New energy vehicle charging mode analysis method based on evolutionary game theory

Abstract

The invention discloses a new energy automobile charging mode analysis method based on an evolutionary game theory, and the method comprises the steps: firstly, determining a government, an automobile manufacturing enterprise and a consumer as game participants, and defining a strategy set and influence factor variables of the game participants; based on this, a payment matrix coupling benefits of three parties is constructed, and then a replication dynamic equation is established by taking the strategy selection probability of each party as a state variable; a system equilibrium point is obtained by solving an equation, stability analysis is carried out by using a Jacobian matrix eigenvalue method, and a stability condition for enabling the equilibrium point to become an evolution stability strategy point is deduced; and finally, based on the condition analysis, factor variables needing to be adjusted for realizing the expected stable strategy are analyzed, and a decision support result is generated. According to the method, the defect that the prior art lacks a dynamic view angle, a system framework and a quantitative model is overcome, the three-party strategy interaction evolution process can be quantitatively depicted, the stability condition is determined, and a scientific and quantitative basis is provided for industrial policy making and enterprise strategic decision making of a battery charging and replacing mode.

Description

Technical Field

[0001] This invention relates to the field of new energy vehicle industry policy analysis and decision support technology, and in particular to a method for analyzing new energy vehicle charging and swapping modes based on evolutionary game theory. Background Technology

[0002] The choice of refueling method for new energy vehicles is a key factor influencing their promotion, involving three stakeholders: the government, automakers, and consumers. The government needs to balance infrastructure investment, industrial development, and environmental goals; automakers need to make decisions between R&D costs, modification costs, and market potential; and consumers' choices are influenced by multiple factors such as purchase cost, ease of use, refueling experience, and expected residual value.

[0003] To address the selection of charging and battery swapping modes, existing technologies offer a variety of analytical methods, including: comparative analysis of technical routes from the perspectives of charging speed and battery life; economic evaluation of the return on investment of battery swapping stations; business model design for operating entities and pricing strategies; and policy effectiveness evaluation through case studies.

[0004] However, these existing analytical methods have significant limitations. First, most studies employ static comparisons or cross-sectional data analysis, assuming that the behavior of relevant stakeholders is relatively fixed, failing to depict the dynamic adjustments and interactions of the strategies of the government, automakers, and consumers over time. Second, the analytical perspectives are often singular, focusing solely on government policy or the cost-benefit considerations of automakers, lacking a systematic analysis that places all three stakeholders within a unified framework. Most importantly, current technology lacks mathematical models capable of quantitatively characterizing the evolutionary process of the interaction among these three strategies. Therefore, existing analytical methods cannot quantitatively reveal the evolutionary paths and stable equilibrium states of the strategic combinations of the government, automakers, and consumers under different policy support intensities, cost-benefit structures, and market acceptance conditions, making it difficult to provide strong support for relevant decision-making. Summary of the Invention

[0005] The technical problem to be solved by this invention is to provide a method for analyzing the charging and swapping modes of new energy vehicles based on evolutionary game theory. This method can quantitatively characterize the dynamic interaction process of the strategies of the government, automobile manufacturers and consumers, and can determine the stability conditions of evolutionary stable strategies.

[0006] The technical solution adopted by this invention to solve the above-mentioned technical problems is: a method for analyzing the charging and swapping modes of new energy vehicles based on evolutionary game theory, characterized by comprising the following steps: S1. Identify the main participants in the evolutionary game of charging and swapping modes for new energy vehicles, including the government, automobile manufacturers, and consumers; S2. Define the strategy set for each participating entity; S3. Identify the variables that influence the strategy choices of each participating entity; S4. Based on the strategy set and the factor variables, construct the payoff matrix for the three-party game; S5. Based on the payment matrix, and using the probability of each participating entity choosing a specific strategy as the state variable, establish the replication dynamic equation for each participating entity. S6. Solve the replication dynamic equation to obtain the equilibrium point of the three-party game; S7. Perform stability analysis on the equilibrium point to obtain the stability conditions required for the equilibrium point to become an evolutionary stable strategy point. S8. Based on the stability conditions, analyze the factor variables that need to be adjusted to achieve the evolutionary stable strategy expected in the three-party game, and generate decision analysis results.

[0007] In some embodiments, the strategy set includes: The government's strategy set is represented as {actively supporting the development of battery swapping, and not supporting the development of battery swapping}. The strategy set of the automobile manufacturing enterprise is represented as {producing battery swapping vehicles, not producing battery swapping vehicles}. The consumer's strategy set is represented as {buy a battery swapping vehicle, do not buy a battery swapping vehicle}.

