Research on the supervision mechanism of new energy time-sharing rental vehicles: An evolutionary game analysis

: Background ： It is difficult to break the “production and marketing dilemma” by relying only on the production enterprises and consumers. This paper introduces the government into market subject and constructs a three-party dynamic evolution game model between government, enterprises, and consumers to reveal the control strategy. This paper makes a concrete analysis and verifies the model with a case study by revealing the game process between the regulation strategy and behavior decision of enterprises and consumers. Results ： When the key parameters are in different numerical ranges, the system has four evolutionary stability results. By appropriately increasing the amount of subsidies and penalties, increasing the proportion of compensation coefficient to consumers, and urging enterprises to reduce operating costs, the government is conducive to the healthy development of the new energy timesharing automobile industry. Conclusions ： The subsidy range and punishment intensity have a positive effect on the evolution of the system to the ideal state, the consumer compensation coefficient has a positive effect on the evolution of the system to the ideal state, the effort of operating costs has a negative effect on the evolution of the system to the ideal state. The study can provide a theoretical basis and a reference for policy formulation and decision-making.


Introduction
With the booming development of the Internet and the popularity of mobile terminals, the sharing economy, based on the platform created by a third party, adopts a new economic model that makes full use of idle resources, integrates offline resources such as cars, bicycles and labor, and connects the supply and demand sides to maximize social benefits. Time-sharing leasing is a quasi-public transportation mode that has been emerging in China in recent years. It is a combination of the new thinking mode of "Internet +" and new car rental services. The concept of the time-sharing lease first appeared in the Zurich cooperative in Switzerland in 1948, and now the time-sharing lease is a car rental model based on the Internet and Internet of Vehicles' technology (Shaheen et al., 1998;Dimatulac et al., 2018). Time-sharing leases have potential advantages, such as cost savings, improved transportation efficiency, and environmental protection. The cost involved in time-sharing to rent this type of travel is not very expensive compared to that of both carpooling and private car travel. Leasing also provides some private car owners with certain benefits, thereby attracting more private car owners to join and use time-sharing, which reduces vehicle use costs and improves vehicle utilisation (Xiao, 2017;Smallbone et al,2020). Some scholars use North American time-share leasing as their research object. At the same time, some scholars take time-sharing lease in North America as the research object. The study shows that the increase of time-sharing lease members reduces the average number of vehicles owned by families, and users who use time-sharing lease also use less cars than those who use private cars (Millard et al., 2006;Katzev, 2003).The study on this economic model can be divided into time-sharing lease application mode, scheduling and optimization, and government policy.
The operating model can be divided into an employee-based operating model and a consumer-oriented operating model. The earliest employee operation mode is divided into the shortest time type and the balanced inventory type. Under this premise, some scholars have proposed a new model, which is a time-sharing company called a deployment system that dynamically adjusts the vehicles in the system. The quantity allows the time-sharing leasing company to achieve maximum profit, and it is optimised at the end of a Monte-Carlo simulation based stochastic optimisation (Fan et al., 2008;Duan and Pu, 2017). The second mode can be divided into travel binding and travel splitting. From the perspective of the promotion of time-sharing leases, the current development mode of time-sharing leasing and the particularity of its leasing outlets make this mode of travel more suitable. It is the first to be used in cities with large-scale economies and more developed floating populations. The point is that leasing can alleviate the small number of parking spaces to a certain extent, and it is also an emerging public transportation mode (Levine et al., 2009;Qiu and Wang,2016). Time-sharing lends the theoretical content of the sharing economy, which is an important step in the process of sharing the economic theory.
Time-sharing leasing allows car owners and users to achieve a win-win situation, meet the needs of market development, and create new space for their own development (Bardhi et al., 2012;Lü et al,2020).
Regarding the research on time-sharing lease scheduling, some study found that the biggest problem with time-sharing is the lack of number of rental points and coverage (Xu, 2016). In view of the location of the rental points, some scholars have In summary, the existing research lacks analysis of the new energy vehicle supervision system in the time-sharing field, and most of the studies are static research. In the regulation of the new energy industry, government, enterprises and consumers form a dynamic multiple game relationship. In light of the particular circumstances of the electric vehicle industry, it is difficult to break the "production and marketing dilemma" using only the game between producers and consumers.
Only by including the government as the third party in the game process can stimulate demand growth and promote sustainable development of the industry. How to design the combination of regulatory strategies, so as to give full play to the role of regulatory policies in expanding the scale of electric vehicle market is of great significance for the electric vehicle industry with sluggish market performance.
