Introduction

According to the ground transportation carbon emissions data from the Global Carbon AtlasFootnote 1, China’s transportation sector is experiencing a significant increase in carbon emissions from 2020 to 2024. China’s 13th Five-Year Plan aims to achieve carbon peaking by 2030. However, based on the current carbon emission trends, the public transportation sector is projected to reach its carbon peaking target only by 2035. Globally, among different modes of transportation, private cars account for approximately 45% of carbon emissions, heavy-duty vehicles contribute about 20%, and public transportation has a relatively lower share (Wang et al. 2023). The carbon emissions from private cars are significantly higher than those from public transportation. To accelerate the achievement of China’s carbon peaking goal by 2030 and carbon neutrality by 2060 (Li et al. 2023; Hou et al. 2024).

To prevent the transportation system from becoming the country’s largest carbon sink, considerations should be given to gradually shifting public travel modes from private cars to public transportation systems, thereby alleviating the pressure on carbon emissions in the transportation sector. Additionally, renewable energy manufacturers should be encouraged to strengthen technological research and development, particularly in HFCV, to accelerate the process of energy transition in public transportation. Furthermore, the public transportation industry should seize the opportunity of energy integration and upgrading, adjust its revenue structure, strengthen cooperation with the renewable energy industry, and ensure sustainable development of the sector (Sun et al. 2022; Sisan et al. 2022).

In summary, to achieve decarbonization goals, the focus should be on the following three aspects:

Firstly, the public transportation industry should establish cooperative relationships with new energy manufacturers to jointly address the existing technical challenges of HFCV.

Secondly, OPTE (assuming it refers to a relevant organization or authority in charge of energy policy and transportation) should clarify its energy adjustment strategy and allocate a reasonable proportion of HFCV among fossil fuel vehicles (FFV) and battery electric vehicles (BEV). Simultaneously, appropriate adjustments should be made to the industry’s revenue structure to reduce the dependence of public transportation revenue on bus fares.

Thirdly, in the post-pandemic era, price and green emotional value have become significant factors influencing public decision-making (Long et al. 2022). To guide the public’s travel choices to gradually shift from private cars to public transportation systems, changes in consumer behaviour resulting from the post-pandemic era need to be considered in the overall research.

This study focuses on the impact of hydrogen energy application and changes in consumer behaviour in the post-pandemic era on carbon reduction in the public transportation industry. Previous research has explored carbon reduction strategies in the transportation industry from aspects such as energy selection for buses, vehicle scheduling, enterprise operations (Wu et al. 2023; Coppitters et al. 2022), policy constraints, and public awareness (Chen et al. 2019). From the perspective most conducive to sustainable development of the industry, this paper selects hydrogen energy, which has the lowest carbon emissions, as a key strategy for low-carbon reform. Additionally, it examines the technological development of upstream renewable energy suppliers, the energy transformation strategies of OPTE in the middle of the supply chain, and the acceptance level of HFCV public transportation among downstream consumers in the post-pandemic era.

Energy Structure Adjustment in the Public Transportation Industry

The global carbon emission landscape has undergone some changes post-pandemic. China continues to rank first in emissions, accounting for 34% of global carbon dioxide emissions, while the United States and India take the second and third spots respectively. Following the pandemic, various industries in China have made positive progress in emission reduction, but challenges still remain (Song et al. 2025; Zhang et al. 2024; Krantz et al. 2022; Chen et al. 2022; Zou et al. 2022; Balsa-Barreiro et al. 2019). As China is still in the midst of economic transformation, the overall carbon emission base is large and the increment is significant, making energy structure transformation essential for changing this status quo in relevant industries. During the initial period of the 14th to 15th Five-Year Plans, the power industry will contribute to stabilizing total carbon dioxide emissions by adjusting power generate on methods for carbon reduction. The steel, cement, transportation, and petrochemical industries, which have relatively slower emission reduction rates, could help achieve dual goals of economic growth and carbon emission control if they double their carbon reduction speeds during the 14th Five-Year Plan period. Essentially, the realization of emission reduction targets in the public transportation industry is an “energy revolution” (Lu et al. 2017). Energy structure adjustment can promote industry-wide emission reduction from the root and serve as a guarantee for sustainable industry development. Expanding the use of low-carbon and zero-carbon energy sources is crucial for achieving future carbon peaking and carbon neutrality goals in the industry (Rose and Neumann, 2020).

Several scholars have conducted comparative analyses of different energy sources used in public transport vehicles, seeking stable alternatives to traditional fossil fuels (Depren et al. 2022; (Li and Kimura, 2021; Hensher et al. 2022; Wang et al. 2018). From a global perspective, electric buses are widely used in the public transport industry and are becoming the mainstream choice for city buses). There is also a relatively large amount of research on the emission reduction effectiveness of electric buses. Compared to other clean energy sources, electric power has the advantage of relatively mature technology, easy access to energy, and the ability to effectively control carbon emissions. However, further research is needed on battery range, charging station locations, and long-distance transport. The use of bioenergy, hybrid power, and electric power as power sources for buses can produce significant emission reductions compared to fossil fuels, but to achieve zero carbon emissions, hydrogen energy is needed. The chemical reaction product of hydrogen fuel cells is water, which is completely harmless to the environment. Hydrogen is one of the most effective energy carriers, with an energy density of up to 39.39 kWh/kg, exceeding that of most batteries. Hydrogen fuel cells can not only solve the problem of excessive pollution from traditional fossil fuel vehicles but also overcome the disadvantages of long charging times for electric vehicles. Therefore, hydrogen is an ideal choice for future transport fuel.

Life Cycle Assessment (LCA) of Carbon Emissions for HFCV

HFCV can offer higher environmental benefits compared to fossil FFV and BEV. The LCA assessment of HFCV should encompass four key stages: hydrogen production pathways, hydrogen transportation, hydrogen storage at fuelling stations, and fuel cell recycling. Among these, selecting cleaner hydrogen production pathways is crucial for controlling both the economic and carbon emission costs of HFCV (Teng et al. 2024).

The primary method for producing hydrogen is through coal gasification hydrogen (CGH), while approximately 32% of hydrogen is produced as an industrial byproduct, 12% through methane pyrolysis, and only a small amount is produced through water electrolysis. Comparing LCA hydrogen production routes from different studies and contrasting them from the perspective of carbon emission costs, CGH and grid-based hydrogen electrolysis have the highest carbon emission costs, followed by industrial byproduct production, methane pyrolysis, and coke oven gas hydrogen (COGH) (Muhammad and Ibrahim, 2024; Naser and William, 2023; Li et al. 2024; Hyejeong et al. 2024; Rui et al. 2024). The lowest carbon emission costs are associated with nuclear energy and bio-renewable energy sources (such as wind, water, etc.) (Sadeghi and Ghandehariun, 2023; Zhang et al. 2023). The carbon emissions generated from hydrogen energy production vary across different production pathways. While CGH technology is relatively mature and can achieve large-scale hydrogen production, from a sustainability perspective, HFCV utilizing nuclear energy and bio-renewable energy for hydrogen electrolysis can provide higher environmental benefits (Adem and Semiha, 2020; Ji et al. 2023).