[0008] In some embodiments, the factor variables include: The variables influencing the government's strategy choices include: the R&D support coefficient β and the corresponding benchmark subsidy amount S set by the government to actively support the development of the battery swapping model; the battery swapping fee reduction coefficient α and the corresponding benchmark reduction amount D; the infrastructure construction investment coefficient γ and the corresponding benchmark investment amount F; and the additional social benefits M brought about by the government's choice to actively support the development of the battery swapping model. Among these, the government's R&D support amount is βS, the battery swapping fee reduction amount is αD, and the infrastructure construction investment amount is γF. The variables influencing the strategy choices of the automobile manufacturing companies include: the profit R1 obtained by the automobile manufacturing companies by choosing to produce battery swapping vehicles and the R&D costs C1 they need to bear; and the profit R2 obtained by the automobile manufacturing companies by choosing to produce charging vehicles and the R&D costs C2 they need to bear. The factors influencing the consumer's strategy choice include: the comprehensive benefit R3 obtained by the consumer from choosing to purchase a battery swapping vehicle and the comprehensive benefit R4 obtained from choosing to purchase a charging vehicle. In addition, parameters for measuring the externalities of social benefits resulting from different consumer strategy choices include: the social benefits H1 from consumers choosing to purchase battery-swapping vehicles and the social benefits H2 from consumers choosing to purchase charging vehicles.

[0009] In some embodiments, the process of constructing the payment matrix includes: First, based on the government's strategy set and the consumer's strategy set, the three-way game is divided into four strategy combination scenarios, namely: Scenario 1: The government chooses to actively support the development of the battery swapping model, and consumers choose to purchase vehicles using the battery swapping model. Scenario 2: The government chooses to actively support the development of the battery swapping model, and consumers choose not to purchase vehicles using the battery swapping model. Scenario 3: The government chooses not to support the development of the battery swapping model, and consumers choose to purchase vehicles using the battery swapping model. Scenario 4: The government chooses not to support the development of the battery swapping model and consumers choose not to purchase vehicles using the battery swapping model. Then, for each scenario, a sub-payment matrix is ​​constructed. The rows of the sub-payment matrix correspond to the automobile manufacturer choosing to produce battery-swapping vehicles and choosing not to produce battery-swapping vehicles, respectively. The columns record the payments of each participating entity when the automobile manufacturer chooses the strategy in the corresponding row under the corresponding scenario. The payments of each participating entity are calculated based on the strategy it chooses in the current scenario and the related factor variables.

[0010] In some embodiments, the process of establishing the replicative dynamic equation is as follows: Let x be the probability that an automaker chooses to produce a battery-swapping vehicle, y be the probability that a consumer chooses to purchase a battery-swapping vehicle, and z be the probability that the government chooses to actively support the development of the battery-swapping model, where x, y, z ∈ [0, 1] and are functions of time t. Then: The replication dynamic equation for automobile manufacturing enterprises is: U1(x)=x(1-x)(βSz+R1-R2-C1+C2); The consumer's replication dynamic equation is: U2(y)=y(1-y)[αDxz+(R3-R4)x-R4]; The government's replication dynamic equation is: U3(z)=z(1-z)[(-αD+M)xy-(βS+γF)]; Wherein, U1(x), U2(y), and U3(z) represent the rates of change of probabilities x, y, and z with time t.

[0011] In some embodiments, in step S6, U1(x) = 0, U2(y) = 0, U3(z) = 0, and a system of simultaneous equations is formed and solved. The resulting equilibrium points include: eight boundary equilibrium points formed by combinations of the probabilities of each participating entity choosing a specific strategy taking boundary values ​​of 0 or 1, and one internal equilibrium point E(x). * ,y * ,z *), x * ,y * ,z * It is a solution to the system of equations βSz+R1-R2-C1+C2=0, αDxz+(R3-R4)x-R4=0, (-αD+M)xy-(βS+γF)=0, and satisfies 0 <x * ,y * ,z * <1.

[0012] In some embodiments, the stability analysis of the equilibrium point includes: Based on the aforementioned replication dynamic equation, construct the Jacobian matrix; Calculate the eigenvalues ​​of the Jacobian matrix at each equilibrium point; Based on the relationship between the eigenvalues ​​and the factor variables, the stability conditions expressed by the factor variables that the equilibrium point must satisfy to become an evolutionarily stable strategy point are determined. Based on the stability conditions, the stable strategy point is determined from each equilibrium point.

