© Wuhan University 2026

0 Introduction

The expansion of new energy, particularly photovoltaic power and wind energy, has been prioritized in national policy as a fundamental element for achieving China's dual carbon goals of emission peak and carbon neutrality^[1-2]. To promote the rapid development of new energy, the Chinese government has introduced incentive measures represented by feed-in tariffs (FITs)^[3-7]. However, with the expanded generation of new energy power, limitations of the feed-in tariff policy have become more apparent, including insufficient motivation for enterprise innovation, increased government financial pressure, and distorted market pricing mechanisms. Thus, it has become necessary to gradually remove protections and subsidies for new energy electricity prices and encourage full market competition in new energy for deepening electricity market reforms. In February 2025, the National Development and Reform Commission issued the Notice on Deepening the Market-Oriented Reform of New Energy Feed-in Tariffs and Promoting the High-Quality Development of New Energy ("Document No. 136"), whose core is to promote comprehensive marketization of new energy electricity prices.

The new "Document No. 136" will profoundly reshape the interests and decision logic of three key entities: new energy power generators, power grid enterprises, and governments. New energy generators will face market-oriented electricity price fluctuations and largely cancelled subsidies; their development will depend on technological innovation, cost reduction, operational efficiency, and market opportunity identification. Their strategies (active/passive grid-connection) are constrained by the balance between market returns and innovation costs. Power grid enterprises must enhance new energy absorption capacity and maintain grid stability; their strategies (active/passive cooperation) depend on balancing grid transformation investment costs and new energy absorption obligations. Governments need to shift from "direct intervenors" to "rule-makers and supervisors"; their strategies (strong supervision/weak supervision) must balance regulatory costs (e.g., subsidies), potential benefits (e.g., tax revenue), and policy goals (e.g., a higher proportion of new energy). Under this policy, the three parties' strategic choices are highly interactive and game-oriented, with their final decisions significantly affecting policy effectiveness and the sustainability of the new energy industry.

A new policy's ability to meet expected goals hinges on stakeholders reaching a stable, coordinated strategic equilibrium^[8-9]. Under the new energy electricity price marketization framework of "Document No. 136", the enthusiasm of new energy enterprises for grid connection, the cooperative integration by power grid enterprises, and government regulatory intervention are interdependent and mutually constraining. Any party's strategic deviation, such as new energy enterprises passively responding to market risks, power grid enterprises delaying transformation investment, or governments over-regulating or under-regulating, may reduce policy effectiveness or cause failure. Thus, in-depth analysis of the policy's incentive and constraint mechanisms on the three entities' decision-making, and revelation of the dynamic process and stable conditions of their strategic interaction evolution, is theoretically and practically significant for evaluating policy effectiveness and guiding benign collaboration.

Current research on electricity market policy effects has yielded some achievements^[10-16], but gaps exist in methodology and objects. On one hand, studies on electricity market policies (including investment decisions, trading mechanisms, and quota systems) mostly focus on game analysis in traditional energy or mixed markets^[8,17-19]. Special evaluations of new policies for new energy electricity price reform, such as "Document No. 136", which centers on comprehensive market-oriented pricing, remain scarce. Moreover, existing literature mainly involves policy interpretation and qualitative recommendations^[20-23], lacking support from data-driven simulation experiments.

On the other hand, regarding policy research methodologies, evolutionary game theory has become a mainstream tool for analyzing multi-agent policy responses, as it can effectively depict dynamic strategy adjustments among boundedly rational agents^[8,24-27]. However, traditional game models often rely on researchers' subjective assumptions of "representative agents" and "rational expectations". The selection of influencing factors in such models may deviate from agents' complex considerations in real decision-making, risking disconnection between models and reality due to "strong assumptions"^[28]. In recent years, large language models (LLMs) have shown great potential in simulating human decision-making. Studies indicate they can exhibit certain economic rationality without explicit optimization guidance and map behavioral characteristics of different groups in specific scenarios^[28-31]. This offers a novel solution to the shortcoming of traditional game theory methods.

This paper proposes a simulation analysis framework integrating LLM screening and a tripartite evolutionary game, aiming to more realistically evaluate the policy effects of "Document No. 136". Given that photovoltaic power generation is a major new energy source^[32-35], this paper selects photovoltaic power generation enterprises for simulation research.

This paper's research approach is as follows. First, four mainstream LLMs (DeepSeek-V3, ChatGPT-4.1, Llama-4-Scout-B10, and Hunyuan) are used to play the roles of photovoltaic enterprises, power grid enterprises, and the government. Guided by designed prompts, each LLM independently reasons and outputs key factors influencing its core strategic choices under the new policy based on its role. Second, systematic statistics and integration of LLM responses screen out core influencing factors frequently mentioned and shared by different models. These factors form the basis for the game model's parameter system, avoiding subjectivity in traditional factor selection. Finally, based on these more "realistic" factors, a tripartite asymmetric evolutionary game model of photovoltaic enterprises, power grid enterprises, and the government is constructed, with replicator dynamics equations and equilibrium stability conditions derived. Python-based numerical simulation analyzes key parameter changes within a reasonable range to quantify how each factor affects their strategic evolution paths and stable equilibrium.