Challenges facing hydrogen energy reform in ground transport sector

Enterprises can contribute to reducing carbon emissions in the industry through technological reforms. However, due to the immaturity of HFCV technology (Yang et al. 2023), its high R&D costs, and safety issues related to the combustibility of hydrogen, HFCV have high operating and management costs. Currently, electric vehicle batteries have insufficient range to meet long-distance transport needs. Therefore, the current solution is to use traditional fuel vehicles on long-distance routes, while using electric vehicles on shorter routes to compensate for the lack of range of electric vehicles.

Upstream manufacturer research and development

For renewable energy manufacturers, there are still numerous technical aspects of HFCV that require improvement, and cost issues pose a major obstacle to the development and application of HFCV technology (Mancino et al. 2023).

Considering economic costs, the economic cost of HFCV is higher than that of BEV, primarily due to the relatively high production and research and development costs of HFCV fuel cells. Proton exchange membrane fuel cells (PEMFC), which are relatively mature and have high safety, require advancements in key component manufacturing technologies to reduce manufacturing costs. Solid oxide fuel cells (SOFC), which have an energy utilization rate of up to 85%, can effectively reduce costs through the use of metal-supported cells (Fang et al. 2024).

However, when considering the cost of carbon emissions, the carbon emission cost of HFCV is much lower than that of BEV. HFCV offer advantages such as high mileage, fast charging times, strong cold-start capabilities, quiet operation, continuous energy supply, and zero carbon emissions. Specifically, manufacturers need to master key technologies such as fuel cell stacks, hydrogen storage tanks, cooling control systems, and direct current to direct current (DCDC) converters to promote the application of HFCV in the industry (Zhou et al. 2023). Due to the immaturity of the technology, manufacturers will face certain research and development risks in the R&D process.

The improvement of technology can expand the application range of HFCV. Currently, the application of renewable energy in the private car sector has brought significant benefits to renewable energy manufacturers, but its application in the public transportation market is insufficient. In an era of increasing public awareness of sustainability and environmental protection, hydrogen energy reform presents a rare opportunity for both manufacturers and the public transportation industry.

Midstream OPTE reform

In the context of carbon trading policies, when enterprises undergo reforms, they need to consider various economic factors such as their carbon quota, market carbon trading prices, carbon taxes, reform costs, and operational profits. Among them, carbon quotas, carbon trading prices, and carbon taxes depend on market changes and government regulation, which are difficult for enterprises to control. Reform costs depend on the choice of technology reform solutions. Operational profits are closely related to the choice of enterprise pricing strategy, and ticket prices are the main factor affecting whether consumers choose low-carbon travel (He et al. 2019). The pricing strategies of public transport enterprises vary depending on their operating nature.

For OPTE, low-price strategies with excessive public welfare have a limited impact on stimulating the public to choose low-carbon transportation and also make it difficult to ensure the profitability of public transportation enterprises (Kholodov et al. 2021). OPTEs with less public welfare and a smaller government participation ratio in public transportation operations often adjust their bus pricing in response to changes in external factors such as fuel prices and carbon trading prices. For example, Europe’s energy crisis (including oil, electricity, etc.) can affect bus prices, with most of the resulting surcharges borne by the public.

In summary, carbon quotas, carbon prices, the scale of adoption, and pricing strategies are all critical factors influencing OPTEs’ energy transformations. Finding a reasonable operational strategy that meets both social welfare and their own profitability is a key challenge facing OPTE. During the period of energy structure adjustment, if OPTE can seize the opportunity to adjust their revenue structure, strengthen cooperation with the new energy industry, and reduce dependence on ticket prices, it will greatly benefit their long-term development (Wang et al. 2023).

Downstream consumer acceptance

Existing studies have found that the factors influencing consumer acceptance of HFCV are mainly economic factors such as public transport fares, government subsidies, convenience of travel, safety, and carbon taxes, from the perspective of consumers (Loría et al. 2019; Wang et al. 2022; Adu-Gyamfi et al. 2023; Yu et al. 2020). During the COVID-19 pandemic, significant dynamic changes occurred in the market, which had a crucial impact on the downstream consumers’ evolving needs and preferences in the industry supply chain. The rapid perception of these changes becomes essential for decision-making among the upstream participants in the supply chain and for ensuring the overall resilience of the entire supply chain (Klöckner et al. 2023). AccentureFootnote 2 conducted a survey on changes in consumer behaviour after the COVID-19 epidemic, involving more than 3000 consumers in 15 countries. The survey results show that the COVID-19 pandemic may create a more sustainable and healthy consumption era, and this trend of development can cause permanent changes in consumer behaviour and persistent market structure changes for products and industries over the next decade. Therefore, when studying the implementation plan for carbon reduction in ground transport sector, attention should be paid to some changes in consumer behaviour after the COVID-19 epidemic (Loaiza-Ramírez et al. 2022). The restrictions on population mobility during the COVID-19 pandemic and changes in daily habits have led to increased depression, loneliness, and fear in consumers when facing some issues (Alsukah et al. 2020; Mehta et al. 2020). When facing environmental issues, they will have a stronger sense of moral responsibility. Existing research on consumer decision-making regarding new energy vehicles in the supply chain has mostly considered economic benefits or convenience from the consumer’s perspective, but lacks analysis of changes in consumer consumption preferences (Harichandan and Kar, 2023). Therefore, considering non-economic factors in the model when studying carbon reduction after the COVID-19 epidemic will make the conclusions more persuasive.

Compared with existing research, this article chooses hydrogen energy reform as the main means to achieve carbon reduction in ground transport sector, which can fundamentally solve the problem of difficult control of carbon emissions in the industry. A three-party evolutionary game model is established for manufacturers, OPTE, and consumers to analyze the decision-making changes that occur among the three parties during hydrogen energy reform. The article also innovatively considers some non-economic factors of consumers in the model, and effective conclusions on achieving the industry’s decarbonization goals are drawn based on experimental results.

Methods

Model Description

The three parties involved in the game are OPTE, manufacturers, and consumers, all of whom have limited rationality. Therefore, the initial choices made by the three parties are not optimal strategies, and it is necessary to adjust their strategies over time to achieve the optimal state. As shown in Fig. 1, OPTE’s strategy choices are reform and no reform. Reform refers to a series of reforms in technology, pricing strategy, and system that OPTE carries out to achieve the industry’s emission reduction target as soon as possible. The strategy choices for HFCV manufacturers are R&D and no R&D. R&D refers to the hydrogen HFCV manufacturers choosing to innovate their technology to produce HFCV that use less carbon quota, but R&D requires a large amount of investment in the early stages and carries a certain research risk. No R&D means that manufacturers remain at their current level and do not produce low-carbon emission vehicles. The strategy choices for consumers are to choose or not to choose. Choosing means that consumers, influenced by compensation psychology and carbon taxes, are willing to pay a certain premium to actively choose to ride in HFCV with lower carbon emissions, while not choosing means that consumers do not choose HFCV with lower carbon emissions as a means of public transport.

Fig. 1
figure 1

Three-party game diagram.

Full size image

Assumption 1: The quality of the two types of cars before and after carbon emissions reduction is the same in terms of basic demand, and they can bring the same utility to OPTE in meeting its basic needs. The differences in aspects such as colour, interior, and exterior appearance do not affect the decision-making of OPTE and consumers in choosing cars.