Therefore, this paper draw lessons from the study of the multi-party game of the green supply chain, build evolutionary game model to study strategy choices of three kinds of groups in different periods, find out the control strategy combinations and the relationship between the enterprise and consumer behavior decision-making, finally to meet the new energy car rental industry regulations state of optimal time-sharing, and gives the corresponding policy recommendations. regulation and non-regulation, that is, the two strategies are adopted to supervise the behaviour of enterprises to achieve the optimal situation of industry governance and let the industry develop freely to achieve a stable state.
Enterprise: A shared automobile enterprise that adopts the characteristics of new energy for automobile power, a time-lease business mode for renting while running, and parking mode for vehicles as "stop and go". Due to either cost constraints or greater benefits, enterprises involved in the production of new energy vehicles will have to deduct the subsidies paid by the government and cut corners. In addition, in the operation process of time-sharing car rental, consumers are not strictly audited, the service is not good, and the number of parking and charging points is too small or the planning is unreasonable. Under the supervision of the government and consumers, enterprises plan to adopt the two strategies of "endeavor" and "don't endeavor".
Consumers: As direct users of this emerging shared economic phenomenon, there will be negative comments on the new energy time-sharing car rental industry in the process of using the new energy timesharing car rental service due to enterprises' bad operation and other behaviors. Weighing the gains and losses of participation in supervision costs and service improvement and compensation gains determines the set of strategies of consumers in the game system, which are to either participate in supervision, report and feedback related bad behaviours, or maintain a wait-and-see attitude.From the above definition of concepts and model assumptions, a three-party game model of government-enterprise-consumer in the new energy-time leasing period and supervision process is established, as shown in Figure 1. Hypothesis 2: The total amount of government subsidies provided to enterprises is . If the subsidy is issued normally every year, the business status of the enterprise must meet the government's auditing standards. If they are not met, there will be cases where either consumers do not participate or the government supervises. Parameter ! is the probability of subsidy cancellation after being discovered.
Hypothesis 3: The cost of the government's choice of regulatory strategy is ! .
After discovering that the company does not work hard, the government will charge the enterprise a fine of . The social benefit obtained after the successful supervision is . chooses not to work hard, the amount of damage caused to the government is .
Hypothesis 5: The cost of the business operation phase is divided into fixed cost " and effort cost ′. The fixed cost is the basic cost when the enterprise maintains normal operation, and the effort cost is paid by an enterprise to achieve the audit requirements and market demands.
Hypothesis 6: When a consumer experiences a substandard product, the loss suffered is ! . After the consumer chooses to participate in the supervision and feedback to the government department, the probability that the government supervises the enterprise's ineffective business behaviour is " ( " > ! ), and the cost of consumer participation supervision is # . After the enterprise's inactivity is detected, the consumers are compensated with a value of ′, is the compensation coefficient of the enterprise to consumers, and the reputation loss suffered by the enterprise is " .
Hypothesis 7: When consumers choose to participate in the supervision and enterprises do not work hard to operate, if the government's strategy is to choose non-supervision, then consumers' willingness is not responded, leading to a decline in the credibility of the government, and the loss value is # .
Hypothesis 8: When the company chooses not to work hard, the income obtained is ! . When the company chooses to work hard, the income obtained is " ( " > ! ).

Function
According to the above assumptions, under the condition that all three parties are bounded rational and the information is asymmetric, the payment matrix is listed as shown in Table 1 and Table 2.   Tables 1 and 2, the first function item in each table represents government revenue, the second function item represents enterprise revenue, and the third function item represents consumer revenue.

Analysis
Before the game analysis, we first analyse the expected returns of the government, enterprises, and consumers.
The expected return of the government's choice of a regulatory strategy is The expected return of the government's choice of a non-regulatory strategy is The average expected return of the government is The expected return of the enterprise's choice of a hard work strategy is The expected return of the company's choice of not working hard is The average expected return of the company is The expected return of consumers choosing to participate in the monitoring strategy is The expected return of consumers choosing not to participate in supervision is The average expected return of consumers is

Government regulatory stability strategy
The government's choice of supervision of the replication dynamic equation is If y > % and = 0, $ ( ) < 0, when = 0, it is in a stable state.
Conclusion 1 is proved. Therefore, the conclusion is as follows: Conclusion 2: The probability that the government chooses a regulatory strategy increases as the probability of consumers choosing to participate in supervision increases.
Conclusion 2 is proved.