This paper proposes a methodological framework that combines multi‑LLM role‑playing with factor screening in policy evolutionary game analysis. Large language models are used to capture the heterogeneous cognition of different decision‑making agents, providing more realistic parameters for traditional game models and relaxing their strong assumptions. Using China's "Document No. 136" as a case, a tripartite evolutionary game model is built and validated with real data from photovoltaic enterprises. The results show how key policy variables, such as market‑driven electricity price fluctuations and subsidy withdrawal, dynamically affect the strategies of photovoltaic enterprises, grid enterprises, and governments, and identify the conditions under which stable outcomes emerge. Critical thresholds are also determined, including a lower bound for market electricity prices and an upper bound for innovation costs of new energy enterprises. The findings empirically confirm that subsidy removal and absorption responsibility mechanisms can promote market self‑regulation, offering governments a theoretical basis for targeted policy design and enterprises practical guidance for strategy optimization.

1 Construction of the Tripartite Evolutionary Game Model

1.1 Selection of Influencing Factors

This study integrates LLMs into influencing factors analysis, providing a novel policy research approach. The core reason why LLMs are applicable to such game-theoretic scenarios in electricity market policies lies in their alignment with the essential demands of policy gaming and their ability to effectively overcome the limitations of traditional methods. First, electricity market policy games involve multiple stakeholders including government, power generation enterprises, and grid enterprises, whose decisions are influenced by complex factors such as policy orientation, market conditions, and self-interests. Through role-playing, LLMs can capture the decision-making logic and behavioral preferences of different agents without requiring researchers to subjectively assume "representative agents", thereby enabling a more realistic simulation of the bounded-rational decision-making process among multiple stakeholders.Second, the dynamic nature of policy games demands that models adapt to the dynamic adjustment of stakeholders' strategies. Benefiting from strong contextual understanding and generation capabilities, LLMs can dynamically output decision responses of each agent that conform to realistic situations based on policy content, thus avoiding the problem of disconnection from reality caused by the strong assumptions embedded in traditional models.Third, for the specialized evaluation of new policies such as new energy electricity price reform, LLMs can rapidly identify key influencing factors from policy texts and market data to achieve objective factor screening. This effectively addresses the shortcoming of strong subjectivity in factor selection in traditional game models^[28,31], providing more practically meaningful support for the accurate assessment of policy effects. Inspired by real-world human group decision-making heterogeneity, the four models simulate three subjects: photovoltaic enterprises, power grid enterprises, and government. Each role undergoes 5 independent tests to address potential response variations. The experimental design follows a structured protocol for consistency and repeatability.

1.1.1 The prompts provided to each LLM

We design a unified multiLLM roleplaying prompt for three decisionmaking agents: photovoltaic enterprises, power grid enterprises, and government agencies. All prompts follow the same setting: read Document No. 136, assume the scenario is after June 1, 2025, and roleplay as the corresponding Chinese stakeholder. For photovoltaic enterprises, the prompt asks for factors influencing the choice between active and passive grid connection; for power grid enterprises, it asks for factors affecting active or passive cooperation in new energy transmission and absorption; for government agencies, it asks for factors affecting strong or weak supervision. Each prompt requires an explanation and concludes with the fixed statement: "Final answer: I believe that … factors will affect my choice because …".

Although the prompt design in this paper takes policy background and role-playing as its core framework, the role-playing settings implicitly incorporate the micro decision-making constraints of each stakeholder: For photovoltaic generation enterprises, the prompt defines the role of "photovoltaic power generation enterprise", which implicitly reflects financial constraints such as investment costs and returns, as well as technical R&D bottlenecks. For power grid enterprises, the positioning of "responsible for new energy transmission and absorption" is specified, implying constraints including technical renovation pressure, accommodation capacity limitations, and regional industrial characteristics. For government, the role of "relevant government agencies" implicitly reflects realistic constraints such as market-oriented regulatory objectives, fiscal capacity, and regional disparities in new energy development. Meanwhile, by guiding each stakeholder to explain its decision-making logic within the policy context of Document 136, the micro-orientation of the prompt is further strengthened. This prevents excessively macro and homogeneous outputs from LLMs and ensures that the results conform to the actual decision-making logic of each participant.

1.1.2 LLM's subject role-playing process

1) Provide standardized prompts;

2) Record complete model responses;

3) Clear conversation history;

4) Repeat steps 1)-3), with a total of 5 independent tests conducted for each subject role;

5) Switch to the next subject role and repeat 1)-4) until the role-playing for all three subjects is completed;

6) Switch to the next LLM and repeat 1)-5).

It should be noted that conversation history is cleared before each new prompt to ensure test independence, with responses based solely on the current prompt. All responses are standardized. Default LLM temperature settings are retained for natural reasoning.