Assumption 2: The probability that the HFCV manufacturer chooses to conduct R&D is x, and the probability of choosing not to conduct R&D is \(1-x\); the probability that OPTE chooses to implement low-carbon reforms is y, and the probability of choosing not to implement low-carbon reforms is \(1-y\); the probability that consumers choose low-carbon transport is z, and the probability of not choosing low-carbon transport is \(1-z\).

Assumption 3: The cost of not conducting R&D for the manufacturer is \(C\), and the revenue is P; the additional cost of conducting R&D for producing HFCV with lower carbon quota occupancy is \(\Delta C\), and the additional revenue is \(\Delta P\). \(a\) represents carbon quota, and the green environmental benefits obtained by the manufacturer at time \(t\) are \(A=a-a(t)\). A positive value of green environmental benefits means that the manufacturer has surplus carbon quota, which can be sold at the market carbon quota trading price to obtain more additional revenue. The green reputation boost obtained by developing low-emission cars is represented by G.

Assumption 4: The basic operating cost of OPTE without low-carbon reform is L, and the basic revenue obtained is M. The additional cost required for low-carbon reform is \(\Delta {L}_{1}\), and the cost incurred due to the manufacturer’s failure to develop lower-emission cars is \(\Delta {L}_{2}\). The additional revenue obtained after low-carbon reform is ∆M. The green reputation boost obtained is represented by G.

Assumption 5: The consumer group with compensation psychology chooses not to use HFCV for public transport, and the cost incurred is F, while the revenue obtained is Q. The additional premium paid for choosing HFCV for public transport due to compensation psychology is ∆F, while the additional revenue obtained from saving carbon tax is ∆Q. The subsidy obtained for choosing HFCV for transport is represented by S, and \(0\, <\, \alpha\, <\, 1\) represents the compensation psychology coefficient of consumers.

Based on the above assumptions, a three-party game matrix on low-carbon supply chain evolution is constructed among manufacturers, retailers, and consumers in the hydrogen fuel cell vehicle industry. The parameter comparison table for the three-party game model is shown in Table 1.

Table 1 Parameter comparison table of tripartite game evolution model.
Full size table

Derivation of Evolution Equation

Based on the variable settings and decision relationships of the three-party game model, the payoff matrix of the manufacturer, OPTE, and consumers was obtained, as shown in Table 2.

Table 2 Profit matrix of tripartite game.
Full size table

According to the three-party revenue matrix, the manufacturer can get the corresponding expected revenue function.

When HFCV manufacturers actively produce hydrogen fuel cell vehicles with lower carbon emissions, the expected revenue function is:

$${E}_{1}={E}_{11}+{E}_{12}+{E}_{13}+{E}_{14}=z\left(\Delta P+G\right)+\left(y-{yz}\right)\Delta P+P-C-\Delta C+A$$
(1)
$${E}_{11}={yz}\left(P+\Delta P-C-\Delta C+A+G\right)$$
(2)
$${E}_{12}=y\left(1-z\right)\left(P+\Delta P-C-\Delta C+A\right)$$
(3)
$${E}_{13}=\left(1-y\right)z\left(P+\Delta P-C-\Delta C+A+G\right)$$
(4)
$${E}_{14}=\left(1-y\right)\left(1-z\right)\left(P-C-\Delta C+A\right)$$
(5)

When new energy industry manufacturers do not produce hydrogen fuel cell vehicles with lower carbon emissions, the expected revenue function is:

$${E}_{2}={E}_{21}+{E}_{22}+{E}_{23}+{E}_{24}=\left({yz}-y-z\right)G+P-C$$
(6)
$${E}_{21}={yz}\left(P-C-G\right)$$
(7)
$${E}_{12}=y\left(1-z\right)\left(P-C-G\right)$$
(8)
$${E}_{13}=\left(1-y\right)z\left(P-C-G\right)$$
(9)
$${E}_{14}=\left(1-y\right)\left(1-z\right)\left(P-C\right)$$
(10)

The average expected revenue of the manufacturer is:

$$\bar{{E}_{A}}=x{E}_{1}+\left(1-x\right){E}_{2}$$
(11)

From this, the replication dynamic equation of manufacturers in the new energy industry is:

$$f\left(x\right)=\frac{{dx}}{{dt}}=x\left({E}_{1}-\bar{{E}_{A}}\right)=x\left(1-x\right)\left[\left(y-{yz}+z\right)\left(\Delta P+G\right)+{zG}-\Delta C+A\right]$$
(12)

The partial derivative of the replicated dynamic equation of the probability that manufacturers in the new energy industry choose to produce hydrogen fuel cell vehicles with lower carbon emissions can be obtained:

$$\frac{{df}(x)}{{dt}}=\left(1-2x\right)\left[y\left(1-z\right)\left(\Delta P+G\right)+z\Delta P+2{zG}-\Delta C+A\right]$$
(13)

According to the stability theorem of differential equations, in order for the HFCV manufacturer to choose to produce hydrogen fuel cell vehicles with lower carbon emissions and maintain a stable state, certain conditions need to be met:\(f(x)=0\) and \(\frac{{df}(x)}{{dt}} < 0\). So when \(y=\frac{-z\Delta P-2{zG}+\Delta C-A}{(1-z)(\Delta P+G)}\), \(\frac{{df}(x)}{{dt}}\equiv 0\), \(f\left(x\right)\equiv 0\). At this time, all x are stable. When \(y > \frac{-z\Delta P-2{zG}+\Delta C-A}{(1-z)(\Delta P+G)}\),\(f(x)\, >\, 0\), take x = 1 as the manufacturer’s evolutionary stable strategy. When \(y < \frac{-z\Delta P-2{zG}+\Delta C-A}{(1-z)(\Delta P+G)}\), \(f(x)\, <\, 0\).take x = 0 as the manufacturer’s evolutionary stable strategy. The phase diagram of the evolution of manufacturers’ strategies is shown in Fig. 2.

Fig. 2
figure 2

Manufacturer strategy evolution phase diagram.

Full size image

Similarly, according to the three-party revenue matrix, we can get the OPTE corresponding expected revenue function.

When OPTE actively carries out low-carbon reforms to reduce industry carbon emissions, the expected revenue function is:

$${E}_{3}={E}_{31}+{E}_{32}+{E}_{33}+{E}_{34}=z\left(\Delta M+G-\Delta {L}_{2}\right)-{xz}\Delta {L}_{2}+M-L-\Delta {L}_{1}$$
(14)
$${E}_{31}={xz}\left(M+\Delta M-L-\Delta {L}_{1}+G\right)$$
(15)
$${E}_{32}=x\left(1-z\right)\left(M-L-\Delta {L}_{1}\right)$$
(16)
$${E}_{33}=\left(1-x\right)z\left(M+\Delta M-L-\Delta {L}_{1}-\Delta {L}_{2}+G\right)$$
(17)
$${E}_{34}=\left(1-x\right)\left(1-z\right)\left(M-L-\Delta {L}_{1}\right)$$
(18)

When OPTE not actively carries out low-carbon reforms to reduce industry carbon emissions, the expected revenue function is:

$${E}_{4}={E}_{41}+{E}_{42}+{E}_{43}+{E}_{44}=z\left(-G-\Delta {L}_{2}\right)+{xz}\Delta {L}_{2}+M-L$$
(19)
$${E}_{41}={xz}\left(M+-L-G\right)$$
(20)
$${E}_{42}=x\left(1-z\right)\left(M-L\right)$$
(21)
$${E}_{43}=\left(1-x\right)z\left(M-L-\Delta {L}_{2}-G\right)$$
(22)
$${E}_{44}=\left(1-x\right)\left(1-z\right)\left(M-L\right)$$
(23)