[0013] Compared with the prior art, the advantages of the present invention are as follows: 1) For the first time, the government, automobile manufacturers and consumers are placed in a unified dynamic analysis framework, and a unified evolutionary game model with the interests of the three parties is constructed. This overcomes the limitations of existing technologies that only conduct static analysis from the perspective of a single subject, and realizes a systematic analysis of the charging and swapping mode selection problem.

[0014] 2) By introducing the replication dynamic equation, the strategy choices of each party are modeled as probabilistic variables that evolve continuously over time. This enables quantitative simulation and characterization of the dynamic adjustment and long-term interaction of the three parties' strategies under mutual influence, solving the problem that existing technologies cannot reflect the dynamics of strategies.

[0015] 3) The entire process, from qualitative definition to quantitative modeling, and then to stability assessment and decision support, forms a complete and computable decision support chain. The final decision analysis results can provide quantitative basis for policy making and corporate strategy. Attached Figure Description

[0016] Figure 1 This is a flowchart illustrating the implementation process of the method of the present invention. Detailed Implementation

[0017] The present invention will be further described in detail below with reference to the accompanying drawings and embodiments.

[0018] This invention proposes an analysis method for charging and swapping modes of new energy vehicles based on evolutionary game theory, such as... Figure 1 As shown, it includes the following steps: S1. Identify the main participants in the evolutionary game of charging and swapping modes for new energy vehicles, including the government, automobile manufacturers, and consumers. There are both conflicting and interdependent relationships among them.

[0019] S2. Define the strategy set for each participating entity.

[0020] In some embodiments, the strategy set includes: a government strategy set, represented as {actively supporting the development of battery swapping mode, not supporting the development of battery swapping mode}; a car manufacturer strategy set, represented as {producing battery swapping mode vehicles, not producing battery swapping mode vehicles}; and a consumer strategy set, represented as {purchasing battery swapping mode vehicles, not purchasing battery swapping mode vehicles}.

[0021] S3. Identify the variables that influence the strategy choices of each participating entity.

[0022] In some embodiments, factor variables include: The variables influencing the government's strategy choices include: the R&D support coefficient β and the corresponding benchmark subsidy amount S set by the government to actively support the development of the battery swapping model; the battery swapping fee reduction coefficient α and the corresponding benchmark reduction amount D; the infrastructure construction investment coefficient γ and the corresponding benchmark investment amount F; and the additional social benefits M brought about by the government's choice to actively support the development of the battery swapping model. Among these, the government's R&D support amount is βS, the battery swapping fee reduction amount is αD, and the infrastructure construction investment amount is γF.

[0023] To encourage consumers to use battery swapping stations and leverage their advantage in matching peak and off-peak power generation with new energy technologies, the government will implement fee reductions for battery swapping; to promote the construction of battery swapping stations, the government will invest in infrastructure construction.

[0024] The variables influencing the strategy choices of automobile manufacturers include: the profit R1 and R&D cost C1 obtained by automobile manufacturers choosing to produce battery swapping vehicles, and the profit R2 and R&D cost C2 obtained by automobile manufacturers choosing to produce charging vehicles.

[0025] The variables influencing consumer strategy choices include: the overall benefit R3 obtained by consumers choosing to purchase vehicles using the battery swapping model, and the overall benefit R4 obtained by consumers choosing to purchase vehicles using the charging model.

[0026] In addition, parameters for measuring the externalities of social benefits resulting from different consumer strategy choices include: the social benefits H1 from consumers choosing to purchase battery-swapping vehicles and the social benefits H2 from consumers choosing to purchase charging vehicles.

[0027] Here, all key economic and policy parameters influencing the decisions of the three parties (such as the benchmark subsidy amount S, R&D costs C1 and C2, profits R1 and R2, and social benefits H1 and H2) are defined in detail and quantified. The defined factor variables (such as the R&D support coefficient β and the exemption coefficient α) directly correspond to controllable policy tools (subsidies, preferential treatment, and exemptions) and market outcomes (profits and social benefits), enabling the evolutionary game model to be used to evaluate policy effectiveness.

[0028] S4. Based on the strategy set and factor variables, construct the payoff matrix for the three-party game.

[0029] In some embodiments, the payment matrix is ​​a logical three-dimensional composite structure, and the construction process includes: First, based on the government's and consumers' strategy sets, the three-way game is divided into four strategy combination scenarios: Scenario 1: The government chooses to actively support the development of the battery swapping model, and consumers choose to purchase vehicles using the battery swapping model.

[0030] Scenario 2: The government chooses to actively support the development of the battery swapping model, and consumers choose not to purchase vehicles using the battery swapping model.

