Fiscal centralization versus decentralization of transport infrastructure operation and maintenance

Abstract

The issue of fiscal decentralization and centralization of China’s transport sector has been controversial in the past. Based on vertical fiscal relations and horizontal competitive relations, this paper constructs a stochastic evolutionary game model to examine the behavioral strategies and interactions among the central and two local governments for transport infrastructure operation and maintenance (TIOM). Using the Chinese case study, this paper simulates the strategy evolution trajectories of the governments and their sensitivities to key determinants in various scenarios. The model analysis indicates that when the central government implements a centralized system, the two local governments cannot be simultaneously motivated to improve TIOM; however, when the central government adopts a decentralized approach, the two local governments can be simultaneously motivated under certain conditions. Case simulations based on the latter scenario reveal that increased regulatory costs, opportunity costs, and transfers lead the central government to choose a decentralized system. Additionally, greater benefits, reduced costs, improved transfers and penalties, intensified competition, and significant spillover effects can incentivize local governments to improve TIOM. These findings contribute to a better understanding of the evolutionary process and dynamics of the central-local fiscal relations in the transport sector.

Introduction

Since China’s economic reform, the principal contradiction in the transport sector has evolved from a mismatch between supply and demand for infrastructure to an incompatibility between service capabilities and the people’s ever-growing needs for better travel and logistics (MTPRC, 2016). The immediate cause is that the pace at which the operational efficiency and service quality is being improved lags far behind that of the increase in transport infrastructure stock (Jia et al., 2022). In fact, the cumulative level of China’s transport infrastructure has been gradually approaching the optimal demands of current economic growth, and then additional investments may only generate insignificant marginal revenues (Shi et al., 2016). At this stage, the transport sector should allocate more resources to improve the support systems of transport infrastructure operation and maintenance (TIOM) (CSC, 2022). However, Chinese politicians are more inclined to build large-scale transport infrastructure to bolster economic growth and accomplish political achievements. That is, they are less interested in TIOM than in construction investments (Robinson and Stiedl, 2001; Lei and Zhou, 2022). By the end of 2020, the outstanding loans for toll roads borne by local governments totaled 7066.12 billion yuan, and the revenue gap expanded to 747.82 billion yuan (MTPRC, 2021). It is expected that, in the short-term, local governments will prioritize the payment of debts incurred during the construction phase instead of increasing investments in TIOM.

The strong coupling of political centralization and fiscal decentralization (Lv and Landry, 2014) provides a potential explanation for the construction-oriented policy-making preferences of local governments. In China, economic development has long been central to national strategy. It serves as the primary driver of modernization and a key metric for evaluating local officials’ performance, embedded within their promotion incentive mechanisms. Consequently, local governments are endowed with the administrative discretion to take responsibility for economic growth and public service delivery within their jurisdictions (Jin et al., 2005; Giuliano, 2007; Lei and Zhou, 2022; Li et al., 2022; Yuan and Wang, 2023; Mai et al., 2025). Political achievement assessments based on economic growth give local governments an inherent demand to maximize local interests (Yusuf et al., 2011; Pu et al., 2022). They are often banking on massive investments in transport infrastructure to attract large inflows of labor and capital. To avoid the export of productive factors to neighboring jurisdictions, local governments may be trapped in a vortex of hyper-competition in transport infrastructure investment (Borger and Proost, 2012; Kis-Katos and Sjahrir, 2017; Han et al., 2021; Zhang et al., 2025). In contrast, due to shorter tenures, they lack the incentive to improve traffic service and operation efficiency, which requires substantial investments in the long-term (Lei and Zhou, 2022). Specialized transfer payments deployed by the central government can help local governments balance the trade-offs between construction investment and TIOM. However, information superiority and promotion incentives can stimulate local politicians to lobby or bribe their superiors, thus weakening the coordinating function of transfers. (Kappeler et al., 2013; Lei, 2023). As a principal constrained by information asymmetry, bounded rationality, and economic development goals, the central government lacks sufficient motivation and ability to change the policy-making preferences of local governments (Borger and Proost, 2012; Carlucc et al., 2017; Hammes and Mandell, 2019).

Based on the above analysis, both practical evidence and theoretical support suggest that Chinese-style fiscal decentralization seems to promote excessive investment in transport infrastructure rather than improving the efficiency of TIOM. This finding triggers a rethinking of China’s fiscal system and raises an important policy question: what are the optimal fiscal relations between the central and local governments to improve the efficiency of TIOM? In other words, under what circumstances can fiscal centralization (or decentralization) increase government incentives for TIOM?

The optimal government level that should be responsible for investment decisions of transport infrastructures has been debated for many years. Prevailing theories advocate that well-designed fiscal decentralization can increase investment efficiency, as local governments are better informed about the transport needs of residents (Chen et al., 2023; Mohanty et al., 2024). However, the impact of fiscal decentralization on TIOM has only been discussed in a few studies. They recommend that TIOM-related functions, such as amelioration and renewal, tax collection and pricing, fire and rescue, policing and law enforcement, publicity and education, asset management, and pollution control, should be decentralized to the local level (Borger and Proost, 2016). Using US state-level data, Escaleras and Calcagno (2018) find that fiscal decentralization increases investment in improving the quality of existing highway infrastructure. In contrast, Castillo-Manzano et al. (2022) indicate that local traffic police management might be less effective than central traffic police governance for road safety in Spain. These studies provide contradictory empirical evidence for the impact of fiscal decentralization on TIOM. In the Chinese-style decentralized system, local governments have limited fiscal autonomy, with central finance dominating. As a developing country, China’s current priority remains economic development. Policymakers must decide between improving TIOM and constructing new transport infrastructure, and determine which government level should be responsible for TIOM (Escaleras and Calcagno, 2018). This issue motivates us to explore the impact of fiscal centralization or decentralization on improving TIOM and establish suitable coordination rules in the Chinese context.

To address the research question, a stochastic evolutionary game model is employed to portray the dynamic interaction process in which the central and local governments attempt to establish optimal fiscal relations for TIOM by continuously imitating, learning, and adjusting their strategies. Within the TIOM framework, the central-local fiscal relationship is inherently evolutionary (Jiang et al., 2024). Government players are boundedly rational: their strategic choices are shaped by limited information, local interests and incentives for political promotion, and are revised over time in response to experience and feedback (Zhang et al., 2023). At the same time, policy shifts, economic fluctuations, natural disasters and other shocks in the broader environment introduce stochastic disturbances into the decision-making process (Jiang et al., 2024). Traditional static or deterministic game models struggle to represent the dynamic processes of intergovernmental interaction (Su and Stewart, 2025; Wang et al., 2024). The stochastic evolutionary game model, by integrating evolutionary dynamics with random perturbations, provides a more suitable framework for modeling how boundedly rational actors adapt their strategies and how systems evolve under uncertainty. Its key advantages include: (1) the use of replicator dynamics to describe how the distribution of strategies adjusts in response to changing payoffs (Su and Stewart, 2025), which aligns more closely with the gradual learning and convergence patterns observed in governmental behaviors; and (2) the incorporation of stochastic noise to capture unpredictable policy shocks and external risks, thereby enhancing the model’s explanatory power regarding real-world uncertainty (Shan et al., 2023; Yi et al., 2024). For these reasons, this study employs a stochastic evolutionary game model not only for its methodological suitability but also for its ability to provide a more compelling analytical tool for understanding the evolving logic of central-local fiscal relations within the TIOM framework. Using the Chinese case, the process of intergovernmental interaction is simulated and related policy recommendations are presented. The contributions are as follows:

• (1) Existing literature about the impact of fiscal decentralization (or centralization) on transport infrastructure investment has overlooked TIOM. Especially for developing economies like China, the local fiscal autonomy is authorized and regulated by the central government. It is necessary to harmonize the central-local interests for transitioning from stock increase to TIOM improvement (Escaleras and Calcagno, 2018). As a result, the central-local game analysis based on the Chinese case can enrich fiscal decentralization knowledge in the field of TIOM.

• (2) Economic growth assessments and transport infrastructure spillovers encourage local governments to compete for productive factors. Over-competition may weaken the benefits of decentralization, such as efficiency gains and regional equalization (Borger and Proost, 2012). Thus, both vertical fiscal relations and horizontal competitive relations affect the efficiency of TIOM, which has not been discussed within the same theoretical framework. This paper establishes a broader theoretical link between the two-dimensional relations and develops a composite game structure involving the center and two local governments. It helps to explain the impact of fiscal decentralization (or centralization) on TIOM from a multidimensional perspective (Zhang et al., 2025).

• (3) Escaleras and Calcagno (2018) and Castillo-Manzano et al. (2022) provide evidence for the impact of fiscal decentralization on TIOM using a static approach, but fiscal relations are determined by the government through dynamic policy adjustments, which co-evolve with the economic market (Chen et al., 2023). In addition, many studies use regression models to calculate the direct effect of fiscal relations on TIOM, which may be uncertain due to various factors, such as benefits, penalties, competition, and random perturbations. Compared to traditional static game models and regression methods focused on static causal identification, the stochastic evolutionary game model demonstrates distinct advantages. It captures the dynamic learning and strategy adaptation processes of boundedly rational agents (Ahmad et al., 2023) and incorporates stochastic perturbations to simulate real-world uncertainties (Li et al., 2023; Yi et al., 2024). Consequently, this study employs a stochastic evolutionary game model to simulate the imitation, learning, and strategic adjustments undertaken by central and local governments in pursuing optimal fiscal arrangements. The model explicitly accounts for the bounded rationality, information asymmetries, and behavioral heterogeneity among local governments in practice (Jiang et al., 2024), yielding richer and more applicable insights.

This paper is structured as follows. Section “Literature review” discusses the related literature. Section “Modeling and analysis” constructs a stochastic evolutionary game model and derives the equalization strategies and their constraints for the governments. Section “Numerical analyses of determinants” simulates the mechanisms by which various factors affect the equilibrium strategies using the Chinese case. Section “Conclusions and implications” contains the findings and policy suggestions.

Literature review

Fiscal decentralization

In the decentralized system, local governments, as incompletely independent stakeholders and policy-makers, are granted fiscal discretion by the central government to invest in transport infrastructure (Oates, 1972; Kappeler et al., 2013; Hörcher et al., 2023). The primary benefit lies in the diversified transport services customized by local governments to match the preferences of their citizens (Kis-Katos and Sjahrir, 2017; Bucci et al., 2023; Mohanty et al., 2024; Amougou et al., 2025; Mai et al., 2025). In most cases, more complex preferences of citizens for transport services imply higher social welfare and economic performance arising from decentralization, as shown in Table 1. However, decentralization is not always efficient for transport services and may bring about many problems, such as weaker macro-control, diluted technical capability, ineffective tax competition, and local debt distress (Robinson and Stiedl, 2001; Zegras et al., 2013; Bucci et al., 2023; Amougou et al., 2025). At this point, the policy performance of local governments will deviate from the objective function of the central government (Hammes and Mandell, 2019; Chen et al., 2023), forming the principal-agent problem of “top-down policies and bottom-up countermeasures” (Zhang et al., 2023).

Table 1 Effects of fiscal decentralization.