The average expected revenue of the OPTE is:

$$\bar{{E}_{B}}=y{E}_{3}+(1-y){E}_{4}$$
(24)

From this, the replication dynamic equation of OPTE is:

$$f\left(y\right)=\frac{{dy}}{{dt}}=y\left({E}_{3}-\bar{{E}_{B}}\right)=y\left(1-y\right)\left(2{zG}-\Delta {L}_{1}\right)$$
(25)

The partial derivative of the replicator dynamic equation for the probability of OPTE actively carrying out low-carbon reforms and reducing industry carbon emissions can be obtained.

$$\frac{{df}(y)}{{dt}}=\left(1-2y\right)\left(2{zG}-\Delta {L}_{1}\right)$$
(26)

According to the stability theorem of differential equations, in order for OPTE to choose to actively carry out low-carbon reforms, reduce industry carbon emissions, and remain in a stable state, certain conditions need to be met: \(f(y)=0\) and \(\frac{{df}(y)}{{dt}} < 0\). So when \(z=\frac{\Delta {L}_{1}}{2G}\), \(\frac{{df}(y)}{{dt}}\equiv 0\), \(f(y)\equiv 0\), all y = 0 is the OPTE evolutionarily stable strategy. The phase diagram of OPTE strategy evolution is shown in Fig. 3.

Fig. 3
figure 3

HFCV strategy evolution phase diagram.

Full size image

Similarly, the expected revenue function of consumers can be obtained according to the tripartite revenue matrix.

When consumers in the new energy industry actively choose hydrogen fuel cell vehicles with lower carbon emissions, the expected revenue function is:

$${E}_{5}={E}_{51}+{E}_{52}+{E}_{53}+{E}_{54}=Q+\Delta Q-F-\Delta F+\left. (y-{xy}\right)S$$
(27)
$${E}_{51}={xy}\left(Q+\Delta Q-F-\Delta F+S\right)$$
(28)
$${E}_{52}=x\left(1-y\right)\left(Q+\Delta Q-F-\Delta F\right)$$
(29)
$${E}_{53}=\left(1-x\right)y\left(Q+\Delta Q-F-\Delta F+S\right)$$
(30)
$${E}_{54}=\left(1-x\right)\left(1-y\right)\left(Q+\Delta Q-F-\Delta F\right)$$
(31)

When consumers do not choose HFCV with lower carbon emissions, the expected revenue function is:

$${E}_{6}={E}_{61}+{E}_{62}+{E}_{63}+{E}_{64}=Q-F$$
(32)
$${E}_{61}={xz}\left(Q-F\right)$$
(33)
$${E}_{62}=x\left(1-z\right)\left(Q-F\right)$$
(34)
$${E}_{63}=\left(1-x\right)z\left(Q-F\right)$$
(35)
$${E}_{64}=\left(1-x\right)\left(1-z\right)\left(Q-F\right)$$
(36)

The average expected revenue of consumers is:

$$\bar{{E}_{C}}=z{E}_{5}+\left(1-z\right){E}_{6}$$
(37)

From this, the replication dynamic equation of consumers in the new energy industry is:

$$f\left(z\right)=\frac{{dz}}{{dt}}=z\left({E}_{3}-\bar{{E}_{B}}\right)=z\left(1-z\right)\left[\Delta Q-\Delta F+\left(y-{xy}\right)S\right]$$
(38)

The partial derivative of the replicated dynamic equation of the probability that manufacturers in the new energy industry choose to produce hydrogen fuel cell vehicles with lower carbon emissions can be obtained:

$$\frac{{df}(y)}{{dt}}=\left(1-2y\right)\left[\Delta Q-\Delta F+\left(y-{xy}\right)S\right]$$
(39)

According to the stability theorem of differential equation, we can see that consumers in the new energy industry who choose HFCV with lower carbon emissions and are in a stable state need to satisfy: \(f(z)=0\),\(\frac{{df}(z)}{{dt}}\, <\, 0\). So when \(y=\frac{\Delta F-\Delta Q}{(1-x)S},\frac{{df}(y)}{{dt}}\equiv 0,f(y)\equiv 0\), all z are stable. When \(y\, >\, \frac{\Delta F-\Delta Q}{(1-x)S}\), \(f(z) > 0\), z = 1 is the evolutionary stable strategy of consumers, and when \(z < \frac{\Delta F-\Delta Q}{(1-x)S}\), \(f(z)\, <\, 0\), z = 0 is the evolutionary stable strategy of consumers. The phase diagram of consumers’ strategy evolution is shown in Fig. 4.

Fig. 4
figure 4

Consumers strategy evolution phase diagram.

Full size image

Combining the above replication dynamic equations, the replication dynamic equations of the tripartite evolutionary game can be obtained:

$$f(u)=\left\{\begin{array}{c}f(x)=x(1-x)[(y-{yz}+z)(\Delta P+G)+G-\Delta C+A]\\ f(y)=y(1-y)(2{zG}-\Delta {L}_{1})\\ f(z)=z(1-z)[\Delta Q-\Delta F+(y-{xy})S]\end{array}\right.$$
(40)

Analysis of Model Stability

The equilibrium solution of the three-party evolutionary game model can be obtained by solving the replicated dynamic equations. According to the Lyapunov criterion, in a linear constant system, all eigenvalues are non-positive and stable. If there is an eigenvalue greater than zero, or there is a zero multiple root, it is unstable. In the asymmetric evolutionary game, we can consider the stability of pure strategy equilibrium, so we only need to discuss the stability of 8 equilibrium points, and the equilibrium points and eigenvalues are shown in Table 3.

Table 3 Equilibrium point and eigenvalue.
Full size table

The Jacobian matrix can be constructed by taking partial derivatives of the three replicator dynamics equations as follows:

$$J=\left[\begin{array}{ccc}\frac{{df}(x)}{{dx}} & \frac{{df}(x)}{{dy}} & \frac{{df}(x)}{{dz}}\\ \frac{{df}(y)}{{dx}} & \frac{{df}(y)}{{dy}} & \frac{{df}(y)}{{dz}}\\ \frac{{df}(z)}{{dx}} & \frac{{df}(z)}{{dy}} & \frac{{df}(z)}{{dz}}\end{array}\right]=\left[\begin{array}{ccc}{j}_{11} & {j}_{12} & {j}_{13}\\ {j}_{21} & {j}_{22} & {j}_{23}\\ {j}_{31} & {j}_{32} & {j}_{33}\end{array}\right]$$
(41)
$${j}_{11}=\left(y-{yz}+z\right)\left(\Delta P+G\right)-2a\left(y-{yz}+z\right)\left(\Delta P+G\right)$$
(42)
$${j}_{12}=x\left(1-x\right)\left(1-z\right)\left(\Delta P+G\right)$$
(43)
$${j}_{13}=x\left(1-x\right)\left(1-y\right)\left(\Delta P+G\right)$$
(44)
$${j}_{21}=0$$
(45)
$${j}_{22}=\left(1-2y\right)\left(2{zG}-\Delta {L}_{1}\right)$$
(46)
$${j}_{23}=2{Gy}\left(1-y\right)$$
(47)
$${j}_{31}=-{Syz}\left(1-z\right)$$
(48)
$${j}_{32}=S\left(1-x\right)z\left(1-z\right)$$
(49)
$${j}_{33}=\left(1-2z\right)\left[\Delta Q-\Delta F+\left(y-{xy}\right)S\right]$$
(50)

According to the first Lyapunov method, when the eigenvalues of the Jacobian matrix satisfy the real part equals or lesser than 0, the equilibrium solution is stable. At the same time, considering that in the whole simulation model, the evolution process of the three-party strategy depends on the exogenous variables in the model, when the exogenous variables change, the strategy choice of the three parties will also change. Through the mathematical calculation of the eigenvalues corresponding to each equilibrium solution of the matrix, it can also be found that when each parameter variable changes, the stable state of the evolutionary game model’s equilibrium solution will also change. Different situations are divided aaccording to the eigenvalues of each equilibrium point in Table 4.