[0031] Scenario 3: The government chooses not to support the development of the battery swapping model, and consumers choose to purchase vehicles using the battery swapping model.

[0032] Scenario 4: The government chooses not to support the development of the battery swapping model, and consumers choose not to purchase vehicles using the battery swapping model.

[0033] Then, for each scenario, a sub-payment matrix is ​​constructed. The rows of the sub-payment matrix correspond to the automobile manufacturers choosing to produce battery-swapping vehicles and choosing not to produce battery-swapping vehicles, respectively. The columns record the payments of each participating entity when the automobile manufacturer chooses the strategy in the corresponding row under the corresponding scenario. The payments of each participating entity are calculated based on the strategy it chooses in the current scenario and the related factor variables.

[0034] Here, the three-dimensional composite structure of the payment matrix clearly reveals the direct impact of different production decisions of automobile manufacturing enterprises on the interests of the three parties under specific policy and market conditions, and intuitively demonstrates the interdependence and conflict of interests among the parties in the game. This structured payment matrix is ​​the only and explicit input for deriving the replication dynamic equation, ensuring the logical rigor of the transition from the static game structure to the dynamic evolution model.

[0035] Scenario 1: The government chooses to actively support the development of the battery swapping model, and consumers choose to purchase vehicles using the battery swapping model. The corresponding sub-payment matrix is ​​as follows: Wherein, βS+R1-C1, αD+R3, and -βS-αD-γF+H1+M represent the payments made by the car manufacturer, consumers, and the government when the car manufacturer chooses to produce battery-swapping vehicles under scenario one, respectively. R2-C2, 0, and -βS-γF represent the payments made by the car manufacturer, consumers, and the government when the car manufacturer chooses not to produce battery-swapping vehicles (i.e., to produce charging vehicles) under scenario one.

[0036] Scenario 2: The government chooses to actively support the development of the battery swapping model, and consumers choose not to purchase vehicles using the battery swapping model (i.e., purchase vehicles using the charging model). The corresponding sub-payment matrix is ​​as follows: Wherein, βS+R1-C1, 0, and -βS-γF represent the payments made by the car manufacturer, consumers, and the government when the car manufacturer chooses to produce battery-swapping vehicles under scenario two, and R2-C2, R4, and -βS-γF+H2 represent the payments made by the car manufacturer, consumers, and the government when the car manufacturer chooses not to produce battery-swapping vehicles (i.e., to produce charging vehicles) under scenario two.

[0037] Scenario 3: The government chooses not to support the development of the battery swapping model, and consumers choose to purchase vehicles using the battery swapping model. The corresponding sub-payment matrix is ​​as follows: In this context, R1-C1, R3, and H1 represent the payments made by the car manufacturer, consumers, and the government when the car manufacturer chooses to produce battery-swapping vehicles under scenario three. R2-C2, 0, and 0 represent the payments made by the car manufacturer, consumers, and the government when the car manufacturer chooses not to produce battery-swapping vehicles (i.e., to produce charging vehicles) under scenario three.

[0038] Scenario 4: The government chooses not to support the development of the battery swapping model, and consumers choose not to purchase vehicles using the battery swapping model (i.e., they purchase vehicles using the charging model). The corresponding sub-payment matrix is ​​as follows: In this context, R1-C1, 0, and 0 represent the payments made by the car manufacturer, consumers, and the government when the car manufacturer chooses to produce battery-swapping vehicles under scenario four. R2-C2, R4, and H2 represent the payments made by the car manufacturer, consumers, and the government when the car manufacturer chooses not to produce battery-swapping vehicles (i.e., to produce charging vehicles) under scenario four.

[0039] S5. Based on the payment matrix, and using the probability of each participant choosing a specific strategy as the state variable, establish the replication dynamic equation for each participant.

[0040] In establishing a three-party evolutionary game model for the charging and swapping modes of new energy vehicles, the derivation process from the payoff matrix to the replicating dynamics equations follows the general paradigm of evolutionary game theory. This process uses the constructed payoff matrix as the sole input, first calculating the expected payoffs of each participant under different strategy choices and the group's average expected payoff; then, based on the replicating dynamics principle, directly establishing a set of differential equations describing the evolution of the probability of each participant choosing a specific strategy over time, i.e., the replicating dynamics equations. Therefore, the payoff matrix is ​​the foundation for determining all payoff calculations, while the replicating dynamics equations are the direct mathematical expression of its dynamic evolutionary form.

[0041] In some embodiments, the process of establishing the replicated dynamic equations is as follows: The basic components of an evolutionary game model are participating agents, a set of strategies, the probability of strategy selection, and the expected payoff function. The following assumptions should be followed when establishing the replication dynamic equations for each participating agent.