The central government usually designs the following rules to handle principal-agent problems. First, accountability. Effective accountability ensures that local governments are accountable to their citizens and that the central government is responsible for local politicians (Kis-Katos and Sjahrir, 2017). The key to accountability is consensus on the allocation of risks and responsibilities through strong leadership and asymmetrical political power (Giuliano, 2007). Second, secondary distribution. The central government generally adopts transfers and subsidies to balance the transport infrastructure supply in scale and quality between regions. The core objective of secondary distribution is to ensure that all regions, especially those that are economically underdeveloped or geographically inaccessible, also enjoy relatively balanced transport services (Borger and Proost, 2012; Kappeler et al., 2013; Leon-Moreta et al., 2025). Third, political promotion. Lei and Zhou (2022) demonstrate that local politicians can maximize short-term political profits from large-scale infrastructure investments in China’s top-down political hierarchy. The GDP-oriented achievement assessment reinforces inter-regional competition (Yuan and Wang, 2023), which motivates local politicians to invest in transport infrastructure at or above the objective function of the central government (Kappeler et al., 2013).

In these discourses of fiscal decentralization, empowerment and rules are the core concepts. Empowerment refers to the devolution of policy-making and implementation powers from the central to local governments, with rules ensuring effective implementation and preventing power abuses (Levitas, 2017). These concepts explain the success of most transport infrastructure investments. However, little is known about whether decentralization contributes to improving TIOM. Especially in a developing economy like China, where decentralization may fail for TIOM due to the lack of effective rules. In addition, with limited resources, policymakers must decide whether to invest in improving TIOM. Therefore, it is worth exploring whether decentralization is optimal for developing economies to enhance TIOM and how to formulate compatible rules (Chen et al., 2023).

While most studies support fiscal decentralization’s positive impact on transport infrastructure investment (Table 1), its effects on TIOM vary across contexts. For instance, Escaleras and Calcagno (2018) found improved highway maintenance under US state-level decentralization, whereas Castillo-Manzano et al. (2022) observed lower local traffic enforcement efficiency compared to central governance in Spain. Bucci et al. (2023) confirmed local governments’ positive role in enhancing road conditions, a finding echoed by Amougou et al. (2025) regarding urban public infrastructure operational spending in Cameroon. This contradiction may stem from variations in local governance capacity: decentralization enhances local efficiency and need-matching where local capacity is strong (Kappeler et al., 2013), but can fragment oversight and reduce TIOM effectiveness when local fiscal autonomy is constrained and monitoring is weak (Borger and Proost, 2012; Amougou et al., 2025; Mehr-Un-Nisa et al., 2025). It may also arise from phased goal conflicts: decentralization often benefits construction phases, while its impact on TIOM—demanding sustained investment and inter-regional coordination—remains uncertain. Furthermore, decentralization’s efficiency critically depends on supporting institutional design, essential for ensuring implementation and preventing power misuse (Robinson and Stiedl, 2001; Digdowiseiso, 2023). Consequently, fiscal decentralization constitutes a complex phenomenon driven by multiple forces (Delgado and Landajo, 2025), whose suitability for TIOM requires reassessment based on national governance institutions, local government capacity, and infrastructure lifecycle stage.

Inter-governmental competition

Transport infrastructure forms a complex network where individual nodes or links add connective or access value to others—the spillover effect of transport infrastructure (Giuliano, 2007). Spillover effect can be either beneficial (e.g., lower traffic costs, higher labor productivity) or detrimental (e.g., diffuse air pollution, increased traffic congestion) (Badura et al., 2023). It depends on the scale and quality of transport infrastructure and the resource endowment in the regions (Borger and Proost, 2012; Li et al., 2022). Spillovers emerge as productive factors move between regions by means of transport infrastructure. If the transport infrastructure in one region becomes more attractive for capital and labor, it will “steal” or absorb businesses from neighboring regions (Feder, 2018). Local governments can attract more resources from other regions by investing massively in transport infrastructure to enhance spillovers (Zegras et al., 2013; Badura et al., 2023). However, fiscal decentralization can lead to excessive competition, which may produce transport infrastructure beyond the optimal scale and additional agency costs (Leon-Moreta et al., 2025; Mehr-Un-Nisa et al., 2025; Zhang et al., 2025).

The macro-control capacity of the central government is viewed as a good solution to the vertically undesired agency behavior and the horizontally excessive competition (Taylor and Schweitzer, 2005; Borger and Proost, 2012). In a centralized system, the central government can uniformly plan, allocate and use fiscal resources to foster regional equalization of transport infrastructure (Hörcher et al., 2023). However, local governments may adopt free-rider strategies in a centralized system when higher levels of transport infrastructure are provided in neighboring regions (Kim et al., 2024). Thus, there are some trigger conditions for maximizing the benefits of centralization due to the spillovers of transport infrastructure. Where spillovers are negative, decentralization increases citizens’ welfare and economic performance in the case of competitive local policies, whereas, if there are positive spillovers between regions, centralization increases welfare and economic performance with complementary local policies (Borger and Proost, 2016; Carlucci et al., 2017). That is, centralization should compensate for inefficiencies generated by limitations in spillovers and/or economies of scale; otherwise, a decentralized system should be established (Kappeler et al., 2013; Feder, 2018).

A basic consensus emerges from these discourses: in decentralized systems, spillover effects from transport infrastructure led to intergovernmental competition. However, existing studies have neglected to explore the impact of intergovernmental competition on TIOM. During the construction phase, competition under decentralization often drives local governments to overinvest in infrastructure projects and widen regional development disparities (Han et al., 2021). For TIOM, however, the competitive logic fundamentally shifts. Where local governments possess fiscal autonomy and the public is sensitive to service quality, competition may evolve into a “race to the top” (Badura et al., 2023; Cao et al., 2025). In developing regions with stringent fiscal constraints, local governments might prioritize new projects over TIOM due to pressures for short-term achievements, leading to a “race to the bottom” (Pu et al., 2022; Kim et al., 2024; Zhang et al., 2025). This divergence likely relates to the spillover effects of TIOM. Central coordination or compensation becomes more effective when TIOM enhances neighboring economic efficiency, but local governments underinvest because they cannot internalize benefits (Castillo-Manzano et al., 2022). Decentralization proves more efficient when poor TIOM generates cross-jurisdictional costs like congestion and accidents, as competition incentivizes stricter oversight to avoid “not-in-my-backyard” effects (Bucci et al., 2023; Amougou et al., 2025). Furthermore, governance institutions critically shape competitive outcomes. Effective accountability and incentive mechanisms can curb opportunistic behavior among local officials, channeling competition toward service quality improvements (Kappeler et al., 2013; Badura et al., 2023). Where institutions are weak, however, local governments tend to adopt myopic strategies, engaging in detrimental competition at the expense of service quality (Pu et al., 2022). Moreover, the role of government also shifts from policymaker and financier to regulator of transport services. In this case, do spillover effects still lead to intergovernmental competition for TIOM, and does it promote improvements in TIOM? This paper develops a game model that embeds horizontal competition in vertical fiscal relations to explore the impact of fiscal decentralization and TIOM and its coordination rules from a multidimensional perspective (Zhang et al., 2025).

Evolutionary game theory

Many studies develop game-theoretical models to analyze the interaction process between central and local governments within various fiscal systems. For example, focusing on target setting and performance-led rewards, Sen et al. (2013) analyze the challenges faced by the transport sector in coordinating policies between different levels of government in conjunction with the full control centralization model, the Nash equilibrium model, and the Stackelberg equilibrium model. Hammes and Mandell (2019) integrate fiscal federalism and the lobbying for influence model to examine how lobbying affects the investment of the central government in transport infrastructure when local governments voluntarily co-finance. Han et al., (2021) developed a simultaneous and sequential game model comprising the central government and two competing local governments to examine the impact of tax and infrastructure competition on regional development disparities. Game-theoretical models use mathematical symbols and formulas to depict the payoff functions and behavioral interactions of the governments. These models can predict the interactive outcomes of policies or behaviors implemented by governments and provide references for policy-making through mathematical models and computer simulations. However, traditional models are hypothetically deterministic and static systems where players are perfectly rational, and information is completely symmetric (Feng et al., 2020; Yuan and Wang, 2023). These assumptions contradict the reality that players are unlikely to be perfectly rational and will inevitably make mistakes (Feng et al., 2020), and that multi-party games are inherently dynamic and susceptible to disruptions, such as natural disasters and policy adjustments (Ahmad et al., 2023; Shan et al., 2023; Yi et al., 2024).

To overcome these limitations, a stochastic evolutionary game model is proposed to simulate the strategic interactions between the governments (Shan et al., 2023; Jiang et al., 2024). Evolutionary game theory is a theoretical tool that integrates game theory with evolutionary biology. It assumes that players achieve game equilibrium through trial and error, rather than that players are perfectly rational and have complete information (Smith, 1976). The core principles are: (1) players adopt different strategies to interact with each other and adjust their strategies according to received payoffs; (2) the percentage of players adopting high-yield strategies increases as the game continues, while the percentage of the low-yield strategies gradually decreases; and (3) the game system evolves towards one or more evolutionary stable strategies (ESS) with higher payoffs and adaptability (Nowak and Sigmund, 2004; Roca et al., 2009). Evolutionary game theory involves two key concepts: ESS (Smith and Price, 1973) and replicator dynamics (Taylor and Jonker, 1978). ESS is a stable strategy that can be maintained in the long time by natural selection. Players adopting ESS can achieve higher payoffs or survival rates, and are able to resist the intrusion of minor mutation strategy (Xiao and Yu, 2006). Replicator dynamics is a mathematical model used to describe how the probability of different strategies changes over time. In the process of change, high-yield strategies will be imitated and adopted by more players, while low-yield strategies will be eliminated (Friedman, 1998). ESS characterizes the stable state of the game system, and replicator dynamics portrays the convergence process oriented to this state (Roca et al., 2009). Therefore, compared with traditional game theory, the advantages of evolutionary game theory are: (1) bounded rationality is more consistent with the behavioral characteristics of players in reality; (2) the stable state of game system depends on the initial state and historical events; and (3) ESS can explain why some strategies remain stable over time in the game system (Ahmad et al., 2023; Yuan and Wang, 2023; Qiu et al., 2025).

Evolutionary game theory fits well with the research problem of this paper. Firstly, the allocation and utilization efficiency of fiscal resources are the focus of the central-local evolutionary game. TIOM requires substantial investment beyond the capacity of local governments. However, it is also difficult for the central government to completely meet local demands for funding as it is responsible for balancing inter-regional public services. Secondly, the central-local fiscal relations are dynamic (Jiang et al., 2024). In China, fiscal relations have gone through four stages: unified revenue collection and spending, the fiscal contracting system, the separating tax system, and modernized fiscal reform (Jin et al., 2005). Finally, governments are constrained by incomplete information and limited capacity. A government cannot fully grasp key information about the financial status, funding needs, and policy intentions of others, and may not be able to accurately assess the effectiveness of various strategies (Zhang et al., 2023). Furthermore, both vertical fiscal and horizontal competitive relations are disturbed by random factors, such as social risks, policy shifts, and economic crises (Jiang et al., 2024). Therefore, this paper integrates a stochastic process into the evolutionary game theory to analyze the dynamic interaction and its influencing factors between the central and local governments for TIOM under fiscal decentralization. Its core advantages lie in: (1) quantifying the immediate and persistent impacts of uncertainty on governmental decision-making; (2) examining the robustness of ESS to assess policy resilience; (3) capturing the stochastic fluctuations and path dependence inherent in strategic evolution; and (4) measuring how disturbance intensity influences convergence speed and cooperation difficulty (Shan et al., 2023; Yi et al., 2024). Overall, the stochastic evolutionary game model offers a more realistic representation of the complex dynamics and their implications in the strategic interactions between central and local governments over TIOM within China’s fiscal decentralization framework (Jiang et al., 2024), yielding more resilient and actionable insights.