Table 4 Stable point equilibrium analysis.
Full size table

For simplicity and generality of stability analysis, initial parameters \(\Delta P+2G-\Delta C+A\, <\, 0,\Delta Q-\Delta F\, <\, 0\) are set.

Proposition 1 is set to \(2G-\Delta {L}_{1}\, <\, 0\), proposition 2 is set to \(2G-\Delta {L}_{1}\, >\, 0\). The stable equilibrium analysis corresponding to the two cases is shown in Table 4. The rest of the cases are the same, and only the value range of each parameter needs to be changed.

Proposition 1: According to the equilibrium analysis of Jacobian matrices, when the value of the double goodwill gain obtained by OPTE is less than the additional cost of low-carbon reform investment, the equilibrium points (0, 0, 0), (1, 0, 0), and (1, 1, 0) have all negative real parts of eigenvalues. Thus, the three evolutionary stable strategies are (no R&D, no reform, no selection), (R&D, no reform, no selection), and (R&D, active reform, no selection), as shown in the evolutionary stable phase diagram in Fig. 5. The points (0, 0, 1), (1, 0, 1), and (1, 1, 1) have one or more eigenvalues that are not negative, which means they are a saddle point of the system.

Fig. 5
figure 5

Proposition 1 Evolutionary stable phase diagram.

Full size image

Explanation 1: Under the constraint of Proposition 1, the first ESS of the manufacturer, OPTE, and the consumer is (0, 0, 0) (no R&D, no reform, no selection), which is a bad stable state and not the issue we want to investigate. The second ESS is (1, 0, 0) (R&D, no reform, no selection), which generally occurs in the early stage of HFCV R&D, where a large amount of infrastructure construction is required, and OPTE’s low-carbon reform poses a high risk. Moreover, consumers have limited knowledge of HFCV and are less willing to choose them. At this stage, due to OPTE’s short-sighted behaviour, it tends to choose a no-reform strategy, focusing only on the current construction cost rather than the long-term increase in green goodwill value. Consumers generally do not choose hydrogen fuel cell vehicles, which emit less carbon, because they are not familiar with them. According to the random values set for the stable point, the simulation verification shows that (1, 0, 0) is a reliable ESS for Proposition 1. The third ESS is (1, 1, 0) (R&D, reform, no selection). In this case, the manufacturer and OPTE are aware of the importance of green goodwill value and take the initiative to reduce carbon quotas and emissions. However, due to the high cost of R&D and production, and the high initial construction costs, consumers are faced with too much product premium or insufficient subsidies, leading to a decision of not choosing HFCV. This stable point reduces the enthusiasm of manufacturers to conduct R&D, which is not conducive to the development of HFCV and the green transformation of ground transport sector, and therefore, this situation is not discussed.

Proposition 2: Based on the analysis of the stable equilibrium points, when the value of the improved goodwill added to the environmental benefits exceeds the additional cost of R&D investment in HFCV manufacturing, the equilibrium points (0, 0, 0), (1, 0, 0), (0, 0, 1), (1, 1, 0), (1, 0, 1), and (1, 1, 1) correspond to Jacobian matrix eigenvalues with negative real parts. Therefore, the six evolutionarily stable strategies are: (not investing in R&D, passive reform, not choosing), (investing in R&D, passive reform, not choosing), (not investing in R&D, passive reform, choosing), (investing in R&D, active reform, not choosing), (investing in R&D, passive reform, choosing), and (investing in R&D, active reform, choosing). At this point, the stable phase diagram of the three-party evolutionary game is shown in Fig. 6.

Fig. 6
figure 6

Proposition 2 Evolutionary stable phase diagram.

Full size image

Explanation 2: The stable points studied in Proposition 2 exclude the stable points that are repeated in Proposition 1, and they are (0, 0, 1), (1, 0, 1), and (1, 1, 1). The point (0, 0, 1), (not investing in R&D, not reforming, choosing) indicates that consumers have an excessively compensatory mentality and will still choose HFCV green transport when manufacturers do not invest in manufacturing and retailers do not reform. This is a state with strong randomness that is not consistent with the real market situation, so it will not be discussed. The point (1, 0, 1), (investing in R&D, not reforming, choosing) is a bad state where the manufacturer has already invested a lot of costs in R&D and the consumers have a strong compensatory mentality and desire to choose, but the retailer chooses passive reform, which is not conducive to the green transformation of ground transport sector. Therefore, it will not be discussed. The point (1, 1, 1), (investing in R&D, reforming, choosing) generally occurs in the implementation stage of carbon quota system and the mid-term of the subsidy for low-carbon hydrogen fuel cell vehicles. Under the circumstance of OPTE’s active reform and excessive carbon emissions leading to environmental crisis, consumers’ willingness to choose HFCV travel has significantly increased, and they prefer low-carbon emission products. This situation can promote the green transformation of ground transport sector and accelerate the achievement of emission reduction goals. In-depth discussion of this situation was conducted, and with randomly set simulation values under the constraints of Proposition 2, it was verified that (1, 1, 1) is a reliable ESS of Proposition 2.

Simulation and Numerical Simulation

Simulation model

Parameter setting

Based on the above evolutionary game model, the system dynamics simulation model established by Vensim PLE 9.3.3 software is shown in Fig. 7.

Fig. 7
figure 7

System dynamics simulation overall model diagram.

Full size image

In the research on the direction of low-carbon reform in ground transport sector, the model focuses on three main entities: HCFV manufacturers, OPTE, and consumers. HCFV manufacturers can choose to innovate and invest in R&D to master the core technology of hydrogen fuel cells, which may result in certain government subsidies and long-term benefits. It can also enhance the company’s green reputation. OPTE in ground transport sector can choose to reform towards low-carbon development by implementing technological, pricing, and institutional reforms to reduce carbon quotas and earn profits in the carbon trading market while also assisting the industry in achieving carbon reduction goals. Consumers are influenced by carbon taxes, premium pricing for new technology R&D, and compensation psychology, which can affect their decision to choose low-carbon travel methods. Consumer decisions can significantly impact the low-carbon reform in the entire public transport industry and change the industry’s environment.

