{1ex}{$\mathrm{d}\left(\mathrm{F}\right(\mathrm{x}\left)\right)$}\!\left/ \!\raisebox{-1ex}{$\mathrm{d}\mathrm{x}$}\right.}=0$, and the government cannot ascertain a stable strategy. When $\mathrm{y}<\mathrm{y}\ast$, $\mathrm{G}\left(\mathrm{y}\right)<0,{\left.{\displaystyle \raisebox{1ex}{$\mathrm{d}\left(\mathrm{F}\right(\mathrm{x}\left)\right)$}\!\left/ \!\raisebox{-1ex}{$\mathrm{d}\mathrm{x}$}\right.}\right|}_{\mathrm{x}=1}<0$, and $\mathrm{x}=1$ is evolutionary stable strategies (it means that participants continually adjust their strategies based on vested interests to enhance their own benefits, ultimately achieving a strategy in dynamic equilibrium known as the Evolutionarily Stable Strategy (ESS)). When $\mathrm{y}>\mathrm{y}\ast$, $\mathrm{x}=0$ is ESS. The replication dynamic phase diagram of government strategy evolution is shown in Figure 5.

Figure 5 indicates that the probability of the government providing policy support is V_A1, representing the volume of A₁, and not providing policy support is V_A2, representing the volume of A₂. The calculations yield is as follows:

$${\mathrm{V}}_{\mathrm{A}1}={\int }_0^1{\int }_0^1{\displaystyle \frac{{\mathrm{R}}_1-{\mathrm{C}}_1-\mathrm{z}({\mathrm{Q}}_1-{\mathrm{b}\mathrm{Q}}_1)}{{\mathrm{K}}_1+{\mathrm{S}}_1-\mathrm{a}{\mathrm{S}}_1}}\mathrm{d}\mathrm{z}\mathrm{d}\mathrm{x}={\displaystyle \frac{2{\mathrm{R}}_1-2{\mathrm{C}}_1-({\mathrm{Q}}_1-\mathrm{b}{\mathrm{Q}}_1)}{2{\mathrm{K}}_1+2({\mathrm{S}}_1-\mathrm{a}{\mathrm{S}}_1)}}$$

$${\mathrm{V}}_{\mathrm{A}2}=1-{\mathrm{V}}_{\mathrm{A}1}$$

Proposition 1. 

The probability that the government provides policy support is positively correlated with the enhancement of its comprehensive benefits, while it is negatively correlated with the costs incurred by providing policy support, the degree of “land-use-right” grants to expressway groups, and the tax concessions to expressway groups and logistics enterprises.

Proof. 

Based on the expression for the probability ${\mathrm{V}}_{\mathrm{A}1}$ that the government provides policy support, the first-order partial derivatives of each factor can be obtained, ${\displaystyle \raisebox{1ex}{$\partial \left({\mathrm{V}}_{\mathrm{A}1}\right)$}\!\left/ \!\raisebox{-1ex}{$\partial {\mathrm{R}}_1$}\right.}>0,{\displaystyle \raisebox{1ex}{$\partial \left({\mathrm{V}}_{\mathrm{A}1}\right)$}\!\left/ \!\raisebox{-1ex}{$\partial {\mathrm{C}}_1$}\right.}<0,{\displaystyle \raisebox{1ex}{$\partial \left({\mathrm{V}}_{\mathrm{A}1}\right)$}\!\left/ \!\raisebox{-1ex}{$\partial {\mathrm{K}}_1$}\right.}<0,{\displaystyle \raisebox{1ex}{$\partial \left({\mathrm{V}}_{\mathrm{A}1}\right)$}\!\left/ \!\raisebox{-1ex}{$\partial ({\mathrm{Q}}_1-\mathrm{b}{\mathrm{Q}}_1)$}\right.}<0,{\displaystyle \raisebox{1ex}{$\partial \left({\mathrm{V}}_{\mathrm{A}1}\right)$}\!\left/ \!\raisebox{-1ex}{$\partial ({\mathrm{S}}_1-{\mathrm{a}\mathrm{S}}_1)$}\right.}<0$. Hence, an increase in R₁ or a decrease in C₁, K₁, (Q₁-bQ₁), and (S₁-aS₁) can lead to an increase in the probability of the government providing policy support. □

According to Proposition 1, ensuring the enhancement of the government’s comprehensive benefits can effectively prevent the scenario where it refrains from providing policy support. The government can promote its likelihood of choosing policy support by controlling costs, adjusting the degree of “land-use-right” grants, and regulating the extent of tax concessions to expressway groups and logistics enterprises.

Proposition 2. 

The probability of government policy support decreases as the probability of expressway groups choosing cooperation and logistics enterprises choosing entry increases.

Proof. 

From the analysis of government strategy stability, it is evident that when $\mathrm{z}<{\displaystyle \frac{{\mathrm{R}}_1-{\mathrm{C}}_1-\mathrm{y}({\mathrm{K}}_1+{\mathrm{S}}_1-\mathrm{a}{\mathrm{S}}_1)}{{\mathrm{Q}}_1-\mathrm{b}{\mathrm{Q}}_1}}$ and $\mathrm{y}<\mathrm{y}\ast$, $\mathrm{G}\left(\mathrm{y}\right)<0,{\left.{\displaystyle \raisebox{1ex}{$\mathrm{d}\left(\mathrm{F}\right(\mathrm{x}\left)\right)$}\!\left/ \!\raisebox{-1ex}{$\mathrm{d}\mathrm{x}$}\right.}\right|}_{\mathrm{x}=1}<0$, and $\mathrm{x}=1$ is ESS. Conversely, $\mathrm{x}=0$ is ESS. Thus, as y, z gradually increase, the government’s stable strategy shifts from $\mathrm{x}=1$ (policy support) to $\mathrm{x}=0$ (no policy support). □

Proposition 2 demonstrates that the probability of government policy support is influenced by the strategic choices of expressway groups and logistics enterprises. When expressway groups tend to choose cooperation and logistics enterprises tend to choose entry, the government may reduce its policy support, lower the degree of “land-use-right” grants, and reduce tax concessions, leading to decreased governmental engagement and potential damage to societal reputation.

6.2. Evolutionary Stable Strategy of Expressway Group

Let V₂₁ be the expected revenue for the expressway group when choosing the “cooperation” strategy and V₂₂ be the expected revenue when choosing the “no cooperation” strategy. The average expected revenue is denoted as V₂.

$$\begin{gathered} {\mathrm{V}}_{21}=({\mathrm{K}}_1+{\mathrm{K}}_{\mathrm{b}}+{\mathrm{S}}_3-\mathrm{a}{\mathrm{S}}_1-{\mathrm{C}}_{\mathrm{a}}-{\mathrm{K}}_2)\mathrm{x}\mathrm{z}+({\mathrm{K}}_1+{\mathrm{S}}_2-\mathrm{a}{\mathrm{S}}_1-{\mathrm{C}}_{\mathrm{a}}-{\mathrm{K}}_2)\mathrm{x}(1-\mathrm{z})+({\mathrm{K}}_{\mathrm{b}}+{\mathrm{S}}_3-{\mathrm{C}}_{\mathrm{a}}-{\mathrm{S}}_1-{\mathrm{K}}_2)(1-\mathrm{x})\mathrm{z} \\ +({\mathrm{S}}_2-{\mathrm{C}}_{\mathrm{a}}-{\mathrm{S}}_1-{\mathrm{K}}_2)(1-\mathrm{x})(1-\mathrm{z}) \end{gathered}$$