Modeling and analysis

Problem description

The policy focus of the transport sector in China is shifting from large-scale infrastructure construction to more elaborate and efficient operation and maintenance. It is a new challenge for the allocation and utilization of intergovernmental financial resources, which requires a better fiscal system to improve TIOM (Escaleras and Calcagno, 2018). To address this challenge, the State Council of China issued the “Reform plan for the division of fiscal powers and expenditure responsibilities between the central government and local governments in the transport sector”, which specifies that the construction, maintenance, management, and operation of highways, waterways, and railroads are to be undertaken by local governments. Within the framework of this reform program, local governments are authorized by the central government to accomplish TIOM activities within their jurisdictions. However, the objectives of governments are inconsistent. The central government aims to increase the overall well-being of the society and ensure the stable functioning of the national economy. Local governments decide on the allocation of funds according to the driving effect of TIOM on local economic growth. Therefore, the central government should regulate the behavior of local governments to avoid principal-agent problems. In this process, the central government, as an information inferior, bears higher agency costs. Horizontally, spillovers from transport infrastructure mean that local governments may compete with each other for productive factors and tax revenues. Competition can enhance TIOM, but it can also lead to resource mismatch and short-term behavior. In summary, the intertwining of vertical fiscal relations and horizontal competitive relations constitutes the basic logic of interactions between governments (Zhang et al., 2025). Based on the above analysis, the strategic interaction between the central and local government A (local government B) is plotted as shown in Fig. 1.

Fig. 1

Strategic interaction between the central and local governments.

Assumptions

This paper simplifies some complex conditions and makes the following assumptions without essentially altering the above strategic interactions.

Assumption 1

The game model involves the central government, local government A, and local government B, all of which are politicians with bounded rationality, some ability to learn, and autonomy. The central government pursues the global maximization of social welfare and transport services, but local governments maximize local interests (Ahmad et al., 2023; Yuan and Wang, 2023; Zhang et al., 2023; Zhang et al., 2025).

Assumption 2

The strategic choice for the central government is whether to employ a decentralized system. The strategy set is {centralization, decentralization}, denoted by $x\in \left[\mathrm{0,1}\right]$ and $1-x$, respectively. Local governments can choose to either positively or negatively operate and maintain the transport infrastructure. The strategy set of local governments is {positive operation, negative operation}. The proportion of local government A and B choosing the positive strategy is $y\in \left[\mathrm{0,1}\right]$ and $z\in \left[\mathrm{0,1}\right]$, and that choosing the negative strategy is expressed as $1-y$ and $1-z$. A positive strategy entails that local governments adopt forward-looking approaches to the high-quality maintenance and management of transport infrastructure. A negative strategy means that local governments adopt remedial measures to address and resolve issues after they have emerged. In the case of bridge management, local governments adopting a positive strategy will formulate long-term plans and utilize advanced detection technologies (e.g., drone patrols, infrared imaging systems) to inspect and repair bridges. This forward-looking approach ensures that potential hazards are identified and addressed swiftly. Local governments that adopt a negative strategy often neglect routine monitoring and maintenance on bridges, and are forced to make repairs only after obvious quality problems (e.g., cracks in the road surface, potholes in the asphalt, broken guardrails) have occurred. This reactive approach potentially reduces the traffic capacity of bridges, triggers traffic congestion, and increases safety incidents.

Assumption 3

The principal-agent relationship reflects the intrinsic power structure in China’s top-down political hierarchy, where the central government endows the local governments with discretion in regard to improving TIOM (Lei and Zhou, 2022; Li et al., 2022; Yuan and Wang, 2023). However, local officials motivated by GDP-driven performance incentives tend to prioritize allocating resources to new projects over TIOM. This misalignment creates a classic principal-agent problem, where the principal (central government) bears high monitoring costs to curb local agents’ opportunism. Given principal-agent problems, if the central government chooses centralization, it will strictly regulate the policy implementation of local governments, pay higher costs (expressed as ${C}_{1}$) to obtain required information, and constrain the local government through higher transfers and penalties. This paper assumes that the transfers to local governments A and B are ${T}_{{rA}}$ and ${T}_{{rB}}$, the fines to local governments are ${F}_{A}$ and ${F}_{B}$, respectively. Conversely, if a decentralized strategy is adopted, the central government enforces more lenient regulations and pays lower information costs, and imposes lower incentives and penalties. In this case, the information cost to the central government is ${\theta C}_{1}$, the transfers to local governments are ${\alpha T}_{{rA}}$ and ${\beta T}_{{rB}}$, the fines are ${\gamma F}_{A}$ and $\delta {F}_{B}$, respectively. Compared with the centralized strategy, $\theta \in \left[\mathrm{0,1}\right]$, $\alpha \in \left[\mathrm{0,1}\right]$ and $\beta \in \left[\mathrm{0,1}\right]$, $\gamma \in \left[\mathrm{0,1}\right]$ and $\delta \in \left[\mathrm{0,1}\right]$ indicates that the central government’s regulatory efforts, subsidies, and penalties to local governments are reduced.

Assumption 4

Local governments are responsible for executing the specific tasks of TIOM, and undertake the corresponding expenditure responsibilities according to central government policies. Funding from non-central governments for expenditures constitutes direct costs for local governments, and the magnitude of the direct costs is related to the efforts made by local governments to improve traffic services. Drawing on Xie et al. (2021), Cheng et al. (2023), and Wang et al. (2024), this study models local governments’ direct costs as a quadratic function of their effort level, which captures the economic principle of increasing marginal costs (Taylor, 2002). This paper assumes that the effort levels of local governments A and B are ${E}_{A}$ and ${E}_{B}$, the effort coefficients are ${\mu }_{A}$ and ${\mu }_{B}$, and the direct costs are ${C}_{2A}={\mu }_{A}{E}_{A}^{2}/2$ and ${C}_{2A}={\mu }_{B}{E}_{B}^{2}/2$. When a local government chooses a positive strategy, ${\mu }_{A}=1$(or ${\mu }_{B}=1$) indicates that the effort level is the highest and will incur higher direct costs; when a local government adopts a negative strategy, ${\mu }_{A} < 1$ (or ${\mu }_{B} < 1$) indicates that the effort level is lower and will incur lower direct costs. In China, local officials motivated by performance-driven incentives prefer new projects that rapidly boost GDP, resulting in relatively low investments in TIOM (Lei and Zhou, 2022). In pursuing more efficient or intelligent TIOM, local governments must address long-term accumulated funding gaps, which leads to a rapid increase in marginal costs. Moreover, China’s vast and complex transport network entails operational complexity and nonlinearly rising costs. The effort coefficient further captures heterogeneity in fiscal capacity and technical proficiency across jurisdictions. For instance, underdeveloped regions often incur higher expenditures to achieve comparable maintenance outcomes as developed areas due to technological backwardness and inefficient supply chains. Such specifications enable the game model to more accurately reflect actual decision-making behaviors under budgetary constraints.

Assumption 5

Local politicians in a system of political centralization are incentivized by both economic growth and promotions. Typically, local politicians are more motivated to expand the scale of transport infrastructure or other public services (e.g., education, health care), as opposed to improving TIOM (Robinson and Stiedl, 2001; Lei and Zhou, 2022). If local governments allocate limited resources to TIOM, they must forgo investments in new projects, which may prevent them from capturing short-term economic growth opportunities and thereby jeopardize officials’ promotion prospects. Local governments incur opportunity costs when “positive operation” is selected; otherwise, there are no opportunity costs. Likewise, the central government must decide whether to increase investment in TIOM. Centralization entails more expenditure responsibilities for the central government, incurring opportunity costs, while decentralization shifts these to local governments, avoiding such costs. This paper assumes that the opportunity costs of the central government, local governments A and B are ${C}_{3}$, ${C}_{3A}$, and ${C}_{3B}$. This assumption enhances the model’s practical relevance while highlighting that reducing opportunity costs is essential to incentivize governments to adopt high-quality O&M strategies.

Assumption 6

There are significant spillovers from TIOM (Zegras et al., 2013; Feder, 2018;), and the global benefits generated by local governments choosing “positive operation” consist of both local and external benefits. The central government enjoys global benefits, while local governments aim for local benefits. Suppose that the global benefits of choosing “positive operation” for local government A and B are ${R}_{A}$ and ${R}_{B}$, then the local benefits are $\sigma {R}_{A}$ and $\tau {R}_{B}$, the external benefits are $\left(1-\sigma \right){R}_{A}$ and $\left(1-\tau \right){R}_{B}$, the external benefits captured by local government B and A are $\varphi \left(1-\sigma \right){R}_{A}$ and $\omega \left(1-\tau \right){R}_{B}$, and the benefits for the central government are ${R}_{A}+{R}_{B}$. Notably, when the local government A and B adopt “negative operation”, it generates lower global benefits, as ${\varepsilon R}_{A}$ and ${\nu R}_{B}$. $\sigma \in \left[\mathrm{0,1}\right]$ and $\tau \in \left[\mathrm{0,1}\right]$ represents the local share of global benefits, $\varphi \in \left[\mathrm{0,1}\right]$ and $\omega \in \left[\mathrm{0,1}\right]$ indicates the impact of TIOM on neighboring areas, and $\varepsilon \in \left[\mathrm{0,1}\right]$ and $\nu \in \left[\mathrm{0,1}\right]$ signifies that a negative strategy yields lower global benefits for local governments than a positive strategy.

Under China’s politically centralized and fiscally decentralized system, local governments exhibit stronger incentives to invest in new projects that directly stimulate local economic growth and tax revenue (Han et al., 2021; Zhang et al., 2025). However, TIOM generates both localized benefits and transboundary spillovers that cannot be fully internalized (Yu et al., 2013; Badura et al., 2023), which explains their underinvestment or opportunistic competition in TIOM. Notably, regional development disparities in China create asymmetric interdependencies: while developed regions enhance TIOM to attract resource inflows from underdeveloped areas and indirectly benefit them through reduced logistics costs, constrained investments by lagging jurisdictions may produce inefficient TIOM that imposes negative externalities on adjacent regions (Wang et al., 2022). Such asymmetric dependencies constitute critical considerations for analyzing fiscal relationships in TIOM under the Chinese context. Furthermore, China’s evolving official performance evaluation systems increasingly emphasize comprehensive indicators such as green GDP, public welfare, and ecological sustainability. Given that social stability and environmental quality represent prerequisites for long-term sustainable development, rational local governments must incorporate socio-environmental factors into their decision-making calculus. Consequently, the perceived “benefits” guiding local government decisions manifest as multidimensional constructs integrating environmental, social, and economic considerations rather than short-term economic gains alone.

Assumption 7

According to the principle of “voting with their feet”, high-quality transport services is likely to attract more investors and labor, which is the primary motivation for local governments to positively operate and maintain transport infrastructure; otherwise, local governments will suffer from shifting industries, the loss of labor, and reduced tax revenues (Borger and Proost, 2012; Yu et al., 2013; Feder, 2018; Li et al., 2022; Kim et al., 2024). When different strategies are implemented, the local government that chooses “negative operation” suffers some losses because of the output of capital and labor, and the local government that adopts “positive operation” gains additional benefits due to the import of capital and labor. If the same strategy is implemented, capital and labor will not transfer between jurisdictions. This paper assumes local governments A and B lose ${Q}_{A}$ and ${Q}_{B}$ with a negative strategy, while local governments B and A can gain $a{Q}_{A}$ and $b{Q}_{B}$ with a positive strategy. $a\in \left[\mathrm{0,1}\right]$ and $b\in \left[\mathrm{0,1}\right]$ indicates only partial capture of lost capital and labor from neighboring jurisdictions.