The dynamic simulation model of the tripartite evolution game system of the OPTE low-carbon reform in ground transport sector sets up the functional relationships between various variables based on the evolutionary game model. In the system dynamics simulation model, the manufacturers, OPTE, and consumers correspond to the six expected revenue functions: \({E}_{1},{E}_{2},{E}_{3},{E}_{4},{E}_{5},{E}_{6}\), under their respective strategy selections. The three proportional changes of manufacturers, OPTE, and consumers under their respective strategy selections are equivalent to the tripartite replication dynamic equation set up in the evolutionary game model.

The proportion of low-carbon car R&D of manufacturers:

$$f\left(x\right)=x\left(1-x\right)\left({E}_{1}-{E}_{2}\right)$$
(51)

The proportion of low-carbon reform of OPTE:

$$f\left(y\right)=y\left(1-y\right)\left({E}_{3}-{E}_{4}\right)$$
(52)

The proportion of low-carbon travel choices of consumers:

$$f\left(z\right)=z\left(1-z\right)\left({E}_{5}-{E}_{6}\right)$$
(53)

Based on the data and numerical setting methods in 2022 China hydrogen fuel cell vehicle industry market status and development prospect analysis report and evolutionary game analysis of government subsidies and hydrogen fuel cell vehicle industry development system dynamics and the opinions of relevant experts in the hydrogen fuel cell vehicle industry, the parameters are initially assigned.

The initial assumptions are as follows: INITIAL TIME = 0, FINAL TIME = 15(or50), TIME STEP = 0.125, (x, y, z) = (0.01, 0.01, 0.01). The initial parameters for manufacturers, OPTE and consumers are as follows: \(C=5,\Delta C=4,P=6,\Delta P=4.5,A=3,G=2.5,L=\)6\(,\Delta {L}_{1}=2,\Delta {L}_{2}=2.5,M=\)5.5\(,\Delta M=\)5\(,F=10,\Delta F=2,Q=12,\Delta Q=4.5,S=3\).

By adding initial values to each variable in the established system dynamics model, the initial stable point of the three-party evolutionary game of the supply chain is obtained shown in Fig. 8.

Fig. 8
figure 8

Game tripartite initial stable point diagram.

Full size image

To ensure the validity of the initial parameter settings, a sensitivity analysis of the parameters related to the decision variable was conducted separately. The analysis results and the effectiveness of the parameter settings are presented in Fig. 9–11.

Fig. 9
figure 9

Sensitivity Analysis of Numerical Values Related to HFCV Manufacturers’ Variables.

Full size image
Fig. 10
figure 10

Sensitivity Analysis of Numerical Values Related to OPTE Variables.

Full size image
Fig. 11
figure 11

Sensitivity Analysis of Numerical Values Related to Consumer Variables.

Full size image

Case study

To validate the effectiveness of the model, we conducted experiments using real datasets sourced from the China Renewable Energy Industry ReportFootnote 3 and the Yutong Bus Market Research ReportFootnote 4. Detailed numerical settings and data references for the experiment are provided in Table 5.

Table 5 Numerical Settings and Sources for Case Study.
Full size table

The experimental results demonstrate the decision-making changes among the three parties involved in the game as shown in Fig. 12. This outcome clearly illustrates that the model can accurately capture the game relationships and the dynamic changes in decision-making among these three entities. This finding strongly supports the practical applicability of the model in real-world scenarios.

Fig. 12
figure 12

Changes in decision-making among the three parties under the case study.

Full size image

Consumer perspective

Adding non-economic benefits

Due to the impact of the COVID-19 epidemic in recent years, consumers’ attitudes towards environmental protection will be affected, and their sense of social ecological responsibility, climate depression, ecological anxiety, etc. will undergo varying degrees of changes. These changes cause consumers to not only focus on their own economic benefits but also on some non-economic benefits. Therefore, considering the quantification of consumers’ non-economic benefits in the model from the perspective of consumers will make the entire model more consistent with the current social situation affected by the COVID-19 epidemic, and the results obtained will have more practical significance. Assuming that the sense of social ecological responsibility, climate depression, and ecological anxiety of consumers are defined as Re, De, and Fe, respectively, the consumer benefit matrix is shown in Table 6.

Table 6 Overall payoff matrix for consumers.
Full size table

According to the consumer payoff matrix, the expected non-economic payoff function when consumers actively choose HFCV public transport is:

$${E}_{7}={E}_{71}+{E}_{72}+{E}_{73}+{E}_{74}=\mathrm{Re}-{De}-{Fe}$$
(54)
$${E}_{71}={xyRe}$$
(55)
$${E}_{72}=x\left(1-y\right)\mathrm{Re}$$
(56)
$${E}_{73}=\left(1-x\right){yRe}$$
(57)
$${E}_{74}=\left(1-x\right)\left(1-y\right)\mathrm{Re}$$
(58)

According to the consumer payoff matrix, the expected non-economic payoff function when consumers not choose HFCV public transport is:

$${E}_{8}={E}_{81}+{E}_{82}+{E}_{83}+{E}_{84}=-{De}-{Fe}$$
(59)
$${E}_{81}={xz}\left(-{De}-{Fe}\right)$$
(60)
$${E}_{82}=x\left(1-z\right)\left(-{De}-{Fe}\right)$$
(61)
$${E}_{83}=\left(1-x\right)z\left(-{De}-{Fe}\right)$$
(62)
$${E}_{84}=\left(1-x\right)\left(1-z\right)\left(-{De}-{Fe}\right)$$
(63)

Average Non-Economic Expected Benefit for Consumers:

$$\bar{{E}_{D}}=z{E}_{7}+\left(1-z\right){E}_{8}$$
(64)

Combining with the average expected economic benefits for consumers, we can see that the replicator dynamics equation for consumers at this time is:

$${\rm{f}}\left({\rm{z}}\right)=\frac{{\rm{dz}}}{{\rm{dt}}}={\rm{z}}\left({{E}_{4}-\bar{{E}_{C}}+E}_{7}-\bar{{E}_{D}}\right)=z\left(1-z\right)\left[\Delta Q-\Delta F+\left(y-{xy}\right)S+\mathrm{Re}+{De}+{Fe}\right]$$
(65)

After incorporating the aforementioned factors related to non-economic benefits for consumers into the model, a new system dynamics tripartite game model was obtained, as shown in Fig. 13.

Fig. 13
figure 13

A system dynamics simulation model for the tripartite evolutionary game of non-economic benefits among consumers.

Full size image

After model optimization, there is a certain impact on the initial stable state of the three decision-making parties. As can be seen from Figs. 12 to 14, the evolution step length for the three parties to reach a stable state change from (3.125, 6, 4) to (2.375, 5, 1.875).

Fig. 14
figure 14

Initial stable state of the three decision-making parties after model optimization.

Full size image

Numerical simulation

When studying the impact of non-economic factors on decision-making before and after the pandemic, it is imperative to ensure the holistic nature of the model and the uniformity of numerical values by comprehensively considering the combined effects of the pandemic on the relevant variables of three parties involved.

Before the pandemic, new energy manufacturers had already recognized the strategic significance of fuel cell technology development, while OPTE began actively advocating for low-carbon transformation. Simultaneously, the concept of low-carbon gradually penetrated the consumer group, sparking their initial awareness of low-carbon travel.

During the pandemic, under the dual pressure of increased economic burdens and potential supply chain disruptions, the motivation of new energy manufacturers and OPTE to advance low-carbon changes weakened. Conversely, consumers, due to heightened environmental awareness, further enhanced their demand for low-carbon travel.