$${\mathrm{V}}_{22}=({\mathrm{K}}_{\mathrm{b}}+{\mathrm{S}}_2-{\mathrm{S}}_1-{\mathrm{C}}_{\mathrm{b}})\mathrm{x}\mathrm{z}+({\mathrm{S}}_2-{\mathrm{S}}_1-{\mathrm{C}}_{\mathrm{b}})\mathrm{x}(1-\mathrm{z})+({{\mathrm{K}}_{\mathrm{b}}+\mathrm{S}}_2-{\mathrm{C}}_{\mathrm{b}}-{\mathrm{S}}_1)(1-\mathrm{x})\mathrm{z}+({\mathrm{S}}_2-{\mathrm{C}}_{\mathrm{b}}-{\mathrm{S}}_1)(1-\mathrm{x})(1-\mathrm{z})$$

$${\mathrm{V}}_2=\mathrm{y}{\mathrm{V}}_{21}+(1-\mathrm{y}){\mathrm{V}}_{22}$$

The replicator dynamic equation for constructing the expressway group’s behavior strategies is defined as follows:

$${\mathrm{F}}_{\left(\mathrm{y}\right)}={\displaystyle \raisebox{1ex}{$\mathrm{d}\mathrm{y}$}\!\left/ \!\raisebox{-1ex}{$\mathrm{d}\mathrm{t}$}\right.}=\mathrm{y}\ast (\mathrm{y}-1)\ast ({\mathrm{C}}_{\mathrm{a}}-{\mathrm{C}}_{\mathrm{b}}+{\mathrm{K}}_2-\mathrm{x}{\mathrm{K}}_1-\mathrm{x}{\mathrm{S}}_1+\mathrm{z}{\mathrm{S}}_2-\mathrm{z}{\mathrm{S}}_3+\mathrm{x}\mathrm{a}{\mathrm{S}}_1)$$

The first derivative of y and the designated $\mathrm{J}\left(\mathrm{z}\right)$ are as follows:

$${\displaystyle \frac{\mathrm{d}\left(\mathrm{F}\left(\mathrm{y}\right)\right)}{\mathrm{d}\mathrm{y}}}=\left(2\mathrm{y}-1\right)\left({\mathrm{C}}_{\mathrm{a}}-{\mathrm{C}}_{\mathrm{b}}+{\mathrm{K}}_2-\mathrm{x}{\mathrm{K}}_1-\mathrm{x}{\mathrm{S}}_1+\mathrm{z}{\mathrm{S}}_2-\mathrm{z}{\mathrm{S}}_3+\mathrm{x}\mathrm{a}{\mathrm{S}}_1\right)$$

$$\mathrm{J}\left(\mathrm{z}\right)={\mathrm{C}}_{\mathrm{a}}-{\mathrm{C}}_{\mathrm{b}}+{\mathrm{K}}_2-\mathrm{x}{\mathrm{K}}_1-\mathrm{x}{\mathrm{S}}_1+\mathrm{z}{\mathrm{S}}_2-\mathrm{z}{\mathrm{S}}_3+\mathrm{x}\mathrm{a}{\mathrm{S}}_1$$

According to the stability theorem of differential equations, the probability that the expressway group chooses cooperation reaches a stable state if it satisfies $\mathrm{F}\left(\mathrm{y}\right)=0$ and ${\displaystyle \raisebox{1ex}{$\mathrm{d}\left(\mathrm{F}\right(\mathrm{y}\left)\right)$}\!\left/ \!\raisebox{-1ex}{$\mathrm{d}\mathrm{y}$}\right.}<0$. Since ${\displaystyle \raisebox{1ex}{$\partial \left(\mathrm{J}\right(\mathrm{z}\left)\right)$}\!\left/ \!\raisebox{-1ex}{$\partial \mathrm{z}$}\right.}<0$, $\mathrm{J}\left(\mathrm{z}\right)$ is a decreasing function with respect to z. Therefore, when $\mathrm{z}={\displaystyle \frac{{\mathrm{C}}_{\mathrm{a}}-{\mathrm{C}}_{\mathrm{b}}+{\mathrm{K}}_2-\mathrm{x}({\mathrm{K}}_1+{\mathrm{S}}_1-\mathrm{a}{\mathrm{S}}_1)}{{\mathrm{S}}_3-{\mathrm{S}}_2}}=\mathrm{z}\ast$, $\mathrm{J}\left(\mathrm{z}\right)=0$. At this point, ${\displaystyle \raisebox{1ex}{$\mathrm{d}\left(\mathrm{F}\right(\mathrm{y}\left)\right)$}\!\left/ \!\raisebox{-1ex}{$\mathrm{d}\mathrm{y}$}\right.}=0$, and the expressway group cannot ascertain a stable strategy. When $\mathrm{z}<{\mathrm{z}}^{\ast },\mathrm{J}(\mathrm{z})>0,{\left.{\displaystyle \raisebox{1ex}{$\mathrm{d}\left(\mathrm{F}\right(\mathrm{y}\left)\right)$}\!\left/ \!\raisebox{-1ex}{$\mathrm{d}\mathrm{y}$}\right.}\right|}_{\mathrm{y}=0}<0$, and $\mathrm{y}=0$ is ESS. When $\mathrm{z}>{\mathrm{z}}^{\ast }$, $\mathrm{y}=1$ is ESS. The replication dynamic phase diagram of expressway group strategy evolution is shown in Figure 6.

Figure 6 indicates that the probability of the expressway group not cooperating is V_B1, representing the volume of B₁, and the probability of cooperative behavior is V_B2, representing the volume of B₂.

$${\mathrm{V}}_{\mathrm{B}1}={\int }_0^1{\int }_0^{{\displaystyle \frac{{\mathrm{C}}_{\mathrm{a}}-{\mathrm{C}}_{\mathrm{b}}+{\mathrm{K}}_2}{{\mathrm{K}}_1+{\mathrm{S}}_1-{\mathrm{a}\mathrm{S}}_1}}}{\displaystyle \frac{{\mathrm{C}}_{\mathrm{a}}-{\mathrm{C}}_{\mathrm{b}}+{\mathrm{K}}_2-\mathrm{x}({\mathrm{K}}_1+{\mathrm{S}}_1-\mathrm{a}{\mathrm{S}}_1)}{{\mathrm{S}}_3-{\mathrm{S}}_2}}\mathrm{d}\mathrm{x}\mathrm{d}\mathrm{y}={\displaystyle \frac{{({\mathrm{C}}_{\mathrm{a}}-{\mathrm{C}}_{\mathrm{b}}+{\mathrm{K}}_2)}^2}{2({\mathrm{K}}_1-(-1+\mathrm{a}\left){\mathrm{S}}_1\right)(-{\mathrm{S}}_2+{\mathrm{S}}_3)}}$$

$${\mathrm{V}}_{\mathrm{B}2}=1-{\mathrm{V}}_{\mathrm{B}1}$$

Proposition 3. 

The probability that the expressway group chooses cooperation is negatively correlated with the increase in operational costs incurred by choosing cooperation and the rental subsidies provided to logistics enterprises. Conversely, it is positively correlated with the degree of “land-use-right” grants to the expressway group by the government, the intensity of tax concessions, and the difference in toll fees charged by the expressway group before and after logistics enterprises choose entry.

Proof. 