[0042] Assumption 1: The game participants are the government, automobile manufacturers, and consumers. All three parties are boundedly rational and have imperfectly symmetrical information. All parties are in the initial stage of the game, and other entities that may have a potential impact on the three parties are not considered.

[0043] Assumption 2: The parties involved in the game will dynamically adjust their strategy choices according to their own interests at different stages of the implementation and promotion of the charging and battery swapping modes. However, given that the current battery swapping infrastructure construction is still in its initial stage, the government intends to promote the popularization of the battery swapping mode quickly, and government support will be maintained for a long time to promote the construction of the battery swapping infrastructure.

[0044] Assumption 3: Since the battery ownership of vehicles using the battery swapping model generally belongs to the battery swapping service provider, consumers save on battery costs during the purchase process when the vehicle and battery are separated. Therefore, the comprehensive benefit R3 obtained by consumers who choose to purchase vehicles using the battery swapping model is greater than the comprehensive benefit R4 obtained by consumers who choose to purchase vehicles using the charging model. The social benefit H1 brought about by consumers choosing to purchase vehicles using the battery swapping model is greater than the social benefit H2 brought about by consumers choosing to purchase vehicles using the charging model.

[0045] Assumption 4: Let x be the probability that an automaker chooses to produce battery-swapping vehicles and 1-x be the probability that it chooses not to produce them; let y be the probability that a consumer chooses to purchase battery-swapping vehicles and 1-y be the probability that it chooses not to; let z be the probability that the government chooses to actively support the development of battery-swapping and 1-z be the probability that it chooses not to support it. Where x, y, z ∈ [0, 1] and are functions of time t, then: (The question is incomplete and requires further context.) The replication dynamic equation for manufacturing firms is: U1(x) = x(1-x)(βSz + R1 - R2 - C1 + C2); the replication dynamic equation for consumers is: U2(y) = y(1-y)[αDxz + (R3 - R4)x - R4]; the replication dynamic equation for the government is: U3(z) = z(1-z)[(-αD + M)xy - (βS + γF)]; where U1(x), U2(y), and U3(z) represent the rates of change of probabilities x, y, and z with time t.

[0046] S6. Solve the replication dynamic equations to obtain the equilibrium point of the three-way game.

[0047] In some embodiments, the equilibrium points are solved by setting U1(x)=0, U2(y)=0, and U3(z)=0, and forming a system of simultaneous equations. The resulting equilibrium points include eight boundary equilibrium points formed by combinations of the probabilities of each participating entity choosing a specific strategy taking boundary values ​​of 0 or 1, and one internal equilibrium point E(x). * ,y * ,z * ), x * ,y * ,z * It is a solution to the system of equations βSz+R1-R2-C1+C2=0, αDxz+(R3-R4)x-R4=0, (-αD+M)xy-(βS+γF)=0, and satisfies 0 <x * ,y * ,z * <1.

[0048] Specifically, according to evolutionary game theory, the equilibrium point corresponds to a state where the probability of a strategy no longer changes, that is, the probability of each participant choosing a specific strategy changes by zero over time. Therefore, solving for the equilibrium point is equivalent to solving the following system of equations: U1(x)=0, U2(y)=0, U3(z)=0.

[0049] All points formed by combinations of x, y, z taking boundary values ​​of 0 or 1 are solutions to a system of simultaneous equations. At the vertices of the three-dimensional probability space {(x,y,z)|0≤x≤1,0≤y≤1,0≤z≤1}, there are eight boundary equilibrium points: E0(0,0,0), E1(0,0,1), E2(0,1,0), E3(0,1,1), E4(1,0,0), E5(1,0,1), E6(1,1,0), and E7(1,1,1). These points represent the extreme scenario where all three parties in the game adopt pure strategies (fully supporting / producing / purchasing, or completely not supporting / producing / purchasing).

[0050] In addition to the boundary equilibrium point, there may also exist an internal equilibrium point E(x). * ,y * ,z * At this point, the probability is strictly between 0 and 1, i.e., 0. <x * ,y * ,z * <1,x * ,y * ,z * The solution to the following system of equations is: βSz + R1 - R2 - C1 + C2 = 0, αDxz + (R3 - R4)x - R4 = 0, (-αD + M)xy - (βS + γF) = 0. Solving the above system of equations, we get: x * =βSR4 / [αD(-R1+R2+C1-C2)+βS(R3-R4)], y * ={(βS+γF)[αD(-R1+R2+C1-C2)+βS(R3-R4)]} / [(-αD+M)βSR4], z * =(-R1+R2+C1-C2) / βS.