Enterprises strive to operate stable strategies
The replication dynamic equation that the enterprise chooses to work hard is ; if x > 4 ，when = 1, it is in a stable state；if x < 4 ，when = 0, it is in a stable state. Therefore, the conclusion is as follows: Conclusion 3: The probability that an enterprise chooses to work hard increases as the probability of the government choosing to monitor increases.
Conclusion 3 is proved. Therefore, the conclusion is as follows:

Conclusion 4：The probability that an enterprise chooses to work hard
increases as the probability of consumers choosing to participate in supervision increases.
Conclusion 4 is proved.

Consumer participation in monitoring and stabilising strategies
The replication dynamic equation that consumers choose to participate in supervision is If y > % and = 0， $ ( ) < 0，when = 0, it is in a stable state.
Conclusion 6 is proved.

Evolutionary game path analysis
In the game analysis above, the probabilities that governments, enterprises, and The Jacobian matrix is solved to obtain the eigenvalues corresponding to the respective equalisation points, as shown in Table 3.

Key parameter analysis
The following four boundary equilibrium points of ! 、 " 、 8 , and 9 are analysed, and the real-world situation analysis is used to analyse the key parameters affecting government, enterprise, and consumer strategy choices:

(1) Key parameters affecting government strategy selection
Among the four boundary equilibrium points, the values of 3*(4) 34 in 8 、 9 are significantly less than 0, so they are not analysed in this section.
In the ! and " states, the government's strategic choices are not regulation and supervision. If the condition of 3*(4) 34 < 0 is satisfied, the two evolution states tend to be stable. The condition is ! (2R + S + F) − ! < 0 and ! (2R + S + F) − ! > 0. The analysis of the formula shows that the subsidy amount and the penalty strength are important parameters that influence the choice of government strategy.
In the case of a small amount of subsidy and punishment, the government expects that the expected return of supervision is less than zero. Since the government does not participate in the supervision, the probability of successful government supervision is low, and the income obtained is not enough to offset the cost of supervision ! .
Therefore, changing the government's strategy in the game system to the ideal state requires increasing the amount of subsidies and penalties until the expected return is greater than zero.

(2)Key parameters affecting consumer strategy choices
In the state of " and 8 in the supervision process of the new energy time-sharing car industry, the participation of consumers in the supervision depends on the positive and negative values of the conditional formula " $ − # . In the " and 8 states, since the enterprise's effort cost has a high value, the key parameter that determines the establishment of " $ − # > 0 is the compensation coefficient.
The larger the compensation coefficient, the larger the value on the left side of the inequality. Therefore, it can be seen from the formula that, in the case of small compensation coefficient, the realistic situation corresponding to state " is that consumers would rather bear the loss of ! than pay labor, time and other supervision costs to participate in the supervision of the industry. To change the status of " to 8 , the government needs to provide complaint channels to reduce the cost of consumer participation in supervision, increase the amount of compensation paid to consumers when penalising problems, and increase consumers' willingness to participate in supervision.

(3)Key parameters affecting corporate strategy selection
The most ideal state for the supervision of new energy time-sharing car companies is 9 (not regulated, hard-working, not involved in supervision). In this state, the proportion of enterprises' efforts in business strategy selection is relatively high, and the industry has embarked on the road of self-discipline.Comparing state ! with state 9 , it is found that the key condition affecting enterprise policy selection is When the cost of efforts to select a company to operate is greater than is the difference between " and ! , the strategic choice of the company tends to be not to work hard. As for the enterprise itself, the most important thing is to promote technology upgrades and increase investment in research and development funds in the enterprise's technical department, thereby reducing the cost of efforts to achieve the optimal state of enterprise development.

Simulation analysis
Based on the above analysis, the evolutionary stability The initial proportion of government, enterprises, and consumer behaviour decisions is 0.8.