By obtaining the first-order partial derivatives of each factor ${\displaystyle \raisebox{1ex}{$\partial \left({\mathrm{V}}_{\mathrm{B}2}\right)$}\!\left/ \!\raisebox{-1ex}{${\partial (\mathrm{C}}_{\mathrm{a}}-{\mathrm{C}}_{\mathrm{b}})$}\right.}<0$, ${\displaystyle \raisebox{1ex}{$\partial \left({\mathrm{V}}_{\mathrm{B}2}\right)$}\!\left/ \!\raisebox{-1ex}{${\partial \mathrm{K}}_2$}\right.}<0$, ${\displaystyle \raisebox{1ex}{$\partial \left({\mathrm{V}}_{\mathrm{B}2}\right)$}\!\left/ \!\raisebox{-1ex}{${\partial \mathrm{K}}_1$}\right.}>0$, ${\displaystyle \raisebox{1ex}{$\partial \left({\mathrm{V}}_{\mathrm{B}2}\right)$}\!\left/ \!\raisebox{-1ex}{$\partial ({\mathrm{S}}_1-\mathrm{a}{\mathrm{S}}_1)$}\right.}>0$, ${\displaystyle \raisebox{1ex}{$\partial \left({\mathrm{V}}_{\mathrm{B}2}\right)$}\!\left/ \!\raisebox{-1ex}{$\partial ({\mathrm{S}}_3-{\mathrm{S}}_2)$}\right.}>0$, it can be found that reducing C_a − C_b and K₂ and increasing K₁, (S₁ − aS₁), and (S₃ − S₂) can elevate the probability of the expressway group choosing cooperation. □

According to Proposition 3, when an expressway group choosing cooperation faces high operational costs and provides significant rental subsidies to logistics enterprises, the government should increase the degree of “land-use-right” grants appropriately. Additionally, enhancing the tax concessions for the expressway group can effectively boost its likelihood of choosing cooperation.

Proposition 4. 

The probability of the expressway group choosing cooperation increases with the probability of the government selecting policy support or logistics enterprises choosing entry.

Proof. 

From the analysis of expressway group strategy stability, it is evident that when $\mathrm{x}<{\displaystyle \frac{{\mathrm{C}}_{\mathrm{a}}-{\mathrm{C}}_{\mathrm{b}}+{\mathrm{K}}_2+\mathrm{z}({\mathrm{S}}_2-{\mathrm{S}}_3)}{{\mathrm{K}}_1+{\mathrm{S}}_1-\mathrm{a}{\mathrm{S}}_1}}$ and $\mathrm{z}<z^{*},\mathrm{J}(\mathrm{z})>0,{\left.{\displaystyle \raisebox{1ex}{$\mathrm{d}\left(\mathrm{F}\right(\mathrm{y}\left)\right)$}\!\left/ \!\raisebox{-1ex}{$\mathrm{d}\mathrm{y}$}\right.}\right|}_{\mathrm{y}=0}<0$, and $\mathrm{y}=0$ is ESS. When $\mathrm{z}<{\mathrm{z}}^{\ast }$, $\mathrm{y}=1$ is ESS. Thus, as x, z increase, the stable strategy of the expressway group shifts from $\mathrm{y}=0$ (no cooperation) to $\mathrm{y}=1$ (cooperation). □

Proposition 4 demonstrates that enhancing the willingness of logistics enterprises to choose entry aids the expressway group in adopting cooperation as a stable strategy. The government can increase the probability of the expressway group choosing cooperation by intensifying support efforts. Thus, it can emphasize cost reduction and efficiency improvement for logistics enterprises to promote their willingness for entry, thereby fostering the effective development of the ELD.

6.3. Evolutionary Stable Strategy of Logistics Enterprise

Let V₃₁ be the expected revenue for logistics enterprises when choosing the “entry” strategy and V₃₂ be the expected revenue when choosing the “no entry” strategy. The average expected revenue is denoted as V₃.

$$\begin{gathered} {\mathrm{V}}_{31}=({\mathrm{R}}_{\mathrm{a}\mathrm{a}}+{\mathrm{K}}_2-{\mathrm{b}\mathrm{Q}}_1-{\mathrm{S}}_3-{\mathrm{K}}_{\mathrm{b}}-{\mathrm{V}}_{\mathrm{a}\mathrm{b}}-{\mathrm{V}}_{\mathrm{a}\mathrm{s}})\mathrm{x}\mathrm{y}+({\mathrm{R}}_{\mathrm{a}\mathrm{a}}-{\mathrm{b}\mathrm{Q}}_1-{\mathrm{S}}_2-{\mathrm{K}}_{\mathrm{b}}-{\mathrm{V}}_{\mathrm{a}\mathrm{b}}-{\mathrm{V}}_{\mathrm{a}\mathrm{s}})\mathrm{x}(1-\mathrm{y})+({\mathrm{R}}_{\mathrm{a}\mathrm{a}}+{\mathrm{K}}_2-{\mathrm{Q}}_1 \\ -{\mathrm{S}}_3-{\mathrm{K}}_{\mathrm{b}}-{\mathrm{V}}_{\mathrm{a}\mathrm{b}}-{\mathrm{V}}_{\mathrm{a}\mathrm{s}})(1-\mathrm{x})\mathrm{y}+({\mathrm{R}}_{\mathrm{a}\mathrm{a}}-{\mathrm{Q}}_1-{\mathrm{S}}_2-{\mathrm{K}}_{\mathrm{b}}-{\mathrm{V}}_{\mathrm{a}\mathrm{b}}-{\mathrm{V}}_{\mathrm{a}\mathrm{s}})(1-\mathrm{x})(1-\mathrm{y}) \end{gathered}$$

$$\begin{gathered} {\mathrm{V}}_{32}=({\mathrm{R}}_{\mathrm{b}\mathrm{b}}+{\mathrm{K}}_2-{\mathrm{Q}}_1-{\mathrm{S}}_2-{\mathrm{K}}_{\mathrm{b}}-{\mathrm{V}}_{\mathrm{b}\mathrm{b}}-{\mathrm{V}}_{\mathrm{b}\mathrm{s}})\mathrm{x}\mathrm{y}+({\mathrm{R}}_{\mathrm{b}\mathrm{b}}-{\mathrm{Q}}_1-{\mathrm{S}}_2-{\mathrm{K}}_{\mathrm{b}}-{\mathrm{V}}_{\mathrm{b}\mathrm{b}}-{\mathrm{V}}_{\mathrm{b}\mathrm{s}})\mathrm{x}(1-\mathrm{y})+{\mathrm{R}}_{\mathrm{b}\mathrm{b}}+{\mathrm{K}}_2-{\mathrm{Q}}_1 \\ -{\mathrm{S}}_2-{\mathrm{K}}_{\mathrm{b}}-{\mathrm{V}}_{\mathrm{b}\mathrm{b}}-{\mathrm{V}}_{\mathrm{b}\mathrm{s}}\left)\right(1-\mathrm{x})\mathrm{y}+({\mathrm{R}}_{\mathrm{b}\mathrm{b}}-{\mathrm{Q}}_1-{\mathrm{S}}_2-{\mathrm{K}}_{\mathrm{b}}-{\mathrm{V}}_{\mathrm{b}\mathrm{b}}-{\mathrm{V}}_{\mathrm{b}\mathrm{s}}\left)\right(1-\mathrm{x}\left)\right(1-\mathrm{y}) \end{gathered}$$

$${\mathrm{V}}_3=\mathrm{z}{\mathrm{V}}_{31}+(1-\mathrm{z}){\mathrm{V}}_{32}$$

The replicator dynamic equation for constructing logistics enterprises’ behavior strategies is defined as follows:

$${\mathrm{F}}_{\left(\mathrm{z}\right)}={\displaystyle \raisebox{1ex}{$\mathrm{d}\mathrm{z}$}\!\left/ \!\raisebox{-1ex}{$\mathrm{d}\mathrm{t}$}\right.}=-\mathrm{z}\ast (\mathrm{z}-1)\ast ({\mathrm{R}}_{\mathrm{a}\mathrm{a}}-{\mathrm{R}}_{\mathrm{b}\mathrm{b}}-{\mathrm{V}}_{\mathrm{a}\mathrm{b}}-{\mathrm{V}}_{\mathrm{a}\mathrm{s}}+{\mathrm{V}}_{\mathrm{b}\mathrm{b}}+{\mathrm{V}}_{\mathrm{b}\mathrm{s}}+{\mathrm{x}\mathrm{Q}}_1+\mathrm{y}{\mathrm{S}}_2-\mathrm{y}{\mathrm{S}}_3-\mathrm{x}\mathrm{b}{\mathrm{Q}}_1)$$