[0051] S7. Perform stability analysis on the equilibrium point to obtain the stability conditions required for the equilibrium point to become an evolutionary stable strategy point.

[0052] In some embodiments, the stability analysis of equilibrium points includes: constructing a Jacobian matrix based on the replication dynamic equation; calculating the eigenvalues ​​of the Jacobian matrix at each equilibrium point; determining the stability conditions, expressed by the factor variables, that an equilibrium point must satisfy to become an evolutionarily stable strategy point based on the relationship between the eigenvalues ​​and factor variables; and determining the evolutionarily stable strategy point from among the equilibrium points according to the stability conditions. Here, the stability of equilibrium points is determined by constructing the Jacobian matrix and calculating the eigenvalues, and the parametric constraints (stability conditions) expressed by factor variables are derived. The stability conditions are decision rules expressed in intuitive economic language, which directly generate actionable decision insights.

[0053] Specifically, first, the present invention takes the partial derivatives of the replicator dynamic equations of automobile manufacturing enterprises, consumers, and the government to obtain the Jacobian matrix, denoted as ; then, introducing each equilibrium point into the Jacobian matrix, all the eigenvalues at each equilibrium point can be obtained. There are exactly three eigenvalues for each equilibrium point; next, analyzing the positive and negative of the eigenvalues at each equilibrium point, the stability conditions are deduced as follows: For E0(0, 0, 0), its three eigenvalues are respectively: R1 - R2 - C1 + C2, βS + γF - H2 - R4, -(βS + γF). The stability conditions for E0(0, 0, 0) to become an evolutionary stable strategy point are: R1 - R2 - C1 + C2 < 0 and βS + γF < H2 + R4; when E0(0, 0, 0) is an evolutionary stable strategy point, the evolutionary stable strategy of the three-party game is determined as "automobile manufacturing enterprises do not produce battery swapping mode vehicles, consumers do not purchase battery swapping mode vehicles, and the government does not support the development of the battery swapping mode".

[0054] For E1(0, 0, 1), its three eigenvalues are respectively: βS + R1 - R2 - C1 + C2, βS + γF - H2 - R4, βS + γF. Since βS + γF > 0, E1(0, 0, 1) is an unstable point.

[0055] For E2(0, 1, 0), its three eigenvalues are respectively: R1 - R2 - C1 + C2, βS + γF - H2 + R4, -(βS + γF). The stability conditions for E2(0, 1, 0) to become an evolutionary stable strategy point are R1 - R2 - C1 + C2 < 0 and βS + γF < H2 - R4; when E2(0, 1, 0) is an evolutionary stable strategy point, the evolutionary stable strategy of the three-party game is determined as "automobile manufacturing enterprises do not produce battery swapping mode vehicles, consumers purchase battery swapping mode vehicles, and the government does not support the development of the battery swapping mode".

[0056] For E3(0, 1, 1), its three eigenvalues are respectively: βS + R1 - R2 - C1 + C2, βS + γF - H2 + R4, βS + γF. Since βS + γF > 0, E3(0, 1, 1) is an unstable point.

[0057] For E4(1, 0, 0), its three eigenvalues are respectively: -R1 + R2 + C1 - C2, βS + γF + R3 - 2R4, -(βS + γF). The stability conditions for E4(1, 0, 0) to become an evolutionary stable strategy point are: R1 - R2 - C1 + C2 > 0 and βS + γF + R3 < 2R4; when E4(1, 0, 0) is an evolutionary stable strategy point, the evolutionary stable strategy of the three-party game is determined as "automobile manufacturing enterprises produce battery swapping mode vehicles, consumers do not purchase battery swapping mode vehicles, and the government does not support the development of the battery swapping mode".

[0058] For E5(1,0,1), its three eigenvalues are: -βS - R1 + R2 + C1 - C2, αD + βS + γF + R3 - 2R4, βS + γF. Since βS + γF > 0, E5(1,0,1) is an unstable point.

[0059] For E6(1,1,0), its three eigenvalues are: -R1 + R2 + C1 - C2, βS + γF - R3 + 2R4, M - αD - βS - γF. The stability conditions for E6(1,1,0) to become an evolutionarily stable strategy point are: R1 - R2 - C1 + C2 > 0 and βS + γF < R3 - 2R4, M < αD + βS + γF. When E6(1,1,0) is an evolutionarily stable strategy point, the evolutionarily stable strategy of the three - party game is determined as "automobile manufacturing enterprises produce battery - swapping mode vehicles, consumers buy battery - swapping mode vehicles, and the government does not support the development of the battery - swapping mode".