The impact of subsidy and punishment on system evolution
In the case where the subsidy and the penalty force are set to

The influence of compensation coefficient on system evolution
In the simulation analysis of the compensation coefficient, to avoid the influence of the irrelevant variable subsidy and the penalty force , the amount of the subsidy and the penalty force , respectively, are set to 5. The simulation diagram of the system state evolution under the condition that the compensation coefficients are set to 0.5 and 0.9, respectively, is as shown in Fig. 6 and Fig. 7.
In the case where the compensation coefficient is set large, the consumer's strategy choice evolves to participation in the supervision after a certain time node, meaning that the value of the compensation coefficient plays a decisive role in the consumer's strategy choice if the remaining parameters are not changed.
Therefore, as consumers participate in the supervision of the positive promotion of new energy-time leasing vehicle supervision, the government should require enterprises to compensate consumers to a higher degree when they punish the problem enterprise, and improve consumer participation in regulatory willingness.

The impact of effort cost on system evolution
Combined with the previous analysis, if the whole system is evolved to the state 9 , the fundamental condition is " − ! − $ > 0. The effort cost C′ is set to 10 and 3, respectively, and the obtained system state evolution simulation diagram is shown in Fig. 8 and Fig.9.
Under the condition that enterprises are struggling to operate at low cost, the spontaneous choice of enterprises will tend to be work hard, improve the vitality of the industry, and expand the influence of the industry. The changes brought by this series of actions will drive the choices made by government and consumers. Without supervision and non-participation in supervision, companies will also choose to work hard. Currently, the new energy time-sharing car industry is on the right track, and the necessity of supervision by the government and consumers has declined. To save manpower and material resources, the status 9 has become a dominant strategy in the regulatory game system. This situation is new. Energy time-sharing leasing is the ideal state of the automotive industry governance.
Therefore, the government should urge enterprises to use subsidies to support and streamline institutions; improve R&D technology and optimise operational planning; reduce the construction costs of facilities, such as parking spots and charging points; reduce operating costs, and achieve new energy-time leasing vehicle governance ideal state. assets, when the subsidy is too low, the development of the enterprise will die due to capital factors. When the punishment intensity is too low, the enterprise that does not work hard is in the state of low risk and high return, and the enterprise will be inclined to not work hard because of the interest drive. Therefore, it is necessary to raise the threshold for enterprises to receive subsidies, and strictly supervise the requirement that the number of vehicles produced by enterprises reaches a certain level and the quality meets certain standards to receive subsidies. At the same time, industry access rules, security assurance regulations, and commercial competition standards are set up. Enterprises with malicious competition, fraudulent subsidies, infrequent censorship, and poor car quality are subject to high fines. If the circumstances are serious, they will be shut down and rectified.
From the analysis of Figure 6 and Figure 7, the consumer compensation coefficient has a positive effect on the evolution of the system to the ideal state.
Increasing the consumer compensation coefficient appropriately is conducive to the supervision of the new energy time-sharing car industry. Since consumers are the direct experiencers of new energy time-sharing cars, they are the first to know whether the business is working hard or not. If consumers are involved in supervision, this can reduce the most inevitable lag in government regulation. To enhance consumers' willingness to participate in supervision, on the one hand, the government information platform should be optimised to provide consumers with more reporting channels. On the other hand, when penalising problem enterprises, the income from illegal and illegal enterprises should be compensated to a certain extent in the consumption process. Consumers who have a bad experience and participate in supervision encourage consumers to participate more in the supervision of new energy time-sharing cars, thereby reducing government supervision costs, and urge enterprises to work hard to improve the user experience.
From the analysis of Figure 8 and Figure 9, the effort of operating costs has a negative effect on the evolution of the system to the ideal state. After subsidies, penalties, and compensation factors are at the desired level, the government should further urge enterprises to improve R&D technology and operating costs. In terms of charging points, the layout of charging pile points should be optimized, construction land coordinated and approval time of enterprises reduced. In terms of the use of subsidies provided, enterprises should be required to give preference to technology research and development and new product production; For specific models of new energy vehicles into the time-sharing rental market after the adoption of tax incentives.
The conclusions of this study provide a theoretical basis and reference for policy formulation and decision-making in government departments.
intellectual property. In so doing we confirm that we have followed the regulations of our institutions concerning intellectual property.

Availability of supporting data:
The data used to support the findings of this study are available from the corresponding author upon request.

Competing interests:
We wish to confirm that there are no known conflicts of interest associated with this publication. Authors' contributions: All authors of this manuscript have directly participated in planning, execution, and/or analysis of this study.