The first derivative of z and the designated $\mathrm{H}\left(\mathrm{y}\right)$ are as follows:

$${\displaystyle \frac{\mathrm{d}\left(\mathrm{F}\left(\mathrm{z}\right)\right)}{\mathrm{d}\mathrm{z}}}=\left(1-2\mathrm{z}\right)({\mathrm{R}}_{\mathrm{a}\mathrm{a}}-{\mathrm{R}}_{\mathrm{b}\mathrm{b}}-{\mathrm{V}}_{\mathrm{a}\mathrm{b}}-{\mathrm{V}}_{\mathrm{a}\mathrm{s}}+{\mathrm{V}}_{\mathrm{b}\mathrm{b}}+{\mathrm{V}}_{\mathrm{b}\mathrm{s}}+{\mathrm{x}\mathrm{Q}}_1+\mathrm{y}{\mathrm{S}}_2-\mathrm{y}{\mathrm{S}}_3-\mathrm{x}\mathrm{b}{\mathrm{Q}}_1)$$

$$\mathrm{H}\left(\mathrm{y}\right)={\mathrm{R}}_{\mathrm{a}\mathrm{a}}-{\mathrm{R}}_{\mathrm{b}\mathrm{b}}-{\mathrm{V}}_{\mathrm{a}\mathrm{b}}-{\mathrm{V}}_{\mathrm{a}\mathrm{s}}+{\mathrm{V}}_{\mathrm{b}\mathrm{b}}+{\mathrm{V}}_{\mathrm{b}\mathrm{s}}+{\mathrm{x}\mathrm{Q}}_1+\mathrm{y}{\mathrm{S}}_2-\mathrm{y}{\mathrm{S}}_3-\mathrm{x}\mathrm{b}{\mathrm{Q}}_1$$

According to the stability theorem of differential equations, the probability that logistics enterprises choose cooperation reaches a stable state if it satisfies $\mathrm{F}\left(\mathrm{z}\right)=0$ and ${\displaystyle \raisebox{1ex}{$\mathrm{d}\left(\mathrm{F}\right(\mathrm{z}\left)\right)$}\!\left/ \!\raisebox{-1ex}{$\mathrm{d}\mathrm{z}$}\right.}<0$. Since ${\displaystyle \raisebox{1ex}{$\partial \left(\mathrm{H}\left(\mathrm{y}\right)\right)$}\!\left/ \!\raisebox{-1ex}{$\partial \mathrm{y}$}\right.}<0$, $\mathrm{H}\left(\mathrm{y}\right)$ is a decreasing function with respect to $\mathrm{y}$. Therefore, when $\mathrm{y}={\displaystyle \frac{{\mathrm{R}}_{\mathrm{a}\mathrm{a}}-{\mathrm{R}}_{\mathrm{b}\mathrm{b}}-{\mathrm{V}}_{\mathrm{a}\mathrm{b}}-{\mathrm{V}}_{\mathrm{a}\mathrm{s}}+{\mathrm{V}}_{\mathrm{b}\mathrm{b}}+{\mathrm{V}}_{\mathrm{b}\mathrm{s}}+\mathrm{x}({\mathrm{Q}}_1-\mathrm{b}{\mathrm{Q}}_1)}{{\mathrm{S}}_3-{\mathrm{S}}_2}}={\mathrm{y}}^{\ast \ast }$, $\mathrm{H}\left(\mathrm{y}\right)=0$. At this point, ${\displaystyle \raisebox{1ex}{$\mathrm{d}\left(\mathrm{F}\right(\mathrm{y}\left)\right)$}\!\left/ \!\raisebox{-1ex}{$\mathrm{d}\mathrm{y}$}\right.}=0$, and the logistics enterprises cannot ascertain a stable strategy. When $\mathrm{y}<{\mathrm{y}}^{\ast \ast }$, $\mathrm{H}\left(\mathrm{y}\right)>0$, ${\left.{\displaystyle \raisebox{1ex}{$\mathrm{d}\left(\mathrm{F}\right(\mathrm{z}\left)\right)$}\!\left/ \!\raisebox{-1ex}{$\mathrm{d}\mathrm{z}$}\right.}\right|}_{\mathrm{z}=0}<0$, and $\mathrm{z}=0$ is ESS. When $\mathrm{y}>{\mathrm{y}}^{\ast \ast }$, $\mathrm{z}=1$ is ESS. The replication dynamic phase diagram of logistics enterprises’ strategy evolution is shown in Figure 7.

Figure 7 indicates that the probability of logistics enterprises choosing entry is V_C1, representing the volume of C₁, and the probability of no entry is V_C2, representing the volume of C₂.

$$\begin{gathered} {\mathrm{V}}_{\mathrm{C}1}={\int }_0^1{\int }_0^1{\displaystyle \frac{{\mathrm{R}}_{\mathrm{a}\mathrm{a}}-{\mathrm{R}}_{\mathrm{b}\mathrm{b}}-{\mathrm{V}}_{\mathrm{a}\mathrm{b}}-{\mathrm{V}}_{\mathrm{a}\mathrm{s}}+{\mathrm{V}}_{\mathrm{b}\mathrm{b}}+{\mathrm{V}}_{\mathrm{b}\mathrm{s}}+\mathrm{x}({\mathrm{Q}}_1-\mathrm{b}{\mathrm{Q}}_1)}{{\mathrm{S}}_3-{\mathrm{S}}_2}}\mathrm{d}\mathrm{x}\mathrm{d}\mathrm{z} \\ ={\displaystyle \frac{(-1+\mathrm{b}){\mathrm{Q}}_1-2({\mathrm{R}}_{\mathrm{a}\mathrm{a}}-{\mathrm{R}}_{\mathrm{b}\mathrm{b}}-{\mathrm{V}}_{\mathrm{a}\mathrm{b}}+{\mathrm{V}}_{\mathrm{b}\mathrm{b}}-{\mathrm{V}}_{\mathrm{a}\mathrm{s}}+{\mathrm{V}}_{\mathrm{b}\mathrm{s}})}{2({\mathrm{S}}_2-{\mathrm{S}}_3)}} \end{gathered}$$

$${\mathrm{V}}_{\mathrm{C}2}=1-{\mathrm{V}}_{\mathrm{C}1}$$

Proposition 5. 

The probability that logistics enterprises choose entry is positively correlated with the increased benefits from choosing entry and the tax difference before and after entry. Conversely, it is negatively correlated with the difference in toll fees charged by the expressway group before and after entry, as well as the increased transportation costs after entry.

Proof. 