[0060] For E7(1,1,1), its three eigenvalues are: -βS - R1 + R2 + C1 - C2, βS + γF - αD - R3 + 2R4, αD + βS + γF - M. The stability conditions for E7(1,1,1) to become an evolutionarily stable strategy point are: R1 - R2 - C1 + C2 > βS and βS + γF - αD < R3 - 2R4, M > αD + βS + γF. When E7(1,1,1) is an evolutionarily stable strategy point, the evolutionarily stable strategy of the three - party game is determined as "automobile manufacturing enterprises produce battery - swapping mode vehicles, consumers buy battery - swapping mode vehicles, and the government actively supports the development of the battery - swapping mode".

[0061] For E(x * ,y * ,z * ), it is an unstable point. <了

[0062] The three - party game often presents the bistable characteristics of the competitive attraction domains of E0(0,0,0) and E7(1,1,1): when the net income of automobile manufacturing enterprises is insufficient, the incentives for consumers are insufficient, or the social net benefits of the government are insufficient, the evolutionarily stable strategy of the three - party game is "automobile manufacturing enterprises do not produce battery - swapping mode vehicles, consumers do not buy battery - swapping mode vehicles, and the government does not support the development of the battery - swapping mode"; when all three conditions are met, the evolutionarily stable strategy of the three - party game is "automobile manufacturing enterprises produce battery - swapping mode vehicles, consumers buy battery - swapping mode vehicles, and the government actively supports the development of the battery - swapping mode".

[0063] For E7(1,1,1), the key constraint for the government is M > αD + βS + γF. Its essence is that the additional social benefits M brought by the government's choice to actively support the development of the battery swapping mode must cover the total scale of the R&D support amount βS, the battery swapping cost reduction amount αD, and the infrastructure construction investment amount γF. Otherwise, the government's strategy will evolve into not supporting the development of the battery swapping mode, making it difficult to maintain a cooperative equilibrium in the three-party game. The key constraint for automobile manufacturing enterprises is R1 - R2 - C1 + C2 > βS. Its essence is that when the relative benefits of automobile manufacturing enterprises in producing battery swapping mode vehicles are insufficient, even if government support and consumer purchase意愿 exist, it may lead to the collapse of the supply side, and the three-party game will fall back to the equilibrium attraction domain dominated by non-battery swapping. The key constraint for consumers is βS + γF - αD < R3 - 2R4. Its essence is that when the net advantage of the battery swapping solution for consumers is insufficient, consumers will evolve into not purchasing battery swapping mode vehicles, thus making the market-side demand unable to support the continuous expansion of the battery swapping mode. <00​​​​​​​

Claims

1. A method for analyzing the charging and battery swapping modes of new energy vehicles based on evolutionary game theory, characterized in that, Includes the following steps: S1. Identify the main participants in the evolutionary game of charging and swapping modes for new energy vehicles, including the government, automobile manufacturers, and consumers; S2. Define the strategy set for each participating entity; S3. Identify the variables that influence the strategy choices of each participating entity; S4. Based on the strategy set and the factor variables, construct the payoff matrix for the three-party game; S5. Based on the payment matrix, and using the probability of each participating entity choosing a specific strategy as the state variable, establish the replication dynamic equation for each participating entity. S6. Solve the replication dynamic equation to obtain the equilibrium point of the three-party game; S7. Perform stability analysis on the equilibrium point to obtain the stability conditions required for the equilibrium point to become an evolutionary stable strategy point. S8. Based on the stability conditions, analyze the factor variables that need to be adjusted to achieve the evolutionary stable strategy expected in the three-party game, and generate decision analysis results.

2. The method for analyzing the charging and swapping modes of new energy vehicles based on evolutionary game theory according to claim 1, characterized in that, The strategy set includes: The government's strategy set is represented as {actively supporting the development of battery swapping, and not supporting the development of battery swapping}. The strategy set of the automobile manufacturing enterprise is represented as {producing battery swapping vehicles, not producing battery swapping vehicles}. The consumer's strategy set is represented as {buy a battery swapping vehicle, do not buy a battery swapping vehicle}.