Assumption 8

Inter-jurisdictional heterogeneity in preferences, revenues, and resources plays an important role in the diligence and profitability of local governments, as well as the rewards and penalties imposed by the central government (Carlucci et al., 2017; Li et al., 2022). To reflect inter-jurisdictional heterogeneity, suppose that local government A with relatively competitive advantages and a well-constructed transport network prefers to improve the service quality and operation efficiency of transport infrastructure, while local government B in an underdeveloped context lacks the resources and motivation to improve TIOM. On this basis, the central government provides more fiscal support to local government B and leniently penalizes its opportunistic behavior, aiming to achieve the regional equalization. Then, the evolutionary game should also meet the following requirements: ${F}_{A} > {F}_{B}$, ${T}_{{rA}} < {T}_{{rB}}$, ${R}_{A} > {R}_{B}$, ${C}_{3A} < {C}_{3B}$, ${E}_{A} > {E}_{B}$, ${Q}_{A} > {Q}_{B}$.

The variables and parameters of this game are described in Table 2.

Table 2 Variable and parameter symbol descriptions.

Based on the above assumptions, the expected payoffs of each government under different combined strategies are represented by equations. When the central government chooses a centralized strategy, local government A opts for a positive strategy, while local government B adopts a negative strategy, the benefits to the central government include global benefits (${R}_{A}{+\nu R}_{B}$) and penalties (${F}_{B}$) to local government B, and the costs to the central government include information and opportunity costs (${C}_{1}+{C}_{3}$) and transfers (${T}_{{rA}}$) to local government A; the benefits enjoyed by local government A include local benefits ($\sigma {R}_{A}$), spillovers (${\omega \left(1-\tau \right)\nu R}_{B}$) and resource outflows ($b{Q}_{B}$) from local government B, and transfers (${T}_{{rA}}$) from the central government, and the costs faced by local government A include direct costs (${E}_{A}^{2}/2$) and opportunity costs (${C}_{3A}$); the benefits of local government B include local benefits ($\tau {\nu R}_{B}$) and spillovers (${\varphi \left(1-\sigma \right)R}_{A}$) from local government A, and the costs of local government B include direct costs (${\mu }_{B}{E}_{B}^{2}/2$), resource outflows (${Q}_{B}$), and penalties (${F}_{B}$) from the central government. The payoff functions for other portfolio strategies are similar. Thus, the payment matrix is established, as shown in Table 3.

Table 3 Payoff matrix of three governments.

Deterministic evolutionary game model

Replicator dynamic equations

The replicator dynamic equation is a mathematical model used to describe the changes of strategy probabilities over time, with natural selection and imitative behavior as fundamental mechanisms. Natural selection mechanism dictates that individuals with higher environmental adaptations (i.e., strategies with higher payoffs) are more likely to survive and reproduce. Imitative behavior mechanism refers to the tendency of players to imitate better performing individuals, that is, to adopt strategies with higher payoffs (Taylor and Jonker, 1978; Friedman, 1998). These two mechanisms account for the changes in strategy probabilities: if the payoff of a strategy exceeds the average payoff, its adoption probability will increase, i.e., the rate of change in the probability of adopting that strategy will be greater than the instantaneous value of the equation at that moment; and conversely, its adoption probability will decrease, i.e., the rate of change in the probability of adopting that strategy will be less than the instantaneous value of the equation at that moment (Nowak and Sigmund, 2004; Roca et al., 2009). This paper develops replicator dynamic equations for the central and local governments to explore interactive patterns in TIOM.

① The central government’s replicator dynamic equation

Supposing that the expected payoffs of the central government choosing “centralization” and “decentralization” are ${U}_{11}$ and ${U}_{12}$, and that the average expected utility becomes ${\bar{U}}_{1}$, then:

$$\begin{array}{c}{U}_{11}={yz}\left[{R}_{A}{+R}_{B}-{C}_{1}-{C}_{3}-\left({T}_{{rA}}+{T}_{{rB}}\right)\right]\\ +y\left(1-z\right)\left[{R}_{A}{+\nu R}_{B}-{C}_{1}-{C}_{3}-{T}_{{rA}}+{F}_{B}\right]\\ \begin{array}{c}+\left(1-y\right)z\left[{\varepsilon R}_{A}{+R}_{B}-{C}_{1}-{C}_{3}-{T}_{{rB}}+{F}_{A}\right]\\ +\left(1-y\right)\left(1-z\right)\left[{\varepsilon R}_{A}{+\nu R}_{B}-{C}_{1}-{C}_{3}+\left({F}_{A}+{F}_{B}\right)\right]\end{array}\end{array}$$

(1)

$$\begin{array}{c}{U}_{12}={yz}\left[{R}_{A}{+R}_{B}-{\theta C}_{1}-\left(\alpha {T}_{{rA}}+{\beta T}_{{rB}}\right)\right]\\ +y\left(1-z\right)\left[{R}_{A}{+\nu R}_{B}-{\theta C}_{1}-\alpha {T}_{{rA}}+\delta {F}_{B}\right]\\ \begin{array}{c}+\left(1-y\right)z\left[{\varepsilon R}_{A}{+R}_{B}-\theta {C}_{1}-{\beta T}_{{rB}}+{\gamma F}_{A}\right]\\ +\left(1-y\right)\left(1-z\right)\left[{\varepsilon R}_{A}{+\nu R}_{B}-\theta {C}_{1}+{\gamma F}_{A}+\delta {F}_{B}\right]\end{array}\end{array}$$

(2)

$${\bar{U}}_{1}=x{U}_{11}+\left(1-x\right){U}_{12}$$

(3)

Accordingly, the central government’s replicator dynamic equation can be expressed as follows:

$$\begin{array}{c}F\left(x\right)=\frac{dx}{dt}=x\left({U}_{11}-{\bar{U}}_{1}\right)=x\left(1-x\right)\left({U}_{11}-{U}_{12}\right)\\ =x\left(1-x\right)\left[y\left[\left(\alpha -1\right){T}_{rA}+\left(\gamma -1\right){F}_{A}\right]+z\left[\left(\beta -1\right){T}_{rB}+\left(\delta -1\right){F}_{B}\right]+(1-{\gamma )F}_{A}+\left(1-\delta \right){F}_{B}-{\left(1-\theta \right)C}_{1}{C}_{3}\right]{\rm{\#}}\end{array}$$

(4)

② Local government A’s replicator dynamic equation

Supposing that the expected payoffs of local government A choosing “positive operation” and “negative operation” are ${U}_{21}$ and ${U}_{22}$, and that the average expected utility becomes ${\bar{U}}_{2}$, then:

$$\begin{array}{c}{U}_{21}={xz}\left[\sigma {R}_{A}{+\omega \left(1-\tau \right)R}_{B}{+T}_{{rA}}-{E}_{A}^{2}/2-{C}_{3A}\right]\\ +x\left(1-z\right)\left[\sigma {R}_{A}{+\omega \left(1-\tau \right)\nu R}_{B}{+T}_{{rA}}-{E}_{A}^{2}/2-{C}_{3A}+b{Q}_{B}\right]\\ \begin{array}{c}+\left(1-x\right)z\left[\sigma {R}_{A}{+\omega \left(1-\tau \right)R}_{B}{+\alpha T}_{{rA}}-{E}_{A}^{2}/2-{C}_{3A}\right]\\ +\left(1-x\right)\left(1-z\right)\left[\sigma {R}_{A}{+\omega \left(1-\tau \right)\nu R}_{B}{+\alpha T}_{{rA}}-{E}_{A}^{2}/2-{C}_{3A}+b{Q}_{B}\right]\end{array}\end{array}$$

(5)

$$\begin{array}{c}\begin{array}{c}{U}_{22}={xz}\left[\sigma {\varepsilon R}_{A}{+\omega \left(1-\tau \right)R}_{B}-{\mu }_{A}{E}_{A}^{2}/2-{Q}_{A}-{F}_{A}\right]\\ +x\left(1-z\right)\left[\sigma {\varepsilon R}_{A}{+\omega \left(1-\tau \right)\nu R}_{B}-{\mu }_{A}{E}_{A}^{2}/2-{F}_{A}\right]\\ +\left(1-x\right)z\left[\sigma {\varepsilon R}_{A}{+\omega \left(1-\tau \right)R}_{B}-{\mu }_{A}{E}_{A}^{2}/2-{Q}_{A}-\gamma {F}_{A}\right]\end{array}\\ +\left(1-x\right)\left(1-z\right)\left[\sigma {\varepsilon R}_{A}{+\omega \left(1-\tau \right)\nu R}_{B}-{\mu }_{A}{E}_{A}^{2}/2-\gamma {F}_{A}\right]\end{array}$$

(6)

$${\bar{U}}_{2}=y{U}_{21}+\left(1-y\right){U}_{22}$$

(7)

Accordingly, the replicator dynamic equation of local government A can be expressed as follows:

$$\begin{array}{c}F(y)=\frac{dy}{dt}=y\left({U}_{21}-{\bar{U}}_{2}\right)=y\left(1-y\right)\left({U}_{21}-{U}_{22}\right)\\ =y\left(1-y\right)\left[x\left[\left(1-\alpha \right){T}_{rA}+\left(1-\gamma \right){F}_{A}\right]+z\left({Q}_{A}-b{Q}_{B}\right)+\gamma {F}_{A}{+\alpha T}_{rA}+(1-\varepsilon )\sigma {R}_{A}+b{Q}_{B}-(1-{\mu }_{A}){E}_{A}^{2}/2-{C}_{3A}\right]\end{array}$$

(8)

③ Local government B’s replicator dynamic equation

Supposing that the expected payoffs of local government B choosing “positive operation” and “negative operation” are ${U}_{31}$ and ${U}_{32}$, and that the average expected utility becomes ${\bar{U}}_{3}$, then:

$$\begin{array}{c}\begin{array}{c}{U}_{31}={xy}\left[\tau {R}_{B}{+\varphi \left(1-\sigma \right)R}_{A}{+T}_{{rB}}-{E}_{B}^{2}/2-{C}_{3B}\right]\\ +x\left(1-y\right)\left[\tau {R}_{B}{+\varphi \left(1-\sigma \right)\varepsilon R}_{A}{+T}_{{rB}}-{E}_{B}^{2}/2-{C}_{3B}+a{Q}_{A}\right]\\ +\left(1-x\right)y\left[\tau {R}_{B}{+\varphi \left(1-\sigma \right)R}_{A}{+\beta T}_{{rB}}-{E}_{B}^{2}/2-{C}_{3B}\right]\end{array}\\ +\left(1-x\right)\left(1-y\right)\left[\tau {R}_{B}{+\varphi \left(1-\sigma \right)\varepsilon R}_{A}{+\beta T}_{{rB}}-{E}_{B}^{2}/2-{C}_{3B}+a{Q}_{A}\right]\end{array}$$

(9)

$$\begin{array}{c}\begin{array}{c}{U}_{32}={xy}\left[\tau {\nu R}_{B}{+\varphi \left(1-\sigma \right)R}_{A}-{\mu }_{B}{E}_{B}^{2}/2-{Q}_{B}-{F}_{B}\right]\\ +x\left(1-y\right)\left[\tau \vartheta \nu {+\varphi \left(1-\sigma \right)\varepsilon R}_{A}-{\mu }_{B}{E}_{B}^{2}/2-{F}_{B}\right]\\ +\left(1-x\right)y\left[\tau {\nu R}_{B}{+\varphi \left(1-\sigma \right)R}_{A}-{\mu }_{B}{E}_{B}^{2}/2-{Q}_{B}-{\delta F}_{B}\right]\end{array}\\ +\left(1-x\right)\left(1-y\right)\left[\tau {\nu R}_{B}{+\varphi \left(1-\sigma \right)\varepsilon R}_{A}-{\mu }_{B}{E}_{B}^{2}/2-{\delta F}_{B}\right]\end{array}$$