Entering the post-pandemic era, with the gradual containment of the pandemic and steady economic recovery, the dual-edged sword effect of soaring travel demand and industry carbon emission pressures has become increasingly prominent. Against this backdrop, new energy manufacturers and OPTE have restarted and accelerated their pace of low-carbon transformation, with their willingness even surpassing pre-pandemic levels. Meanwhile, consumers’ awareness of low-carbon travel has also significantly increased.

Based on the analysis of these different pandemic stages, we have set simulation values, as shown in Table 7, to comprehensively reflect and deeply analyze the dynamic changes of the relevant variables before, during, and after the pandemic.

Table 7 Changes in numerical values across different pandemic periods.
Full size table

Based on the numerical values in Table 2, simulation modelling was conducted for the pre-pandemic, pandemic, and post-pandemic periods. The resulting changes in decision-making among the three parties involved in the evolutionary game during these different periods are depicted in Figs. 15–17.

Fig. 15
figure 15

Changes in decision-making among the three parties before the pandemic.

Full size image
Fig. 16
figure 16

Changes in decision-making among the three parties during the pandemic.

Full size image
Fig. 17
figure 17

Changes in decision-making among the three parties in the post-pandemic era.

Full size image

According to the chronological order, consumers’ sense of social and ecological responsibility continues to increase with the duration of the COVID-19 epidemic. Climate depression and ecological anxiety were most evident during the COVID-19 epidemic lockdown period, followed by the post-epidemic era, while these two emotions were not apparent before the COVID-19 epidemic. After the three sets of numerical simulations, the decision-making changes of consumers before and after the COVID-19 epidemic are shown in Fig. 18.

Fig. 18
figure 18

Consumer Decision Changes Before and After the COVID-19 epidemic.

Full size image

It can be seen that in the Fig. 18 consumers will quickly reach a stable point in the post-epidemic era, which is more inclined to choose hydrogen energy public transport. Therefore, in the post-epidemic era, due to the strengthening of consumers’ social and ecological responsibility, climate depression, and ecological anxiety, consumers will tend to choose more environmentally friendly ways of transport, such as hydrogen fuel cell public transport, which is more conducive to the green transformation and development of the entire public transport industry.

OPTE perspective

Technology reform

The main impact of technological reform on OPTE is the reduction in carbon quota usage, as the carbon quota used by hydrogen fuel cell vehicles is the carbon emission reduction quota, which is the amount of carbon dioxide emissions reduced by new energy vehicles compared to traditional fuel vehicles during use. Based on the proportion of new energy vehicles that companies are required to bear, they calculate the total carbon dioxide emissions that must be reduced, which is the total new energy vehicle carbon quota that companies must surrender. OPTE can meet the total carbon quota requirements by increasing the proportion of hydrogen fuel cell vehicles used or by purchasing surplus carbon quotas from other companies through the carbon emissions trading market. The formula for calculating carbon quotas for companies is as follows:

$$a=\mathop{\sum }\limits_{i=1}^{n}\left({a}_{x,i}\right)$$
(66)

a represents the total carbon dioxide emissions quota for the company, x represents the type of vehicle used, and n represents the total number of vehicles used.

The carbon emission of traditional chemical fuel vehicles is 16.25 kg/100 km, the carbon emission of pure electric vehicles BEV is 7.93 kg/100 km, and the carbon emission of HFCV is 0 kg/100 km. The current UN-recognized carbon quota trading price is 8 euros per ton, which is equivalent to RMB 60.39 per ton.

For OPTE, the carbon quotas for BEV and HFCV are calculated and compared based on a total usage of 100,000 units in ground transport sector. According to these, the article sets \({a}_{{BEV}}=7930{tC}{O}_{2}\).

In case 1, if no technological reform is carried out and the industry continues to use BEV as the mainstream vehicle, extra costs will be incurred to purchase additional carbon quotas from companies with surplus quotas, and there will be no need to invest in the cost of purchasing HFCV. In this scenario, \(\Delta {L}_{1}=2\), \(\Delta {L}_{2}=2.5\), and the additional revenue \(\Delta M\) decreases with time at a rate of \(s=0.01\), where t is measured in days and t ranges from 0 to 100.However, not carrying out technological reform will result in a reduction in the company’s green reputation value G = 1.5.

In case 2, a pilot technological reform is carried out, in which some regions use HFCV while other regions continue to use BCV. In this case, the manufacturer itself holds enough carbon quotas and does not need to purchase additional quotas, but there is an additional cost of \(\Delta {L}_{2}=\)4, due to the purchase of HFCV. The values related to HFCV are as follows: \(\Delta M=5\),\(G=2.5\).

In case 3, a comprehensive technological reform is carried out, in which a large number of HFCV are invested in and hydrogen infrastructure is constructed. The cost of investing in HFCV and infrastructure construction is \(\Delta {L}_{1}=3\),\(\Delta {L}_{2}=4\), respectively. The additional revenue value \(\Delta {\rm{P}}\) increases with time at a rate of 0.01, where t is measured in days and \(t\) ranges from 0 to 100. Since the remaining carbon quotas can generate additional revenue of 3.44 for companies, the additional revenue value is \(\Delta {M}_{0}+{st}+3.44\), and the green reputation value increases to 4.

Based on the analysis of Fig. 19, it can be concluded that under the three simulated scenarios, selecting Scenario 3, which involves comprehensive technological reform, will enable the OPTE enterprise to achieve a stable state more quickly. In the long run, choosing the comprehensive technological reform strategy will bring more economic benefits to OPTE and accelerate the industry’s decarbonization process.

Fig. 19
figure 19

OPTE Technology Reform Strategy Decision Change Chart.

Full size image

Pricing strategy reform

Pricing strategy mainly affects consumers’ decisions, OPTE’s revenue, and the sustainability of the industry’s future development. Common pricing strategies include cost-oriented pricing, competition-oriented pricing, demand-oriented pricing, profit-oriented pricing, and government-regulated pricing. Combining with the pricing methods of ground transport sector at home and abroad, this study chooses cost-oriented pricing, profit-oriented pricing, and government-regulated pricing for numerical simulation and comparative analysis, comparing the degree of influence of the three pricing methods on OPTE’s decision-making.

Cost-oriented pricing: The method used in cost-oriented pricing strategy is cost-plus pricing. This method aims to maximize the company’s own interests, but in a competitive environment, this method does not consider price demand elasticity. The price cannot be adjusted with market changes. If the pricing is too high, it will cause consumers to choose other types of transport. The pricing formula is as follows:

$${p}_{1}=L\left(1+\theta \right)$$
(67)

\({p}_{1}\) represents the fare without taxes under the cost-plus pricing method, L represents the average operating cost per vehicle of OPTE, and θ represents the profit margin.

The numerical simulation was conducted with \(\theta\)=0.25 and a total number of vehicles of 100,000. The resulting changes in OPTE are as follows:

$${p}_{1}=\frac{(L+\Delta {L}_{1}+\Delta {L}_{2})}{10}+\left(1+\theta \right)$$
(68)
$$M=5.5+L\times \left(1+0.25\right)-L$$
(69)
$$\Delta M=5+\left(\Delta {L}_{1}+\Delta {L}_{2}\right)\times \left(1+0.25\right)$$
(70)

Numerical simulations are as follows:\({p}_{1}=13.125\), \(M=7\), \(\Delta M6.125\), \(F=11.5\), \(\Delta F=3.325\).