By deriving the first-order partial derivatives of each factor from the expression for the probability of logistics enterprises choosing entry ${\displaystyle \raisebox{1ex}{$\partial \left({\mathrm{V}}_{\mathrm{C}1}\right)$}\!\left/ \!\raisebox{-1ex}{$\partial {(\mathrm{R}}_{\mathrm{a}\mathrm{a}}-{\mathrm{R}}_{\mathrm{b}\mathrm{b}})$}\right.}>0,{\displaystyle \raisebox{1ex}{$\partial \left({\mathrm{V}}_{\mathrm{C}1}\right)$}\!\left/ \!\raisebox{-1ex}{$\partial ({\mathrm{Q}}_1-\mathrm{b}{\mathrm{Q}}_1)$}\right.}>0,{\displaystyle \raisebox{1ex}{$\partial \left({\mathrm{V}}_{\mathrm{C}1}\right)$}\!\left/ \!\raisebox{-1ex}{$\partial ({\mathrm{S}}_3-{\mathrm{S}}_2)$}\right.}<0,{\displaystyle \raisebox{1ex}{$\partial \left({\mathrm{V}}_{\mathrm{C}1}\right)$}\!\left/ \!\raisebox{-1ex}{$\partial ({\mathrm{V}}_{\mathrm{a}\mathrm{b}}+{\mathrm{V}}_{\mathrm{a}\mathrm{s}}-{\mathrm{V}}_{\mathrm{b}\mathrm{b}}-{\mathrm{V}}_{\mathrm{b}\mathrm{s}})$}\right.}<0$, it can be found that increasing $({\mathrm{R}}_{\mathrm{a}\mathrm{a}}-{\mathrm{R}}_{\mathrm{b}\mathrm{b}})$ and ${(\mathrm{Q}}_1-\mathrm{b}{\mathrm{Q}}_1)$ as well as reducing ${(\mathrm{S}}_3-{\mathrm{S}}_2)$ and ${(\mathrm{V}}_{\mathrm{a}\mathrm{b}}+{\mathrm{V}}_{\mathrm{a}\mathrm{s}}-{\mathrm{V}}_{\mathrm{b}\mathrm{b}}-{\mathrm{V}}_{\mathrm{b}\mathrm{s}})$ can raise the probability of logistics enterprises choosing entry. □

According to Proposition 5, the government can attract logistics enterprises to decide on entry by maximizing the tax difference before and after entry. Enhanced logistics efficiency and reduced logistics costs after entry further strengthen their willingness to choose entry. The expressway group can increase the probability of logistics enterprises choosing entry by controlling the differences in toll fees and transportation costs before and after entry.

Proposition 6. 

The probability of logistics enterprises choosing entry increases with the probability of the government selecting policy support and the expressway group choosing cooperation.

Proof. 

From the analysis of the logistics enterprise’s strategy stability, it is evident that when $\mathrm{x}>{\displaystyle \frac{{\mathrm{R}}_{\mathrm{a}\mathrm{a}}-{\mathrm{R}}_{\mathrm{b}\mathrm{b}}+{\mathrm{V}}_{\mathrm{a}\mathrm{b}}+{\mathrm{V}}_{\mathrm{a}\mathrm{s}}-{\mathrm{V}}_{\mathrm{b}\mathrm{b}}-{\mathrm{V}}_{\mathrm{b}\mathrm{s}}+\mathrm{y}({\mathrm{S}}_3-{\mathrm{S}}_2)}{{\mathrm{Q}}_1-\mathrm{b}{\mathrm{Q}}_1}}$, $\mathrm{y}<{\mathrm{y}}^{\ast \ast }$, $\mathrm{H}\left(\mathrm{y}\right)>0$, ${\left.{\displaystyle \raisebox{1ex}{$\mathrm{d}\left(\mathrm{F}\right(\mathrm{z}\left)\right)$}\!\left/ \!\raisebox{-1ex}{$\mathrm{d}\mathrm{z}$}\right.}\right|}_{\mathrm{z}=0}<0$, and $\mathrm{z}=0$ is ESS. When $\mathrm{y}>{\mathrm{y}}^{\ast \ast }$, $\mathrm{z}=1$ is ESS. Thus, as $\mathrm{x},\mathrm{y}$ increase, the stable strategy of logistics enterprises shifts from $\mathrm{z}=0$ (no entry) to $\mathrm{z}=1$ (entry). □

Proposition 6 demonstrates that enhancing the probability of the expressway group choosing cooperation facilitates logistics enterprises in adopting entry as a stable strategy. The government can attract logistics enterprises to choose entry by increasing “land-use-right” grants and tax concessions.

6.4. Stability Analysis of the Equilibrium Point of the Three-Party Evolutionary Game

In the asymmetric game model, the mixed strategy equilibrium is not equivalent to the ESS. The stakeholder continuously adjusts its strategy to maximize its own interests and eventually reaches a dynamic equilibrium state, which is the so-called ESS. Before determining the ESS, it is necessary to find the equilibrium point of the evolutionary game.

Assume $\mathrm{F}\left(\mathrm{x}\right)=0$, $\mathrm{F}\left(\mathrm{y}\right)=0,$ and $\mathrm{F}\left(\mathrm{z}\right)=0$; that is, when the rate of change of the system strategy selection is zero, it can get eight pure strategy equilibrium points of the dynamic system, namely, D₁:(0,0,0), D₂:(0,1,0), D₃:(0,0,1), D₄:(0,1,1), D₅:(1,0,0), D₆:(1,1,0), D₇:(1, 0,1), and D₈:(1,1,1). According to the research of Ritzberger and Weibull [45], only the asymptotic stability of these eight points needs to be examined, while the other points are all non-asymptotically stable. Through Lyapunov stability theory, these eight equilibrium points are substituted into the Jacobian matrix to calculate the eigenvalues and judge the stability. The results are shown in

Table 3. The eigenvalues of equilibrium points.

Equilibrium Point	Jacobin Matrix Eigenvalues		Stability Conclusion
	λ1, λ2, λ3	Real Part of Symbol
D1:(0,0,0)	$(R_1-C_1$$,C_b-C_a-K_2$$,R_{aa}-R_{bb}-V_{ab}-V_{as}+V_{bb}+V_{bs})$	(+,−,×)	Instability
D2:(0,1,0)	$(C_a-C_b+K_2,R_1-K_1-C_1-S_1+a{S}_1$$,R_{aa}-R_{bb}+S_2-S_3-V_{ab}-V_{as}+V_{bb}+V_{bs})$	(+,×,×)	Instability
D3:(0,0,1)	$(R_1-Q_1-C_1+b{Q}_1$$,C_b-C_a-K_2-S_2+S_3,R_{bb}-R_{aa}+V_{ab}+V_{as}-V_{bb}-V_{bs})$	(+,−,×)	Instability
D4:(0,1,1)	$(C_a-C_b+K_2+S_2-S_3$$,R_1-K_1-C_1-S_1+a{S}_1-Q_1+b{Q}_1$$,R_{bb}-R_{aa}+V_{ab}+V_{as}-V_{bb}-V_{bs}-S_2+S_3)$	(+,×,×)	Instability
D5:(1,0,0)	$(C_1-R_1$$,C_b-C_a+K_1-K_2+S_1-a{S}_1$$,R_{aa}-R_{bb}-V_{ab}-V_{as}+V_{bb}+V_{bs}+Q_1-b{Q}_1)$	(−,×,+)	Instability
D6:(1,1,0)	$(C_1+K_1-R_1+S_1-a{S}_1$$,C_a-C_b-K_1+K_2-S_1+a{S}_1$$,R_{aa}-R_{bb}+S_2-S_3-V_{ab}-V_{as}+V_{bb}+V_{bs}+Q_1-b{Q}_1)$	(×,+,×)	Instability
D7:(1,0,1)	$(C_1+Q_1-R_1-b{Q}_1,R_{bb}-R_{aa}+V_{ab}+V_{as}-V_{bb}-V_{bs}-Q_1+b{Q}_1$$,C_b-C_a-K_2-S_2+S_3+K_1+S_1-a{S}_1)$	(×,×,×)	Possible for ESS
D8:(1,1,1)	$(C_1+K_1-R_1+S_1-a{S}_1+Q_1-b{Q}_1,C_a-C_b+K_2+S_2-S_3-K_1-S_1+a{S}_1,R_{bb}-R_{aa}+V_{ab}+V_{as}-V_{bb}-V_{bs}-Q_1+b{Q}_1-S_2+S_3)$	(×,×,×)	Possible for ESS

.

It can be seen from Table 3 that the eigenvalues of equilibrium points D₁, D₂, D₃, D₄, D₅, and D₆ contain positive real parts, so these points are unstable, and the stability of equilibrium points D₇ and D₈ still need further discussion. Whether each equilibrium point meets the evolutionary stability conditions is shown in

Table 4. Conditions for each equilibrium point to meet evolutionary stability.