(10)

$${\bar{U}}_{3}=z{U}_{31}+\left(1-z\right){U}_{32}$$

(11)

Accordingly, local government B’s replicator dynamic equation can be expressed as follows:

$$\begin{array}{c}F(z)=\frac{dz}{dt}=z\left({U}_{31}-{\bar{U}}_{3}\right)=z\left(1-z\right)\left({U}_{31}-{U}_{32}\right)\\ =z\left(1-z\right)\left[x\left[(1-{\beta )T}_{rB}+\left(1-\delta \right){F}_{B}\right]+y\left({Q}_{B}-a{Q}_{A}\right)+{\delta F}_{B}{+\beta T}_{rB}+\left(1-\nu \right)\tau {R}_{B}+a{Q}_{A}-{(1-{\mu }_{B})E}_{B}^{2}/2-{C}_{3B}\right]\end{array}$$

(12)

④ Three-party evolutionary game model

Based on Eqs. (4), (8), and (12), the three-party dynamic system of the game model for TIOM are shown in Eq. (13), where the central government and local governments are all regarded as players.

$$\left\{\begin{array}{c}F(x)=x\left(1-x\right)\left[y{D}_{11}+z{D}_{12}+{D}_{13}\right]\\ F(y)=y\left(1-y\right)\left[{{xD}}_{21}+z{D}_{22}+{D}_{23}\right]\\ F(z)=z\left(1-z\right)\left[x{D}_{31}+y{D}_{32}+{D}_{33}\right]\end{array}\right.$$

(13)

Where ${D}_{11}=\left(\alpha -1\right){T}_{{rA}}+\left(\gamma -1\right){F}_{A}$, ${D}_{12}=\left(\beta -1\right){T}_{{rB}}+\left(\delta -1\right){F}_{B}$, ${D}_{13}=(1-{\gamma )F}_{A}+\left(1-\delta \right){F}_{B}-{\left(1-\theta \right)C}_{1}-{C}_{3}$, ${D}_{21}=\left(1-\alpha \right){T}_{{rA}}+\left(1-\gamma \right){F}_{A}$, ${D}_{22}={Q}_{A}-b{Q}_{B}$, ${D}_{23}=\gamma {F}_{A}{+\alpha T}_{{rA}}+(1-\varepsilon )\sigma {R}_{A}+b{Q}_{B}-(1-{\mu }_{A}){E}_{A}^{2}/2-{C}_{3A}$, ${D}_{31}=(1-{\beta )T}_{{rB}}+\left(1-\delta \right){F}_{B}$, ${D}_{32}={Q}_{B}-a{Q}_{A}$, ${D}_{33}={\delta F}_{B}{+\beta T}_{{rB}}+\left(1-\nu \right)\tau {R}_{B}+a{Q}_{A}-{(1-{\mu }_{B})E}_{B}^{2}/2-{C}_{3B}$.

Stability analysis of the equilibrium point

According to the stability theorem of differential equations, $\varTheta$ is the ESS of the governments when the conditions of $F(\varTheta )=0$ and ${F}^{{\prime} }(\varTheta ) < 0$ are satisfied (Chaab and Rasti-Barzoki, 2016). Based on this theorem, the stable strategies of the governments are analyzed and the following propositions and corollaries are drawn.

(1) Stable strategies of the central-local government

Let ${y}^{* }=\frac{z\left[\left(\beta -1\right){T}_{{rB}}+\left(\delta -1\right){F}_{B}\right]+(1-{\gamma )F}_{A}+\left(1-\delta \right){F}_{B}-{\left(1-\theta \right)C}_{1}-{C}_{3}}{\left(1-\alpha \right){T}_{{rA}}+\left(1-\gamma \right){F}_{A}}$; then, we can obtain Proposition 1 and Corollaries 1.1, 1.2. See Appendix A for the proof.

Proposition 1.

• When ${y=y}^{* }$, ${\left.{F}^{{\prime} }(x)\right|}_{x=0}=0$ and ${\left.{F}^{{\prime} }(x)\right|}_{x=1}=0$, neither “decentralization” nor “centralization” is the stable strategy adopted by the central government.

• When ${y > y}^{* }$, ${\left.{F}^{{\prime} }(x)\right|}_{x=0} < 0$ and ${\left.{F}^{{\prime} }(x)\right|}_{x=1} > 0$, then ${x}^{* }=0$ is the only ESS point and “decentralization” is the stable strategy adopted by the central government under this condition, as shown in Fig. 2a.

• When ${y < y}^{* }$, ${\left.{F}^{{\prime} }(x)\right|}_{x=0} > 0$ and ${\left.{F}^{{\prime} }(x)\right|}_{x=1} < 0$, then ${x}^{* }=1$ is the only ESS point and “centralization” is the stable strategy adopted by the central government under this condition, as shown in Fig. 2a.

Fig. 2: Dynamic replication phase diagram.

(a) Evolutionary phase diagram of the central government's strategy, (b) evolutionary phase diagram of local government A's strategy, and (c) evolutionary phase diagram of local government B's strategy. ${V}_{x=0}$ and ${V}_{x=1}$ denote the probability of the central government choosing “decentralization” and “centralization”; ${V}_{y=0}$ and ${V}_{y=1}$ denote the probability of local government A choosing “negative operation” and “positive operation”; ${V}_{z=0}$ and ${V}_{z=1}$ denote the probability of local government B choosing “negative operation” and “positive operation”.

Corollary 1.1.

The probability of the central government choosing “decentralization” will increase along with the probability of local government A (B) choosing “positive operation”.

Corollary 1.2.

The probability of the central government choosing “decentralization” is positively correlated with ${C}_{1}$, ${C}_{3}$, ${T}_{{rA}}$, ${T}_{{rB}}$, $\gamma$, and $\delta$, and negatively correlated with ${F}_{A}$, ${F}_{B}$,$\,\alpha$, $\beta$, and $\theta$.

Figure 2 Dynamic replication phase diagram.

(2) Stable strategies of local government A

Let ${z}^{* }=\frac{x\left[\left(1-\alpha \right){T}_{{rA}}+\left(1-\gamma \right){F}_{A}\right]+\gamma {F}_{A}{+\alpha T}_{{rA}}+(1-\varepsilon )\sigma {R}_{A}+b{Q}_{B}-(1-{\mu }_{A}){E}_{A}^{2}/2-{C}_{3A}}{b{Q}_{B}-{Q}_{A}}$, if ${Q}_{A}-b{Q}_{B} > 0$, then we can obtain Proposition 2 and Corollaries 2.1, 2.2; if ${Q}_{A}-b{Q}_{B} < 0$, then we can obtain Proposition 3 and Corollaries 3.1. See Appendix B for the proof.

Proposition 2.

If ${Q}_{A}-b{Q}_{B} > 0$,

• When ${z=z}^{* }$, ${\left.{F}^{{\prime} }(y)\right|}_{y=0}=0$ and ${\left.{F}^{{\prime} }(y)\right|}_{y=1}=0$, neither “positive operation” nor “negative operation” is the stable strategy adopted by local government A.

• When ${z < z}^{* }$, ${\left.{F}^{{\prime} }(y)\right|}_{y=0} < 0$ and ${\left.{F}^{{\prime} }(y)\right|}_{y=1} > 0$, then ${y}^{* }=0$ is the only ESS point and “negative operation” is the stable strategy adopted by local government A under this condition, as shown in Fig. 2b.

• When ${z > z}^{* }$, ${\left.{F}^{{\prime} }(y)\right|}_{y=0} > 0$ and ${\left.{F}^{{\prime} }(y)\right|}_{y=1} < 0$, then ${y}^{* }=1$ is the only ESS point and “positive operation” is the stable strategy adopted by local government A under this condition, as shown in Fig. 2b.

Corollary 2.1.

When ${Q}_{A} > b{Q}_{B}$, the probability of local government A choosing “positive operation” will increase as the probability of the central government choosing “centralization” and local government B choosing “positive operation” increase.

Corollary 2.2.

The probability of local government A choosing “positive operation” is positively correlated with ${T}_{{rA}}$, ${F}_{A}$, ${R}_{A}$, ${Q}_{A}$, ${Q}_{B}$, $\alpha$, $\gamma$, $b$, $\sigma$, and ${\mu }_{A}$, and negatively correlated with ${E}_{A}$, ${C}_{3A}$, and $\varepsilon$.

Proposition 3.

If ${Q}_{A}-b{Q}_{B} < 0$,

• When ${z=z}^{* }$, ${\left.{F}^{{\prime} }(y)\right|}_{y=0}=0$ and ${\left.{F}^{{\prime} }(y)\right|}_{y=1}=0$, neither “positive operation” nor “negative operation” is the stable strategy adopted by local government A.

• When ${z < z}^{* }$, ${\left.{F}^{{\prime} }(y)\right|}_{y=0} > 0$ and ${\left.{F}^{{\prime} }(y)\right|}_{y=1} < 0$, then ${y}^{* }=1$ is the only ESS point and “positive operation” is the stable strategy adopted by local government A under this condition, as shown in Fig. 2c.

• When ${z > z}^{* }$, ${\left.{F}^{{\prime} }(y)\right|}_{y=0} < 0$ and ${\left.{F}^{{\prime} }(y)\right|}_{y=1} > 0$, then ${y}^{* }=0$ is the only ESS point and “negative operation” is the stable strategy adopted by local government A under this condition, as shown in Fig. 2c.

Corollary 3.1.

When ${Q}_{A} < b{Q}_{B}$, the probability of local government A choosing “positive operation” will increase as the probability of the central government choosing “centralization” and local government B choosing “negative operation” increase.

(3) Stable strategies of local government B

Given the similarity between the strategic stability of local government B and that of local government A, the propositions, corollaries, and proofs related to local government B are not repeated here and can be viewed in Appendix C.

(4) Stable strategies of the three governments

According to the stability theorems of Lyapunov’s systems (Lyapunov, 1992), the eigenvalues of the Jacobian matrix can be used as criteria for determining the stability of an evolutionary game model (Zhang et al., 2023). Thus, the partial derivatives of the replicator dynamic equations of the governments are calculated to generate the Jacobian matrix as follows:

$$J=\left[\begin{array}{ccc}\frac{\partial F\left(x\right)}{\partial x} & \frac{\partial F\left(x\right)}{\partial y} & \frac{\partial F\left(x\right)}{\partial z}\\ \frac{\partial F\left(y\right)}{\partial x} & \frac{\partial F\left(y\right)}{\partial y} & \frac{\partial F\left(y\right)}{\partial z}\\ \frac{\partial F\left(z\right)}{\partial x} & \frac{\partial F\left({yz}\right)}{\partial y} & \frac{\partial F\left({yz}\right)}{\partial z}\end{array}\right]$$

(14)

When replicator dynamic equations of the three governments is equal to zero, the evolutionary game model will reach an asymptotically stable state and can be solved for its equilibrium points. Notably, the equilibrium points derived from the replicator dynamic equations are not always stable. Stable equilibrium points, also referred to as ESS, can be quickly restored to a stable state through interactions when exposed to weak disturbances. Furthermore, hybrid strategies cannot be observed in an ESS, which must be a strict Nash equilibrium consisting of pure strategies (Yuan and Wang, 2023). To analyze the system’s stability, this paper computes the equilibrium points by setting $F\left(x\right)=0$, $F\left(y\right)=0$, and $F\left(z\right)=0$. The eight pure strategies of the evolutionary game model are calculated as ${E}_{1}\left(\mathrm{0,0,0}\right)$, ${E}_{2}\left(\mathrm{1,0,0}\right)$, ${E}_{3}\left(\mathrm{0,1,0}\right)$, ${E}_{4}\left(\mathrm{0,0,1}\right)$, ${E}_{5}\left(\mathrm{1,1,0}\right)$, ${E}_{6}\left(\mathrm{1,0,1}\right)$, ${E}_{7}\left(\mathrm{0,1,1}\right)$, and ${E}_{8}\left(\mathrm{1,1,1}\right)$. Then, the eight points are respectively substituted into Eq. (14) to solve the eigenvalues, as shown in Table 4.