Profit-oriented pricing strategy: The profit-oriented pricing strategy requires the use of Ramsey pricing, which, in the absence of an optimal solution, uses the theory of suboptimal prices to find the optimal price with the constraint of maximizing social welfare while ensuring that the enterprise obtains profits.

The objective function is:

$$\pi ={\int }_{0}^{Q}{p}_{2}(Q)d{Q}_{s}-L({Q}_{s})+\beta \{{p}_{2}({Q}_{s})\cdot {Q}_{s}-L({Q}_{s})\}$$
(71)

By taking the partial derivative of the objective function and rearranging, we get:

$${p}_{2}=\frac{{L}_{S}}{1-\frac{R}{\left|{E}_{s}\right|}}$$
(72)
$$R=\frac{\beta }{1+\beta }$$
(73)

\({p}_{2}\) is the price for the profit-oriented pricing method, \({Q}_{s}\) is the demand quantity, \({E}_{s}\) is the demand price elasticity index and \({E}_{s}=\frac{{p}_{2}}{Q}\frac{{dQ}}{d{p}_{2}}\), L means cost, \({L}_{S}\) is the marginal cost, R represents the Ramsey coefficient, Numerical simulations are as follows:\({L}_{S}=10.5\), \(1-\frac{R}{\left|{E}_{s}\right|}=0.78\), \({p}_{2}\approx 13.46\).

Government price regulation strategy: Marginal cost pricing is more appropriate for this strategy. Marginal cost pricing can balance the interests of consumers and OPTE, and the government has a strong public interest in providing low-priced services for passengers. The pricing formula is:

$${p}_{3}=\frac{d(L+\Delta {L}_{1}+\Delta {L}_{2})}{d{Q}_{s}}$$
(74)

At this price, OPTE obtains a profit of M = 6, ∆M = 5. For consumer, the expenditure is S = 4, F = 7, and the green reputation is improved by G = 4.

From the analysis of Fig. 20, it can be seen that the cost-oriented pricing strategy has a significantly worse effect compared to the other two strategies. On the other hand, the profit-oriented pricing strategy can help OPTE achieve a stable decision-making state faster. This pricing strategy ensures both OPTE’s own profits and maximizes social welfare as much as possible. It can meet the needs of both the Chinese government-led public transport model and the enterprise-led model in most European countries, producing better results.

Fig. 20
figure 20

Decision-making process of OPTE institutional reform strategy.

Full size image

Conclusions

The decarbonization of ground transport sector has always been a key concern, and in the post-pandemic era, a large number of consumers will turn to public transport, leading to a surge in industry carbon emissions. The reform of technology and pricing strategy by OPTE is an important means to solve the difficulty of industry decarbonization at this stage. This article constructs an evolutionary game model of the three main subjects in ground transport sector, namely OPTE, HFCV manufacturers, and consumers, in the context of cap-and-trade regulation. Starting from the consumer perspective, this study delves into the various dimensions of changes in consumers’ environmental attitudes in the post-pandemic era, the expected benefits of consumers in the model are divided into economic benefits and non-economic benefits. On this basis, from the perspective of OPTE, how to carry out low-carbon reform in a way that is more conducive to achieving the goals of industry carbon neutrality and peaking is analysed from two directions: technology and pricing strategy, to help the entire public transport industry achieve carbon reduction. The research results provide a reference basis for ground transport sector to achieve industry decarbonization. The following conclusions were drawn from the study:

Conclusion 1: In the post-pandemic era, consumers’ social ecological awareness has increased, and they experience a higher level of climate depression and ecological fear compared to before the pandemic. However, these non-economic factors are gradually decreasing and reaching a stable state. These factors continue to influence consumer decision-making and accelerate the speed at which consumers reach a stable decision point to choose to use HFCVs. This indicates that in the post-pandemic era, it is meaningful for OPTE to choose to introduce HFCVs for technological reform in companies and low-carbon reform in the public transportation industry. Moreover, compared to the pre-pandemic period, consumers are more receptive to this technological reform.

Furthermore, when all other conditions are equal, consumers making faster decisions also indicate an increased emphasis on non-economic benefits. They are willing to sacrifice certain economic gains to fulfil their non-economic benefits. The pricing strategy of OPTE is closely related to consumers’ economic benefits. Therefore, researching and reforming the pricing strategy of OPTE is of great significance. Profit-oriented pricing strategy reform enables OPTE to strike a balance between economic and non-economic benefits. It not only achieves a balance between consumers’ economic and non-economic interests but also ensures OPTE’s own economic benefits while meeting consumer demands and social welfare.

Conclusion 2: In the aspect of selecting technological reform strategies, choosing to strengthen infrastructure construction and conduct comprehensive technological reform will accelerate the attainment of the stable decision point for OPTE reform. The process of model simulation quantifies carbon quotas into the model, and the more economic benefits OPTE obtains from carbon quotas, the greater its contribution to carbon emissions reduction. In the current situation, public transportation in most countries and regions mainly relies on battery electric vehicles with a small number of fossil fuel vehicles. Under the influence of increased consumer acceptance of HFCV in the post-pandemic era, if OPTE decides to undergo technological reform by introducing HFCV, choosing the comprehensive technological reform route will be more appropriate. This route can improve infrastructure, bring more economic benefits to OPTE, and is more suitable for OPTE’s sustainable development compared to small-scale pilot introductions. It will facilitate the industry’s decarbonization process.

Conclusion 3: The experimental results show that all three pricing strategies can lead to the stable decision-making of OPTE reform. Profit-oriented pricing strategy is the fastest, followed by government regulation pricing strategy, and cost-oriented pricing strategy is the slowest. Chinese OPTE adopts a low-price strategy for public welfare, but this method cannot guarantee the profit of OPTE. Therefore, it can be considered to gradually shift towards profit-oriented pricing strategy and appropriately raise ticket prices to meet the demand for maximizing social welfare while ensuring OPTE’s economic benefits. In other countries (such as most European countries), OPTE has less government participation and public welfare. Public transport prices are influenced by many factors, such as fuel price fluctuations and energy crises (including oil, electricity, etc.). If the cost-oriented pricing strategy is used, the price cannot be adjusted according to market changes without considering the price demand elasticity. The profit-oriented pricing strategy is also applicable to these countries. It can adjust ticket prices in a timely manner according to factors that have a significant impact on ticket prices in reality, to ensure OPTE’s profit and make pricing more acceptable to consumers.

The subtle trends in downstream consumer behaviour will have a series of impacts on the decisions of OPTE and HFCV manufacturers, aligning with the bullwhip effect in the supply chain. Regarding the achievement of decarbonization goals in the public transportation industry, most articles approach the issue from the perspective of economic regulation through carbon trading policies, focusing on the rational allocation and utilization of carbon quotas. However, they tend to overlook the influences generated by factors such as changes in consumer awareness, which are crucial for the implementation of decarbonization plans in the industry. Furthermore, as HFCV gradually enter the public transportation sector in the future, the issue of hydrogen energy storage and conversion in HFCV requires the establishment of a significant number of hydrogen refuelling stations and other infrastructure. The selection and optimal utilization of these infrastructure facilities need further research.