3. The method for analyzing the charging and swapping modes of new energy vehicles based on evolutionary game theory according to claim 2, characterized in that, The factor variables include: The variables influencing the government's strategy choices include: the R&D support coefficient β and the corresponding benchmark subsidy amount S set by the government to actively support the development of the battery swapping model; the battery swapping fee reduction coefficient α and the corresponding benchmark reduction amount D; the infrastructure construction investment coefficient γ and the corresponding benchmark investment amount F; and the additional social benefits M brought about by the government's choice to actively support the development of the battery swapping model. Among these, the government's R&D support amount is βS, the battery swapping fee reduction amount is αD, and the infrastructure construction investment amount is γF. The variables influencing the strategy choices of the automobile manufacturing companies include: the profit R1 obtained by the automobile manufacturing companies by choosing to produce battery swapping vehicles and the R&D costs C1 they need to bear; and the profit R2 obtained by the automobile manufacturing companies by choosing to produce charging vehicles and the R&D costs C2 they need to bear. The factors influencing the consumer's strategy choice include: the comprehensive benefit R3 obtained by the consumer from choosing to purchase a battery swapping vehicle and the comprehensive benefit R4 obtained from choosing to purchase a charging vehicle. In addition, parameters for measuring the externalities of social benefits resulting from different consumer strategy choices include: the social benefits H1 from consumers choosing to purchase battery-swapping vehicles and the social benefits H2 from consumers choosing to purchase charging vehicles.

4. The method for analyzing the charging and swapping modes of new energy vehicles based on evolutionary game theory according to claim 3, characterized in that, The process of constructing the payment matrix includes: First, based on the government's strategy set and the consumer's strategy set, the three-way game is divided into four strategy combination scenarios, namely: Scenario 1: The government chooses to actively support the development of the battery swapping model, and consumers choose to purchase vehicles using the battery swapping model. Scenario 2: The government chooses to actively support the development of the battery swapping model, and consumers choose not to purchase vehicles using the battery swapping model. Scenario 3: The government chooses not to support the development of the battery swapping model, and consumers choose to purchase vehicles using the battery swapping model. Scenario 4: The government chooses not to support the development of the battery swapping model, and consumers choose not to purchase vehicles using the battery swapping model. Then, for each scenario, a sub-payment matrix is ​​constructed. The rows of the sub-payment matrix correspond to the automobile manufacturer choosing to produce battery-swapping vehicles and choosing not to produce battery-swapping vehicles, respectively. The columns record the payments of each participating entity when the automobile manufacturer chooses the strategy in the corresponding row under the corresponding scenario. The payments of each participating entity are calculated based on the strategy it chooses in the current scenario and the related factor variables.

5. The method for analyzing the charging and swapping modes of new energy vehicles based on evolutionary game theory according to claim 4, characterized in that, The process of establishing the replication dynamic equation is as follows: Let x be the probability that an automaker chooses to produce a battery-swapping vehicle, y be the probability that a consumer chooses to purchase a battery-swapping vehicle, and z be the probability that the government chooses to actively support the development of the battery-swapping model, where x, y, z ∈ [0, 1] and are functions of time t. Then: The replication dynamic equation for automobile manufacturing enterprises is: U1(x)=x(1-x)(βSz+R1-R2-C1+C2); The consumer's replication dynamic equation is: U2(y)=y(1-y)[αDxz+(R3-R4)x-R4]; The government's replication dynamic equation is: U3(z)=z(1-z)[(-αD+M)xy-(βS+γF)]; Wherein, U1(x), U2(y), and U3(z) represent the rates of change of probabilities x, y, and z with time t.

6. The method for analyzing the charging and swapping modes of new energy vehicles based on evolutionary game theory according to claim 5, characterized in that, In step S6, by setting U1(x)=0, U2(y)=0, and U3(z)=0, a system of simultaneous equations is formed and solved. The resulting equilibrium points include: eight boundary equilibrium points formed by combinations of the probabilities of each participating entity choosing a specific strategy taking boundary values ​​of 0 or 1, and one internal equilibrium point E(x). * ,y * ,z * ), x * ,y * ,z * It is a solution to the system of equations βSz+R1-R2-C1+C2=0, αDxz+(R3-R4)x-R4=0, (-αD+M)xy-(βS+γF)=0, and satisfies 0 <x * ,y * ,z * <1.

7. The method for analyzing the charging and swapping modes of new energy vehicles based on evolutionary game theory according to claim 6, characterized in that, The stability analysis of the equilibrium point includes: Based on the aforementioned replication dynamic equation, construct the Jacobian matrix; Calculate the eigenvalues ​​of the Jacobian matrix at each equilibrium point; Based on the relationship between the eigenvalues ​​and the factor variables, the stability conditions expressed by the factor variables that the equilibrium point must satisfy to become an evolutionarily stable strategy point are determined. Based on the stability conditions, the stable strategy point is determined from each equilibrium point.

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