Table 4 Eigenvalues of eight equilibrium points.

The stability theorems of Lyapunov’s systems (Lyapunov, 1992) suggest that, when all three eigenvalues of an equilibrium point are less than zero, this point is an ESS; otherwise, this point is not an ESS. As shown in Table 4, ${E}_{8}$ cannot evolve into an ESS because of $\left(\alpha -1\right){T}_{{rA}}+\left(\beta -1\right){T}_{{rB}}-{\left(1-\theta \right)C}_{1}-{C}_{3} < 0$, while ${E}_{1}$ ~ ${E}_{7}$ may all evolve into an ESS. ${E}_{1}$ ~ ${E}_{6}$ are not discussed in this paper because there is at least one local government that chooses “negative operation”. The ESS of local government A (B) associated with ${E}_{8}$ is a “positive operation”, but “centralization” is not the ESS of the central government. ${E}_{7}$ is the only ESS that can be reached by the game system when both local governments A (B) adopt “positive operation”. Besides, Table 4 shows that the conditions under which only ${E}_{7}$ can evolve into ESS are: $(1-\varepsilon {)\sigma R}_{A}-(1-{\mu }_{A}){E}_{A}^{2}/2-{C}_{3A} > 0$ and $(1-{\nu )\tau R}_{B}-(1-{\mu }_{B}){E}_{B}^{2}/2-{C}_{3B} > 0$. The stability of the equilibrium points under such conditions is shown in Table 5.

Table 5 Stability of the equilibrium point: $(1-\varepsilon {)\sigma R}_{A} > (1-{\mu }_{A}){E}_{A}^{2}/2+{C}_{3A}$ and $(1-{\nu )\tau R}_{B} > (1-{\mu }_{B}){E}_{B}^{2}/2+{C}_{3B}$.

According to Table 5, ${E}_{7}$ is considered as the optimal ESS in the strategic interaction between the central government and local government A (B) for TIOM. In ${E}_{1}$, ${E}_{3}$, and ${E}_{4}$, the central government chooses a decentralized strategy, with at least one local government choosing a negative strategy. The local government is reluctant to improve the service quality and operation efficiency of its jurisdiction’s transport infrastructure due to a lack of endogenous motivation and competitive pressure, as well as the coordination and regulation of the central government. In ${E}_{2}$, ${E}_{5}$, and ${E}_{6}$, the central government intervenes in the policy execution of local governments through regulation, incentives, and penalties. Local governments that implement negative strategies will be severely punished by the central government, and their strategies will move toward “positive operation”. In ${E}_{8}$, both local governments chose positive strategies under the coordination of the central government. However, as “centralization” is not an ESS of the central government according to the stability conditions of ${E}_{8}$, the game system will evolve to the other state. In ${E}_{7}$, the central government chooses the decentralized strategy to adequately mobilize the enthusiasm and discretion of local governments to ensure the stability of the game system. In Section 4, this paper simulates and discusses the impact of model parameters on the optimal ESS (i.e., ${E}_{7}$).

Stochastic evolutionary game model

Modified replicator dynamic equations

The traditional evolutionary game model can portray the dynamics of decision-making processes and the strategic interactions of the players with the precondition that all of the players make deterministic decisions within a deterministic system without accounting for the perturbation of the ESS due to uncertainties (Shan et al., 2023). In reality, however, the strategies chosen by the governments in response to TIOM will be disturbed by a set of non-negligible uncertainties, including external perturbation (e.g., social risks, economic disruption, natural disasters), as well as internal perturbation (e.g., appointment and removal of officials, policy changes) (Jiang et al., 2024). To visualize the impact of the stochastic perturbation on the system stability during the game process, the Gaussian white noise and the random disturbance terms that satisfy the Gaussian assumptions and follow the normal distribution are introduced into the replicator dynamic equations (Li et al., 2023; Shan et al., 2023; Yi et al., 2024). Then, the modified equations of the governments that are susceptible to the stochastic perturbation become available:

$${dx}\left(t\right)=x\left(t\right)\left[1-x\left(t\right)\right]\left[y\left(t\right){D}_{11}+z\left(t\right){D}_{12}+{D}_{13}\right]{dt}+{Wx}\left(t\right){dw}\left(t\right)$$

(15)

$${dy}\left(t\right)=y\left(t\right)\left[1-y\left(t\right)\right]\left[{x(t)D}_{21}+z(t){D}_{22}+{D}_{23}\right]{dt}+{Wy}\left(t\right){dy}\left(t\right)$$

(16)

$${dz}\left(t\right)=z\left(t\right)\left[1-z\left(t\right)\right]\left[x(t){D}_{31}+y{(t)D}_{32}+{D}_{33}\right]{dt}+{Wz}\left(t\right){dz}\left(t\right)$$

(17)

Where $w\left(t\right)$ is a one-dimensional standard Brownian motion, which is an irregular stochastic rise and fall phenomenon that can effectively capture the impact of the stochastic perturbation of uncertainties on the strategic behaviors of the players (Traulsen and Nowak, 2006), and $w\left(t\right) \sim N(0,t)\,\left(t > 0,h > 0\right)$; ${dw}\left(t\right)$ represents the Gaussian white noise and its increments as $\Delta w\left(t\right)=w\left(t+h\right)-w\left(t\right)$ ~ $N\left(0,\sqrt{h}\right)\left(t > 0,h > 0\right)$; $W$ is the intensity of the stochastic perturbation; $h$ is the step size; and Eqs. (15)-(17) are all of the ${It}\hat{o}$ stochastic differential equations in one dimension.

Since $x,y,z\in \left[\mathrm{0,1}\right]$, $1-x$, $1-y$, and $1-z$ are all non-negative numbers and do not affect the outcomes of the evolutionary game. Referring to Shan et al. (2023) and Jiang et al. (2024), the modified equations of the governments are simplified as follows:

$${dx}\left(t\right)=\left[y(t){D}_{11}+z(t){D}_{12}+{D}_{13}\right]x\left(t\right){dt}+{Wx}\left(t\right){dw}\left(t\right)$$

(18)

$${dy}\left(t\right)=\left[{x(t)D}_{21}+z(t){D}_{22}+{D}_{23}\right]y\left(t\right){dt}+{Wy}\left(t\right){dw}\left(t\right)$$

(19)

$${dz}\left(t\right)=\left[x(t){D}_{31}+y{(t)D}_{32}+{D}_{33}\right]z\left(t\right){dt}+{Wz}\left(t\right){dw}\left(t\right)$$

(20)

The existence and stability of equilibrium solutions

For Eqs. (18–20), assuming that $t=0$ at an initial stage (the initial moment of the evolutionary game system), then $x\left(0\right)=0$, $y\left(0\right)=0$, and $z\left(0\right)=0$. Thus, the following equations are obtained:

$$0\times \left[y(t){D}_{11}+z(t){D}_{12}+{D}_{13}\right]+{Wx}\left(t\right){dw}\left(t\right)=0$$

(21)

$$0\times \left[{x(t)D}_{21}+z(t){D}_{22}+{D}_{23}\right]+{Wy}\left(t\right){dw}\left(t\right)=0$$

(22)

$$0\times \left[x(t){D}_{31}+y{(t)D}_{32}+{D}_{33}\right]+{Wz}\left(t\right){dw}\left(t\right)=0$$

(23)

According to Eqs. (21–23), ${dw}\left(t\right){|}_{t=0}={w}^{{\prime} }\left(t\right){dt}{|}_{t=0}=0$. This implies that there is at least one zero solution to the equations (i.e., the evolutionary game system will stabilize in the initial state without stochastic perturbation). Therefore, the zero solution is an equilibrium solution of Eqs. (18)-(20).

In reality, however, the strategic behaviors of the players are bound to be disturbed by internal and external uncertainties, which will affect the system’s stability. Therefore, integrating the uncertainties into the decision-making process enables the game model to more accurately reflect the changing reality. To ascertain the stability of the replicator dynamic equations for the players in uncertain environments, the stability theorems of the stochastic differential equations are utilized as follows.

Given a stochastic differential equation (Baker and Buckwar 2005):

$${dx}\left(t\right)=f\left(t,x\left(t\right)\right){dt}+g\left(t,x\left(t\right)\right){dw}\left(t\right),\,x\left({t}_{0}\right)={x}_{0}$$

(24)

Assume that there is a function $V\left(t,x\right)$ with positive constants ${c}_{1}$, ${c}_{2}$, such that ${c}_{1}{\left|x\right|}^{p}\le V\left(t,x\right)\le {c}_{2}{\left|x\right|}^{p},{t}\ge 0$.

• If there exists a positive constant $c$, such that ${LV}\left(t,x\right) < -{cV}\left(t,x\right),{t}\ge 0$, then the zero solution of Eq. (24) is exponentially stable to the p-th moment and holds $E{\left|x\left(t,{x}_{0}\right)\right|}^{p} < \left(\frac{{c}_{2}}{{c}_{1}}\right){\left|{x}_{0}\right|}^{p}{e}^{-{ct}},{t}\ge 0$.

• If there exists a positive constant $c$, such that ${LV}\left(t,x\right)\ge -{cV}\left(t,x\right),{t}\ge 0$, then the zero solution of Eq. (24) is exponentially unstable to the p-th moment and holds $E{\left|x\left(t,{x}_{0}\right)\right|}^{p}\ge \left(\frac{{c}_{2}}{{c}_{1}}\right){\left|{x}_{0}\right|}^{p}{e}^{-{ct}},{t}\ge 0$.