Scenario	Equilibrium Point	Conditions for Evolutionary Stability
Scenario 1	D7:(1,0,1)	$C_1+Q_1-R_1-b{Q}_1<0$	$C_b-C_a+K_1-K_2+S_1-S_2+S_3-a{S}_1<0$	$R_{bb}-R_{aa}-Q_1+V_{ab}+V_{as}-V_{bb}-V_{bs}+b{Q}_1<0$
Scenario 2	D8:(1,1,1)	$C_1+K_1+Q_1-R_1+S_1-b{Q}_1-a{S}_1<0$	$C_a-C_b-K_1+K_2-S_1+S_2-S_3+a{S}_1<0$	$R_{bb}-R_{aa}-Q_1-S_2+S_3+V_{ab}+V_{as}-V_{bb}-V_{bs}+b{Q}_1<0$

.

7. Numerical Experiments and Simulation Analysis

7.1. Data Simulation Analysis of Equilibrium Points

To verify the above evolutionary game results and analyze the factors affecting them, Matlab 2018b is used for numerical simulation. Combined with the model assumptions with the stability conditions of the equilibrium points, the relevant parameters are reasonably assigned based on the actual situation. The parameters for the two scenarios are shown in

Table 5. Basic parameter settings under two scenarios.

	${\mathit{C}}_1$	${\mathit{R}}_1$	${\mathit{K}}_1$	${\mathit{S}}_1$	$\mathbf{a}$	${\mathit{Q}}_1$	$\mathbf{b}$	${\mathit{R}}_2$	${\mathit{G}}_1$	${\mathit{C}}_{\mathit{a}}$	${\mathit{C}}_{\mathit{b}}$	${\mathit{K}}_2$	${\mathit{S}}_2$	${\mathit{S}}_3$	${\mathit{R}}_{\mathit{a}\mathit{a}}$	${\mathit{R}}_{\mathit{b}\mathit{b}}$	${\mathit{K}}_{\mathit{b}}$	${\mathit{V}}_{\mathit{a}\mathit{b}}$	${\mathit{V}}_{\mathit{a}\mathit{s}}$	${\mathit{V}}_{\mathit{b}\mathit{b}}$	${\mathit{V}}_{\mathit{b}\mathit{s}}$
Scenario 1	1	4	0	5	1	10	0.8	1	0	0	22	0	44	0	110	105	35	5	15	7	11
Scenario 2	1	6	1	5	0.8	10	0.8	1	0	23	22	1	44	45	110	105	35	5	15	7	11

to analyze the evolutionary results of the three parties under each scenario.

For scenario 1, the gradual evolution stability conditions are C₁ + Q₁ − R₁ − bQ₁ < 0, C_b − C_a + K₁ − K₂ + S₁ − S₂ + S₃ − aS₁ < 0, and R_bb − R_aa − Q₁ + V_ab + V_as − V_bb − V_bs + bQ₁ < 0. The systematic evolutionary path diagram is shown in Figure 8. When C₁ + Q₁ − bQ₁ < R₁, that is, the comprehensive benefits of the government’s policy support are greater than the sum of its costs and tax incentives for logistics enterprises, the government’s strategy choice tends to be “policy support”. When K₁ + S₁ − aS₁ − S₂ + S₃ < C_a − C_b + K₂, that is, the increased operating costs and rental subsidies given to logistics enterprises after the expressway group chooses to cooperate are greater than the land-use rights, tax incentives given by the government, and the additional tolls collected after cooperation, the expressway group’s strategy choice is “no cooperation”. When R_aa − R_bb + Q₁ − bQ₁ > V_ab + V_as − V_bb − V_bs, meaning the increased income from the distribution business and the tax incentives given by the government after logistics enterprises choose entry are greater than the increased transportation costs of large and small vehicles after choosing entry, the strategy of logistics enterprises tends to be “entry”.

Therefore, under certain conditions, it is also feasible for the expressway group to choose “no cooperation”. At this time, the expressway group does not have the “land-use-right” grants and tax incentives given by the government, nor does it have the increased operating costs due to cooperation and the rental subsidies and toll concessions given to logistics enterprises. Therefore, the increased income of the expressway group mainly comes from the warehouse rent of logistics enterprises. Therefore, when the warehouse rent of logistics enterprises is greater than the “land-use-right” grants and tax incentives given by the government when the expressway group chooses to cooperate, the stability of the strategy (policy support, no cooperation, entry) will be revealed.

In this scenario, it is essential to address the government’s supervision of unauthorized service area reconstruction. According to the Expressway Service Area Reconstruction Land Control Index, the reconstructed service area should be built and opened to traffic for more than 3 years in principle and meet the relevant requirements of the Control Index on traffic volume, entry rate, and setting spacing. The project construction unit must submit a reconstruction application and demonstration report. The provincial transportation authority should provide continuous monitoring data on traffic volume and entry rate for at least 12 months, and the land scale approval should follow the Control Index. Therefore, for newly built service area sections, the government should strengthen the implementation of the “land-use-right” grant and tax incentive policy to avoid the emergence of strategy (policy support, no cooperation, entry). For service area sections that have been built and opened to traffic for more than 3 years and meet the requirements, the expressway group should submit a reconstruction application, and logistics enterprises can choose “entry” after approval, thus avoiding illegal land use disrupting the high-speed operation environment.

For scenario 2, the asymptotic evolution stability conditions are C₁ + K₁ + Q₁ − R₁ + S₁ − bQ₁ − aS₁ < 0, C_a − C_b − K₁ + K₂ − S₁ + S₂ − S₃ + aS₁ < 0, and R_bb − R_aa − Q₁ − S₂ + S₃ + V_ab + V_as − V_bb − V_bs + bQ₁ < 0. The systematic evolutionary path diagram is shown in Figure 9. When C₁ + K₁ + S₁ − aS₁ + Q₁ − bQ₁ < R₁, that is, when the comprehensive benefits of the government’s support policy are greater than the sum of its costs, tax incentives for expressway groups and logistics enterprises, and “land-use-right” grants for expressway groups that choose to cooperate, the government’s strategic choice tends to be “policy support”. Therefore, when higher-level government departments decide to reward lower-level government departments, they should consider the effectiveness of tax incentives provided to expressway groups and logistics enterprises. The incentive mechanism from higher-level government significantly enhances policy support. Government policy support is crucial for promoting “expressway + logistics distribution” and maintaining market order in logistics distribution. When K₁ + S₁ − aS₁ − S₂ + S₃ > C_a − C_b + K₂, that is, the increased operating costs and rental subsidies given to logistics enterprises after the expressway group chooses cooperation are less than the land-use right and tax incentives granted by the government to expressway group and additional tolls collected after cooperation, the strategy of the expressway group tends to be “cooperation”. When R_aa − R_bb + Q₁ − bQ₁ > V_ab + V_as − V_bb − V_bs + S₃ − S₂, that is, when the increased income from the distribution business after logistics enterprises choose entry and the tax incentives given by the government are greater than the sum of the increased transportation costs and tolls of large and small vehicles, the strategy of logistics enterprises tends to choose “entry”. In this case, the three parties make strategic choices by comprehensively considering all relevant factors and finally obtain an ideal and reliable strategy combination (policy support, cooperation, entry).

From the stability conditions, it can be seen that when transportation costs for large and small vehicles increase after logistics enterprises choose entry, government tax incentives and business rewards from cargo owner enterprises will also rise accordingly. The increased transportation costs for large and small vehicles after logistics enterprises choose entry can highlight the differences in transfer nodes before and after entry, indicating the degree of improvement in distribution efficiency. Thus, logistics enterprises can secure various government tax incentives and business rewards by analyzing changes in transportation costs for large and small vehicles post-entry. They can then calculate when their revenue is maximized to determine the optimal location for the transfer nodes of large and small vehicles, effectively identifying the ideal location for the logistics distribution center.

7.2. Data Simulation Analysis of Factors

To better understand the dynamic evolutionary game process among ELD stakeholders, this section combines the replication dynamic equation and related constraints. This section takes the ideal state D₈(1,1,1), i.e., (policy support, cooperation, entry), and D₇(1,0,1), i.e., (policy support, no cooperation, entry), as the basis, the initial values of $\mathrm{x},\mathrm{y},\mathrm{z}$ are set to (0.5, 0.5, 0.5), and the dynamic system of equations was replicated 50 times and evolved over time. This paper judges the evolution trend of the strategy through changes in parameters such as the degree of “land-use-right” grants by the government to the expressway group that chooses to cooperate, the intensity of government tax incentives for expressway groups and logistics enterprises, and explores the factors affecting the strategy selection of ELD stakeholders.

7.2.1. Policy Support, Cooperation, Entry

(1) The impact of changes in K₁ on system evolution

To analyze the impact of the government “land-use-right” grants to the expressway group on the results of the three-party evolutionary game, the land-use right, K₁, is assigned values, K₁ = 0.5, K₁ = 1, K₁ = 1.9, and other parameters remain unchanged. The system evolution game is shown in Figure 10.

As shown in Figure 10, during the system’s evolution to a stable point, an increase in the government “land-use-right” grants to the expressway group can accelerate the evolution of the expressway group’s cooperation. However, the evolution rate of logistics enterprises choosing “entry” decreases slightly. As K₁ increases, the probability of the expressway group choosing cooperation increases, and the probability of logistics enterprises choosing entry decreases. Therefore, when logistics enterprises face the same rental subsidies, an increase in the government “land-use-right” grants will reduce the probability of logistics enterprises choosing entry. Excessive “land-use-right” grants give expressway groups greater freedom in land planning and more diversity in business formats within their layouts. This leads to resource crowding and a decreased willingness of logistics enterprises to choose entry.

(2) The impact of changes in K₂ on system evolution

To analyze the impact of changes in the rental subsidies given by the expressway group to logistics enterprises on the results of the three-party evolutionary game, the subsidy, i.e., K₂, is assigned values, and K₂ = 0, K₂ = 1, and K₂ = 1.5 are taken, respectively. Other parameters remain unchanged. The system evolution game is shown in Figure 11 and Figure 12.

As shown in Figure 11 and Figure 12, during the system’s evolution to a stable point, an increase in the rental subsidies provided by the expressway group to logistics enterprises can accelerate the government’s policy support and the logistics enterprises’ choice of entry. As K₂ increases, the probability of the government choosing policy support and the probability of logistics enterprises choosing entry increases. Therefore, the expressway group’s proactive increase in rental subsidies for logistics enterprises can enhance the likelihood of government policy support, leading to increased “land-use-right” grants and intensified tax incentives, thereby promoting the positive development of the ELD model.

(3) The impact of changes in a on system evolution

To analyze the impact of changes in the government’s tax incentives for the expressway group on the results of the three-party evolutionary game, a is assigned a = 0.9, a = 0.8, a = 0.61, and other parameters remain unchanged. The system evolution game is shown in Figure 13 and Figure 14.

As shown in Figure 13 and Figure 14, during the system’s evolution toward a stable point, an increase in tax incentives from the government for the expressway group can accelerate its cooperation. As a decreases, the probability of the expressway group choosing cooperation and the probability of logistics enterprises choosing entry increase.

(4) The impact of changes in b on system evolution

To analyze the impact of changes in the government’s tax incentives for logistics enterprises on the results of the three-party evolutionary game, b is assigned b = 0.9, b = 0.8, b = 0.71, and other parameters remain unchanged. The system evolution game is shown in Figure 15 and Figure 16.

As shown in Figure 15 and Figure 16, during the system’s evolution to a stable point, an increase in the government’s tax incentives for logistics enterprises can accelerate their choice of entry. As b decreases, the probability of logistics enterprises choosing entry and the probability of expressway groups choosing cooperation increase.

As shown in Figure 13 and Figure 15, under the same changes in tax incentives intensity, the fluctuation in the evolution path for providing tax incentives to expressway groups is greater than that for logistics enterprises. Therefore, when government funds are tight, priority may be given to providing tax incentives to expressway groups.

(5) The impact of changes in S₃ − S₂ on system evolution

To analyze the impact of changes in the preferential tolls of expressway groups for logistics enterprises on the results of the three-party evolutionary game, S₃ − S₂ is assigned values, and S₃ − S₂ = 1, S₃ − S₂ = 3, and S₃ − S₂ = 4.9 are taken, respectively. Other parameters remain unchanged. The system evolution game is shown in Figure 17 and Figure 18. (Since the traffic volume increases after logistics enterprises choose entry, the toll collected by the expressway group is higher than in the traditional distribution model. S₃ − S₂ = 0 does not mean that the preferential strength of the expressway group’s toll for logistics enterprises is 0.)

As shown in Figure 17 and Figure 18, during the system’s evolution to a stable point, an increase in the preferential strength of expressway group’s tolls for logistics enterprises can accelerate the evolution speed of logistics enterprises’ choice of entry. As S₃ − S₂ decreases, the probability of logistics enterprises choosing entry increases, and the probability of the government choosing policy support increases.

(6) The impact of changes in V_ab + V_as − V_bb − V_bs on system evolution

To analyze the impact of changes in the transportation costs of large and small vehicles before and after logistics enterprises choose entry on the results of the three-party evolutionary game, V_ab + V_as − V_bb − V_bs is assigned, and V_ab + V_as − V_bb − V_bs = 0, V_ab + V_as − V_bb − V_bs = 2, and V_ab + V_as − V_bb − V_bs = 5.9 are taken, respectively. Other parameters remain unchanged. The system evolution game is shown in Figure 19 and Figure 20.

As shown in Figure 19 and Figure 20, during the system’s evolution to a stable point, an increase in the transportation costs of large and small vehicles before and after logistics enterprises choose entry can accelerate the evolution speed of the government’s policy support but reduce the evolution speed of the expressway group’s choice of cooperation. As V_ab + V_as − V_bb − V_bs increases, the probability of the expressway group choosing cooperation decreases, and the probability of the government choosing policy support increases. Therefore, when determining the optimal location of the logistics distribution center based on the degree of transportation cost growth, the strategy choice of the expressway group should also be considered. This means finding the optimal location of the logistics distribution center while ensuring that all three parties can evolve to the ideal strategy.

(7) The impact of changes in a on system evolution under different levels of government “land-use-right” grants

To explore the differences when the government gives the expressway group the same degree of tax incentives under different levels of government “land-use-right” grants, a is assigned when K₁ = 0.5 and K₁ = 1.5, respectively, taking a = 0.85, a = 0.8, and a = 0.77, and other parameters remain unchanged. The system evolution game is shown in Figure 21 and Figure 22.

It can be seen from the figures that when the expressway group faces the same change in tax incentives, the fluctuation of the evolutionary path with a higher degree of government “land-use-right” grants is greater than that with a lower degree of government “land-use-right” grants. Therefore, when the government “land-use-right” grant is at a higher level, the government tax incentive policy for expressway groups is more effective in regulating the evolutionary results.

(8) The impact of changes in b on system evolution under different levels of government “land-use-right” grants

To explore the differences in the same degree of tax incentives given to logistics enterprises by the government under different levels of government “land-use-right” grants, b is assigned values of b = 0.85, b = 0.8, and b = 0.77 when K₁ = 0.5 and K₁ = 1.5, respectively, and other parameters remain unchanged. The system evolution game is shown in Figure 23 and Figure 24.