For Eqs. (18)-(20), let ${V}_{t}\left(t,x\right)=x$, ${V}_{t}\left(t,y\right)=y$, ${V}_{t}\left(t,z\right)=z$, $x,y,z\in \left[\mathrm{0,1}\right]$, ${c}_{1}={c}_{2}=1$, $c=1$, $p=1$, then:

$${LV}\left(t,x\right)=f\left(t,x\right)=\left[y{D}_{11}+z{D}_{12}+{D}_{13}\right]x$$

(25)

$${LV}\left(t,y\right)=f\left(t,y\right)=\left[{{xD}}_{21}+z{D}_{22}+{D}_{23}\right]y$$

(26)

$${LV}\left(t,z\right)=f\left(t,z\right)=\left[x{D}_{31}+y{D}_{32}+{D}_{33}\right]z$$

(27)

• If the moment exponential stability of the zero solution for Eqs. (18–20) is stable, the following conditions need to be satisfied:

  $$\left[y{D}_{11}+z{D}_{12}+{D}_{13}\right]x\le -x$$

  (28)
  $$\left[{{xD}}_{21}+z{D}_{22}+{D}_{23}\right]y\le -y$$

  (29)
  $$\left[x{D}_{31}+y{D}_{32}+{D}_{33}\right]z\le -z$$

  (30)

• If the moment exponential stability of the zero solution for Eqs. (18–20) is unstable, the following conditions need to be satisfied:

$$\left[y{D}_{11}+z{D}_{12}+{D}_{13}\right]x > -x$$

(31)

$$\left[{{xD}}_{21}+z{D}_{22}+{D}_{23}\right]y > -y$$

(32)

$$\left[x{D}_{31}+y{D}_{32}+{D}_{33}\right]z > -z$$

(33)

According to Eqs. (28–30), when the benefits of a decentralized strategy are greater than those of a centralized strategy for the central government and the benefits of a negative strategy are higher than those of a positive strategy for local governments, then there exists a unique ESS as ${E}_{1}$. According to Eqs. (31–33), the only ESS is ${E}_{8}$ when the benefits of a decentralized strategy are smaller than those of a centralized strategy for the central government and the benefits of a negative strategy are lower than that of a positive strategy for local governments. The stable conditions of ${E}_{7}$ are shown in Eq. (34). In the next section, ${E}_{7}$ is numerically simulated and discussed using MATLAB R2021a to analyze in detail the effect of the determinants.

$$\left\{\begin{array}{c}y{D}_{11}+z{D}_{12}+{D}_{13}\le 0\\ {{xD}}_{21}+z{D}_{22}+{D}_{23} > 0\\ x{D}_{31}+y{D}_{32}+{D}_{33} > 0\end{array}\right.$$

(34)

Numerical analyses of determinants

Parameter setting

Based on the theoretical analysis above, it can be inferred that ${E}_{7}$ is the only optimal ESS that can be reached by the governments in TIOM. In order to understand more intuitively the evolutionary dynamics of the central-local fiscal relations, MATLAB R2021b software was used to simulate the evolution of ${E}_{7}$ under the effect of different determinants. This paper examines cases from the geographically proximate provinces of Guangdong and Guangxi in China, providing an ideal context for analyzing the spillover effects of TIOM and intergovernmental competition. Guangdong, the most economically developed province in China, features a well-developed transport network and booming transport industry, with a relatively low dependence on the central finance. Guangxi Province lags behind in both economic development and TIOM, and is highly dependent on the central finance. In order to promote regionally coordinated development, the central government tends to give more financial support to Guangxi for TIOM. These differences offer a comparison of the strategic choices made by the central and local governments in the context of TIOM.

The initial values of parameters were obtained from three sources. (1) Public government data. Data files include the 2022 Financial Accounts Report of the Ministry of Transport of China, the 2022 Financial Accounts Report of Guangdong Province, the 2022 Financial Accounts Report of Guangxi Province, the 2022 Statistical Yearbook of Guangdong Province, and the 2022 Statistical Yearbook of Guangxi Province. (2) Data calculated by regression analysis. Considering the spillover effects of transport, this paper constructs a Spatial Durbin Model to calculate the impact of TIOM on neighboring regions. The detailed results of the Spatial Durbin Model are provided in Appendix D. (3) Data determined according to the principle of equilibrium. In order to comply with the realistic meaning and model assumptions, the initial values need to satisfy $\left(\alpha -1\right){T}_{{rA}}+\left(\beta -1\right){T}_{{rB}}-{\left(1-\theta \right)C}_{1} < 0$, ${Q}_{A}+\gamma {F}_{A}{+\alpha T}_{{rA}}+(1-\varepsilon )\sigma {R}_{A}-(1-{\mu }_{A}){E}_{A}^{2}/2-{C}_{3A} > 0$, and ${Q}_{B}+{\delta F}_{B}{+\beta T}_{{rB}}+\left(1-\nu \right)\tau {R}_{B}-(1-{\mu }_{B}){E}_{B}^{2}/2-{C}_{3B} > 0$. Then, we can obtain the initial values as shown in Table 6. Next, differentiated values for each determinant are assigned based on the initial values to examine the sensitivity of government strategy choices for each determinant.

Table 6 Initial values of parameters.

The effect of initial probability

Initial probability reflects the intensity of the initial willingness of players to choose different strategies. A higher initial probability indicates a stronger willingness to choose different strategies at the beginning of the game. Figure 3 traces the evolutionary trajectories of the strategic behaviors with different initial probabilities, showing that changes in initial probabilities do not affect the final outcome of the game; however, increased initial probabilities accelerate the game in regard to reaching equilibrium. That is, the increased motivation of local politicians in regard to TIOM will facilitate the rapid convergence of their strategic behaviors toward “positive operation”. Besides, local government B reaches equilibrium significantly slower than local government A. Consequently, the key to attaining equilibrium in the game lies in enhancing the vitality of local government B.

Fig. 3: The effect of initial probability.

(a) Strategy evolutionary trajectory with an initial probability of 0.2, (b) strategy evolutionary trajectory with an initial probability of 0.5, and (c) strategy evolutionary trajectory with an initial probability of 0.8.

The effect of uncertainties

Figure 4 depicts the effects of uncertainties on strategic behaviors when $W=1$ and $W=2$. With the given intensity of random disturbances, the rate at which the strategic behaviors of the central government and local government A attain equilibrium remains basically unchanged (i.e., uncertainties display non-significant effects on their strategies). Unlike local government A, local government B is more sensitive to uncertainties. The stronger the stochastic disturbance, the longer it takes for local government B to reach equilibrium. Additionally, as shown in Fig. 4, fluctuations in the evolutionary trajectories of strategic behaviors are more emphatic when initial willingness is lower. This further highlights the importance of enhancing initial willingness to attain equilibrium in the game.

Fig. 4: The effect of uncertainties.

(a) Strategy evolutionary trajectory with random disturbance of 1, (b) strategy evolutionary trajectory with random disturbance of 2, and (c) strategy evolutionary trajectory with random disturbance of 3.

The effect of benefits

On the premise of maintaining the initial values of the other determinants, the mechanism linking the benefits to the strategic choices of the governments is simulated, as shown in Fig. 5. According to Fig. 5a, b, first, when ${R}_{A}$ increases from 61.77 to 80 or ${R}_{B}$ increases from 43.04 to 60, the speed at which the ESS of local governments stabilizes towards 1 improves significantly, indicating that benefits positively motivate local governments to choose “positive operation”. Second, local government A is capable of benefiting more from “positive operation” than is local government B, so its ESS stabilizes at 1 more quickly. However, considering that the sum of the benefits gained by adopting a positive strategy and the potential losses associated with a negative strategy is greater than the sum of the opportunity and direct costs (${Q}_{B}+{\delta F}_{B}{+\beta T}_{{rB}}+\left(1-\nu \right)\tau {R}_{B} > (1-{\mu }_{B}){E}_{B}^{2}/2+{C}_{3B}$), the ESS of local government B will still stabilize at 1. Third, as illustrated in Fig. 5c, d, when $\sigma$ and $\tau$ increase from 0.56 to 0.8, the speed at which the local governments’ ESS stabilizes at 1 improves significantly, showing that lower spillovers encourage local governments to choose “positive operation”. Besides, a comparison of Fig. 5c–f suggests that local governments are more sensitive to local benefits than spillovers from neighboring regions. This is concrete proof that decentralization is a more effective governance structure when spillovers from transport infrastructure are lower (Kappeler et al., 2013). Local governments demonstrate greater responsiveness to localized gains than transboundary spillovers, confirming the “localism” mechanism in China’s politically centralized fiscal decentralization framework (Lei and Zhou, 2022), where tangible local outcomes (e.g., tax revenue and employment) directly influence performance assessments, while cross-jurisdictional benefits (e.g., inter-regional logistics efficiency) yield weaker incentives due to internalization barriers. Finally, Fig. 5g, h suggest that the high benefit coefficient associated with “negative operation” impedes local governments from executing “positive operation”. This effect is more pronounced for local government B. Thus, the key to tightening the ESS of local governments toward “positive operation” lies in improving and internalizing the benefits of TIOM as much as possible.

Fig. 5: The effect of benefits.

(a) Effect of R_A on the strategy evolutionary trajectory of local government A, (b) effect of R_B on local government B, (c) effect of σ on local government A, (d) effect of τ on local government B, (e) effect of ω on local government A, (f) effect of φ on local government B, (g) effect of ε on local government A, and (h) effect of ν on local government B.

The effect of costs

The effect of direct and opportunity costs on ${E}_{7}$ is simulated, as shown in Fig. 6. For the central government, as shown in Fig. 6a, g, when ${C}_{1}$ increases from 4.12 to 15 or $\theta$ increases from 0.4 to 0.6, its ESS stabilizes toward “decentralization” at an accelerated rate because the increased difficulty of obtaining information on the policy enforcement of local governments causes sufficient discretion to be endowed to local governments, with the aim of reducing the central government’s costs. Additionally, opportunity costs encourage the central government, with its limited fiscal funds, to embrace “decentralization”, as depicted in Fig. 6b. For local governments, as shown in Fig. 6c, e, the ESS converges toward “positive operation” over a longer period of time with the increase of ${E}_{A}$ and ${E}_{B}$. As local governments increase effort levels, the convergence speed of adopting positive strategies significantly slows. Specifically, government A exhibits lower sensitivity to cost increases due to higher local returns that offset expenditures, whereas government B demonstrates more pronounced convergence delays, highlighting financially constrained regions’ susceptibility to negative operations. This demonstrates that increasing marginal costs undermine local incentives and validates the model’s specification of effort coefficients capturing regional heterogeneity. Comparing Fig. 6c, e, h, i, it is evident that local government B is more sensitive to costs, while local government A is more likely to reach equilibrium, suggesting that the cost advantage (higher benefit-to-cost ratio) can significantly strengthen the local governments’ enthusiasm for TIOM. In addition, as seen in Fig. 6d, f, when ${C}_{3A}$ increases from 15 to 25 or ${C}_{3B}$ increases from 18 to 28, the duration of local governments’ ESS stabilizing at “positive operation” becomes longer. This phenomenon is more pronounced for local government B. In summary, given the scarce resources available, local governments should not only improve their advantages in terms of costs, but also achieve a balanced allocation of resources between TIOM and other public services to satisfy the actual needs of socioeconomic development in their jurisdictions (Zegras et al., 2013).

Fig. 6: The effect of costs.

(a) Effect of C₁ on the strategy evolutionary trajectory of the central government, (b) effect of C₃ on the central government, (c) effect of E_A on local government A, (d) effect of C_3A on local government A, (e) effect of E_B on local government B, (f) effect of C_3B on local government B, (g) effect of θ on the central government, (h) effect of μ_A on local government A, and (i) effect of μ_B on local government B.

The effect of incentives

Figure 7 depicts the evolutionary paths of the three governments, given different incentives. Financial support such as transfer payments and tax subsidies given to local governments for TIOM actually constitutes expenditures for the central government. Thus, the decentralized strategy of the central government is positively associated with financial support, as shown in Fig. 7a, b. Notably, when $\alpha$ increases from 0.3 to 0.5 or $\beta$ from 0.6 to 0.8, the evolution time it takes for the central government to choose “decentralization” increases, indicating that the incentive coefficient is negatively correlated with the decentralized strategy, as depicted in Fig. 7e, f. That is, a low incentive coefficient (e.g., $\alpha =0.3$ and $\beta =0.6$) implies that local governments are weakly dependent on financial support from the central government, in which case decentralized supply will be a more effective governance structure (Hörcher et al., 2023). For local governments, Fig. 7c, d, g, h show that high incentives (e.g., ${T}_{{rA}}=35$ and $\alpha =0.5$, ${T}_{{rB}}=40$ and $\beta =0.8$) accelerate the stabilization of the local government’s ESS at 1. Financial support provided by the central government can alleviate the debt pressure on local governments, thus increasing their willingness to engage in “positive operation”. For example, when ${T}_{{rB}}$ increases to 21.35, local government B achieves equilibrium simultaneously with local government A, which demonstrates that incentive-driven resource reallocation can alleviate regional imbalances and promote equity in TIOM (Zegras et al., 2013). Moreover, according to the assumptions in section “Assumptions”, regional heterogeneity determines that local government B, which is disadvantaged compared to local government A, is more sensitive to changes in incentives. As a result, the central government can defuse the conflicts of interest among local governments through transfers and subsidies (Zegras et al., 2013), as well as promote the equalization of TIOM between regions.