It can be seen from the figure that when logistics enterprises face the same changes in tax incentives, the fluctuations of the evolutionary path with a higher degree of government “land-use-right” grants are greater than those with a lower degree of government “land-use-right” grants. Therefore, when the government “land-use-right” grants are at a higher level, the government tax incentive policy for logistics enterprises is more effective in regulating the evolutionary results.

7.2.2. Policy Support, No Cooperation, Entry

(1) The impact of the change in b on the system evolution

To analyze the impact of the government’s changes in the intensity of tax incentives for logistics enterprises on the results of the three-party evolutionary game, b is assigned values of b = 0.9, b = 0.8, and b = 0.71, respectively, and other parameters remain unchanged. The system evolution game is shown in Figure 25.

As shown in Figure 25, during the system’s evolution to a stable point, an increase in the government’s tax incentives for logistics enterprises can accelerate the evolution of logistics enterprises choosing entry and expressway groups choosing no cooperation. As b decreases, the probability of logistics enterprises choosing entry and expressway groups choosing no cooperation increases.

(2) The impact of the change in V_ab + V_as − V_bb − V_bs on the system evolution

To analyze the impact of the change in the transportation cost of large and small vehicles before and after the logistics enterprises choose entry on the results of the three-party evolutionary game, V_ab + V_as − V_bb − V_bs is assigned, and V_ab + V_as − V_bb − V_bs = 0, V_ab + V_as − V_bb − V_bs = 2, and V_ab + V_as − V_bb − V_bs = 5.9 are taken, respectively. Other parameters remain unchanged. The system evolution game is shown in Figure 26.

As shown in Figure 26, during the system’s evolution to a stable point, an increase in the transportation costs of large and small vehicles before and after logistics enterprises choose entry can accelerate the evolution speed of the government’s policy support but reduce the evolution speed of the expressway group’s choice of no cooperation. As V_ab + V_as − V_bb − V_bs increases, the probability of the expressway group choosing no cooperation decreases, and the probability of the government choosing policy support increases.

According to the stability conditions of the (policy support, no cooperation, entry) strategy set, when the warehouse rent paid by logistics enterprises is greater than the “land-use-right” grants and tax incentives provided by the government when the expressway group chooses to cooperate, meaning the logistics distribution center occupies a large area and has been operational and open to traffic for 3 years, meets the reconstruction conditions, and is approved, the government can choose not to provide the expressway group with “land-use-right” grants and tax incentive policies. This will allow the system to achieve the evolutionary stability result of (policy support, no cooperation, entry).

Table 6. The impact of parameters on the choice of triadic strategies.

Parameter	The Impact on Government Strategy Choices	The Impact on Government Strategy Choices	The Impact on Government Strategy Choices
(Policy support, cooperation, entry)
$K_1$	Negative	Positive	Negative
$K_2$	Positive	Negative	Positive
$a$	Positive	Negative	Negative
$b$	Positive	Negative	Negative
$S_3-S_2$	Negative	Positive	Negative
$V_{ab}+V_{as}{-V}_{bb}{-V}_{bs}$	Positive	Negative	Negative
(Policy support, no cooperation, entry)
$b$	Positive	Negative	Negative
$V_{ab}+V_{as}{-V}_{bb}{-V}_{bs}$	Positive	Negative	Negative

below summarizes the results of the above simulation. “Positive” indicates that an increase in parameter values has a positive effect on the probability of strategies in the strategy set chosen by the three parties; “Negative” indicates that an increase in parameter values has a negative effect on the probability of strategies in the strategy set chosen by the three parties.

8. Discussion

The analysis demonstrates that the government plays a crucial regulatory role in the ELD model. By controlling “land-use-right” grants, taxation, and the costs associated with policy support, the government can effectively influence the strategic choices of all involved parties.

(1)

An increase in the government “land-use-right” grants and tax incentives will promote the expressway group to choose cooperation. This addresses the issue identified by Mr. Xu [4], who noted that the ELD model faces a lack of corresponding land policy support and incentive mechanisms during implementation;

(2)

Under the government support policy, when the expressway group chooses cooperation and logistics enterprises choose entry, the traditional ELD model is realized. For the expressway group, increased toll income from higher traffic volume and higher rental income from logistics enterprises choosing entry can boost its asset income, thereby supporting expressway operations and debt repayment [2]. However, stability analysis of the equilibrium point reveals that when the warehouse rent of logistics enterprises exceeds the “land-use-right” grants and tax incentives provided by the government for expressway group cooperation, the strategy combination (policy support, no cooperation, entry) can also achieve stability;

(3)

The analysis of equilibrium point stability conditions reveals that changes in transportation costs before and after logistics enterprises choose entry, along with the strategy selection of the expressway group, significantly impact the location of the distribution center. This finding enriches the existing research on the siting of logistics centers within expressway logistics networks [7,8,9,10].

9. Conclusions

This paper analyzes the decision-making processes of expressway groups and logistics enterprises under the government “land-use-right” grant and tax incentive policies, revealing the evolutionary mechanism of strategic choice. By modeling and simulating the behaviors of these entities under governmental regulatory policies, valuable insights into the sustainable practices of expressways were gained, and the following key findings were obtained:

(1)

The increase in the degree of government “land-use-right” grants promotes cooperation among expressway groups, enhancing their land planning flexibility and business diversity. However, when these grants reach a high level, resource crowding occurs, reducing the willingness of logistics enterprises to choose entry. Simulation results demonstrate that, compared to lower levels of “land-use-right” grants, higher levels make the government tax incentive policies significantly more effective in steering the system toward positive evolution. Therefore, the implementation of “land-use-right” grant policies must strike a balance, ensuring fair resource distribution while maximizing the impact of tax incentives on the strategic choices of both expressway groups and logistics enterprises.

(2)

Government tax incentive policies for expressway groups and logistics enterprises boost their willingness to cooperate and entry. Simulation analysis reveals that such policies have varying impacts on the strategic choices of expressway groups and logistics enterprises. In situations of fiscal constraints, it may be preferable for the government to prioritize providing more tax incentives to expressway groups.

(3)

Besides governmental regulatory policies, this study also examines the effects of rent reductions and toll fee discounts provided by expressway groups to logistics enterprises. As these incentives increase, the likelihood of government policy support also rises, thereby fostering the beneficial development of the “expressway + logistics distribution” model.

(4)

From the analysis of eigenvalues and stability, there are two stable strategy sets in the evolutionary system: (policy support, cooperation, entry) and (policy support, no cooperation, entry). According to the current government policy, for newly built service area sections, the government should strengthen the implementation of “land-use-right” grants and tax incentive policies to avoid the emergence of (policy support, no cooperation, entry) strategies. For service areas that have been operational for more than three years and meet the specified criteria, where the expressway group has applied for and received approval for reconstruction, the government can use policy adjustments to guide the selection of the (policy support, no cooperation, entry) strategy. This approach balances fiscal savings with increased asset returns for expressway groups.

(5)

Based on the stability conditions and simulation results of the (policy support, cooperation, entry) equilibrium point, logistics enterprises can make decisions regarding the location of logistics distribution centers based on changes in transportation costs before and after entry and the strategies of expressway groups.

The following limitations exist in this research. From a methodological perspective, although two stable strategy sets were identified through analysis, the limitations of evolutionary game theory preclude determining the probability of occurrence for each strategy set. At the micro-level, the study only considers the strategic choices of collaborative subjects under bounded rationality without accounting for the heterogeneity of these subjects or their interest distribution issues. At the macro level, influenced by the MASI sustainability index proposed by Mr. Yu [46], this research, while providing a feasible pathway for promoting sustainable expressway development, does not evaluate subsequent sustainability. Thus, future research directions include incorporating factors such as risk preferences and operating scales to construct network game models comprising subjects with different characteristics, studying the impact of various elements on the cooperation mechanism, designing an interest distribution system to improve the “expressway + logistics distribution” research framework, and conducting multidimensional sustainability assessments of expressways.