Fig. 7: The effect of incentives.

(a) Effect of T_rA on the strategy evolutionary trajectory of the central government, (b) effect of T_rB on the central government, (c) effect of T_rA on local government A, (d) effect of T_rB on local government B, (e) effect of α on the central government, (f) effect of β on the central government, (g) effect of α on local government A, and (h) effect of β on local government B.

The effect of penalties

Penalties are mechanisms designed to impose constraints on the negative strategies of local governments. Their impact on governments’ strategies is simulated in Fig. 8. For the central government, although penalties constitute its income, the fundamental goal is to guide the strategic behaviors of local governments to quickly converge toward “positive operation”. Thus, as illustrated in Fig. 8a, b, e, f, the evolutionary path of the central government is insensitive to changes in penalties, especially when local governments prefer to choose “positive operation”, which conforms with the assumption that the central government pursues the global interest, as discussed in section “Assumptions”. It highlights how the central government prioritizes institutional frameworks rather than punitive measures to preserve local autonomy when optimizing long-term social welfare, reflecting its dual objectives of centralized coordination and decentralized flexibility. Regarding local governments, as presented in Fig. 8c, d, g, h, high penalties (e.g., ${F}_{A}=28$ and $\gamma =0.8$, ${F}_{B}=20$ and $\delta =0.5$) drive the ESS of local governments to stabilize quickly at 1, since penalties constitute the costs of choosing the negative strategies. Furthermore, the positive correlation between penalties and local government B is more prominent, suggesting that stronger penalties can more effectively guide this government to improve TIOM within its jurisdiction. The finding confirms that effort coefficients in the model effectively reflect regional heterogeneity while aligning with Kappeler et al. (2013)’s framework emphasizing institutional design as critical for fiscal decentralization efficiency, particularly highlighting how external enforcement mechanisms are indispensable to address insufficient endogenous incentives in underdeveloped jurisdictions. A comparison of Figs. 7, 8 further reveals that the game system can attain equilibrium quickly by combining penalties and incentives. The central government needs to combine fiscal transfers (incentives) to ease debt burdens in lagging regions with performance-based accountability systems (penalties) that constrain officials’ short-term prioritization of TIOM.

Fig. 8: The effect of penalties.

(a) Effect of F_A on the strategy evolutionary trajectory of the central government, (b) effect of F_B on the central government, (c) effect of F_A on local government A, (d) effect of F_B on local government B, (e) effect of γ on the central government, (f) effect of δ on the central government, (g) effect of γ on local government A, and (h) effect of δ on local government B.

The effect of competition

By adjusting the competitive intensity, the evolutionary trajectories of local governments’ ESS are simulated, as shown in Fig. 9. First, in order to avoid losses caused by the outflow of capital and labor, local governments will choose “positive operation”. Second, as shown in Fig. 9a, b, the time required for local governments’ ESS to reach equilibrium becomes shorter when ${Q}_{A}$ increases from 13.76 to 23 or ${Q}_{B}$ increases from 11.99 to 22, implying that competition positively contributes to the strategic choices of “positive operation”. Moreover, the effect of competition on the evolutionary trajectory of local government B is more pronounced, as it is less capable of agglomerating capital and labor from surrounding areas. This reveals the dual-edged impact of competition on central governance strategies. On one hand, competition stimulates local autonomy; on the other hand, where intensified competition exacerbates regional disparities, it may compel the central government to adopt centralized governance to mitigate systemic risks (e.g., Guangxi’s vulnerability due to resource constraints). Finally, comparing Fig. 9c–f, it is found that local governments are more sensitive to losses from capital and labor outflows than to gains from capital and labor inflows. In summary, the negative strategy is not a good choice for local governments, but decentralized supply is an effective way of improving TIOM when the externalities of transport infrastructure cause substantial losses in regard to production factors (${Q}_{A} > b{Q}_{B}$ and ${Q}_{B} > a{Q}_{A}$) (Borger and Proost, 2012; Carlucci et al., 2017).

Fig. 9: The effect of competition.

(a) Effect of Q_A on the strategy evolutionary trajectory of local government A, (b) effect of Q_B on local government B, (c) effect of a on local government B, (d) effect of b on local government A, (e) effect of Q_A on local government B, and (f) effect of Q_B on local government A.

Conclusions and implications

Regulating the central-local fiscal relationship will help clarify the fiscal powers and expenditure responsibilities in the transport sector and improve the operation efficiency and service quality of transport infrastructure. Based on the vertical fiscal relations and horizontal competitive relations, this paper sheds new light on the fiscal reform by developing a stochastic evolutionary game model consisting of the central and local governments in China’s top-down political hierarchy. In this paper, we deduce the ESS of each government and its stable conditions from a theoretical perspective, and then simulate the effects of the determinants on the evolutionary trajectories of the strategic behaviors using MATLAB R2021a software. Accordingly, this paper draws some important conclusions and proposes policy implications linked to these conclusions, as follows.

• (1) In a system of multi-tiered government, the optimally stable strategies of the central government, local government A, and local government B used to improve the operation efficiency and service quality of transport infrastructure are: when the central government adopts a decentralized system, local governments all positively improve TIOM efficiency. However, the relative imbalance of transport services between regions in China is currently severe, and most local governments are still biased toward scaling up transport infrastructure. Considering the self-interests of local politicians, optimally stable strategies cannot be achieved by relying only on their self-discipline. Therefore, it becomes important to enhance regulations and incentives for local governments, to enable them to effectively break local protectionism and circumvent the opportunistic behaviors of local politicians. First, implement performance-based fund allocation mechanisms, which tie portions of fiscal transfers to local performance in TIOM to incentivize efficiency improvements. Second, establish a national-level platform for sharing best practices, facilitating cross-regional knowledge exchange and technical support to enhance managerial capabilities in underperforming jurisdictions. Third, create targeted incentive funds that reward high-performing local governments in TIOM, which encourage innovation and efficient operations to promote nationwide adoption of optimal practices.

• (2) The principal-agent relationship reflects the intrinsic power structure in China’s top-down political hierarchy, in which the central government can address the principal-agent problems in TIOM by regulating, rewarding, and punishing local governments. Specifically, incentives and penalties actually constitute the governments’ revenues or expenditures, and high incentives and penalties can shorten the time it takes for local governments to choose “positive operation” and for the central government to choose “decentralization”. Given the strong coupling of political centralization and fiscal decentralization, the central government should restructure the incentive mechanism for local officials in both political and fiscal regards. First, political performance appraisal should incorporate soft elements of TIOM, such as service quality and social satisfaction, to encourage the intrinsic motivation of local officials with political promotions. Second, the central government should establish strict and effective incentive and restraint mechanisms to strengthen its administrative intervention in jurisdictions with less-developed economies and to guide the strategies of local governments to move quickly toward “positive operation”. Finally, given that the high costs of obtaining information may lead to a low level of willingness on the behalf of the central government to regulate local governments, broad channels of public supervision should be established to reduce the costs to the central government while constraining the power exercised by local governments.

• (3) Inter-jurisdictional heterogeneity in regard to the benefits and costs of TIOM is the determinant that divides the strategic choices of local governments. Specifically, when local governments are competitive in terms of revenues, costs, and the supply of transport infrastructure, they are more likely to choose “positive operation”. When local governments are unable to establish a competitive edge, but “positive operation” is still a profitable investment, the strategic trajectories of local governments will converge toward “positive operation” at a slower rate. The key to encouraging local governments to choose “positive operation” is enhancing their own cost advantages and competitiveness. Therefore, regions with underdeveloped economies should optimize their industrial and economic development strategies to resolve the problem of serious shortages in the demand for transport services and to forge a positive feedback loop between economic development and transport industry. Regions with relatively developed economies should promote the construction of a comprehensive transport system and improve the quality of transport services to meet the individual needs of the public. Moreover, central authorities must implement regionally differentiated fiscal decentralization policies that align with local economic statuses and developmental demands, which prioritize resource efficiency while providing underdeveloped jurisdictions with targeted financial allocations and technological capacity-building programs.

• (4) In the asymmetric interactions among geographically neighboring jurisdictions when operating and maintaining transport infrastructure, there is a “race to the top” competition, where the pursuit for capital and labor among local governments that prefer high-quality environments enables them to reject “free-rider” strategies. The development of differentiated financial support systems helps to adapt the central–local fiscal relationship to the actual conditions of different jurisdictions, such as economic development, market changes, government capacity, public demand, and traffic conditions, achieving a dynamic balance in the fiscal relationship and equalizing transport services. First, local governments themselves should internalize the spillovers of transport infrastructure by adjusting their economic and industrial development policies to attract more high-quality production factors. Second, levy a portion of gains from provinces attracting production factor inflows through efficient TIOM to compensate jurisdictions experiencing outflows, thereby preventing siphoning effects. Third, develop and scale public-private partnership (PPP) models that incentivize private capital participation in TIOM within underdeveloped regions, alleviating fiscal burdens while simultaneously promoting regional equilibrium development.

Although this study conducts numerical simulations for Guangdong and Guangxi, the strategic interdependencies between central and local governments revealed are not confined to these provinces. By adjusting parameter values to reflect provincial characteristics, similar patterns emerge: for instance, higher fiscal dependency in underdeveloped regions necessitates stronger incentives to drive positive strategies, whereas pronounced spillovers in metropolitan core cities amplify competitive dynamics. Therefore, our findings exhibit generalizability, offering actionable insights for policy design across diverse jurisdictions. Furthermore, in countries with comparable fiscal decentralization structures (e.g., USA and Germany), decision-making patterns regarding TIOM align with those observed in China. While institutional frameworks and socioeconomic contexts vary, the model’s insights on spillovers, intergovernmental competition, and fiscal coordination mechanisms demonstrate universality. Integrating local contexts into simulations, the stochastic evolutionary game model developed in this study offers valuable references for understanding governance dynamics and policy design in these countries.

There are also some limitations and issues that need to be further studied. First, only the central–local fiscal relationship is considered in this paper but, in practice, TIOM also involves more stakeholders, such as different administrative departments, enterprises, and the public. Future studies could develop more extensive and complex models in order to discuss the interactions between these stakeholders. Second, although this paper analyzes the spillover effects of transport infrastructure, future research could further enhance the model by incorporating additional parameters or functions that capture the distinctive characteristics of transportation infrastructure. This includes incorporating critical decision-influencing factors such as informal cooperation, governmental technical capacity, media oversight, and geographical constraints. This would enable the model to more comprehensively reflect the complexities of fiscal relations within TIOM, thereby offering policymakers a more precise foundation for decision-making. Third, this study has certain limitations in data availability, model simplifications, and methodological choices. For instance, incomplete data coverage in certain domains may prevent game-theoretic models from fully capturing all influencing factors. Simultaneously, assumptions made to streamline analytical complexity might constrain the generalizability and applicability of the findings. Future research should prioritize securing more reliable data sources and exploring refined modeling approaches to enhance the robustness of conclusions.