To enhance the reliability and economic rationality of influencing factors extracted by large language models, this paper adopts a multi-round semantic parsing framework. Rather than relying solely on high-frequency word screening, this study further conducts manual secondary validation and economic logic reduction on the model outputs, integrating theories of electricity market economics and practical experiences from China's new energy tariff market-oriented reforms. Semantic outputs irrelevant to the operational mechanism of the electricity market are excluded, and only critical factors consistent with cost-benefit theory, market equilibrium theory, and the institutional characteristics of China's electricity regulation are retained. During this process, policy text comparison, and industrial expert consultation are employed to ensure that the extracted factors reflect the actual decision-making logic following the 2025 new energy tariff market-oriented reform. These measures mitigate the impacts of the model's general corpus bias and algorithmic deviations, thereby guaranteeing the theoretical validity and practical applicability of factor selection.

Figure 1 summarizes key common factors frequently mentioned by models (per four LLMs) and their mention frequency across 15 independent tests per large model.

Fig. 1 Important influencing factors screened by the four LLMs

Figure 1 shows that, despite differences in the factors identified after role-playing three subjects, the four large models have significant overlap in key factors. This confirms the feasibility and rationality of using LLMs to simulate different groups' basic decision-making and screening^[28,31]. Sorting these more "realistic" LLM-identified factors gives those in Table 1.

1.2 Basic Assumptions of the Model

This paper constructs a three-player evolutionary game model following the mainstream research paradigm in the field of evolutionary games. The model incorporates not only the innovation cost of photovoltaic enterprises and the renovation investment cost of power grid enterprises, but also multi-dimensional factors including market electricity price, subsidy, penalty, market access mechanism (market transaction on-grid electricity, mechanism quantity), and green certificate spillover value, etc.. All the above factors serve as incentive and restraint instruments under the market-oriented reform framework of "Document No. 136", and can comprehensively reflect the core government functions of "guidance, regulation and guarantee" in the policy, as well as the revenue composition of each stakeholder.

In the equilibrium analysis of evolutionary games, the linear return assumption is a general prerequisite that enables the analytical derivation of the replicator dynamics equations and the rigorous determination of strategy stability. From the theoretical logic of evolutionary games, the linear or nonlinear form of the cost function mainly affects the quantitative values of stakeholders' payoffs and the magnitudes of critical thresholds, without changing the sign of the fitness difference between strategies in the replicator dynamics equations. Therefore, it will not alter the evolutionary direction of the system or the qualitative conclusion of the evolutionarily stable strategy (ESS), nor will it impair the core robustness of the model results.

1.2.1 Participants in the game model

Game participants: photovoltaic enterprises, power grid enterprises, and government. All are boundedly rational, not fully grasping decision-making information, but adjusting strategies via trial and error and learning to maximize their interests.

1.2.2 Strategy choices

Following the standard modeling paradigm in the field of three-player evolutionary games, strategy options are: photovoltaic enterprises [active/passive grid-connection]; power grid enterprises [active/passive cooperation]; government [strong supervision/weak supervision]. The three parties achieve coordinated photovoltaic grid-connection via their choices. Assume photovoltaic enterprises choose active grid-connection with probability $x$, passive with $(\mathrm{1}-x)$; power grid enterprises choose active cooperation with probability $y$, passive with $(\mathrm{1}-y)$; government chooses strong supervision with probability $z$, weak supervision with $(\mathrm{1}-z)$; where $x,y,z\in$ [0,1].

1.2.3 Costs and revenues of photovoltaic enterprises

1) If a photovoltaic enterprise chooses active grid-connection, it incurs innovation cost $C_{\mathrm{a}}$. Assume that: generation efficiency improves, costs reduce, market demand is easier to forecast, and market bargaining power rises. If the grid enterprise actively cooperates, the photovoltaic enterprise gains generation revenue of $(Q_{\mathrm{1}}-Q_{\mathrm{0}})(P_{\mathrm{1}}+g)+Q_{\mathrm{0}}{P}_{\mathrm{0}}$. If it passively cooperates, the photovoltaic enterprise may face grid-connection restrictions due to poor absorption. Under such restrictions, the monthly on-grid electricity volume, equal to the mechanism-based electricity quantity, is $Q_{\mathrm{0}}$, and the restricted generation revenue becomes $Q_{\mathrm{0}}{P}_{\mathrm{0}}$. Here, $Q_{\mathrm{1}}$ denotes the average monthly on-grid electricity volume. $Q_{\mathrm{0}}$ does not participate in green certificate transactions, and no premium is considered;its price is solely determined by $P_{\mathrm{0}}$. The segment in market transactions can consider $g$ and depends on $P_{\mathrm{1}}$. Pursuant to "Document No. 136", new energy's $Q_{\mathrm{0}}$ and price $P_{\mathrm{0}}$ shall be specified by provincial price, energy and power operation authorities. The document stipulates that mechanism-included electricity may be appropriately lower than total generation, implying $Q_{\mathrm{0}}<Q_{\mathrm{1}}$ and defining ratio $q$= $Q_{\mathrm{0}}/Q_{\mathrm{1}}$ (0<$q$<1) as the proportion of mechanism-based electricity in actual on-grid quantity.

2) A photovoltaic enterprise choosing passive grid-connection faces grid-connection restrictions by grid enterprise and only gets restricted generation revenue $Q_{\mathrm{0}}{P}_{\mathrm{0}}$.

3) Government strong supervision provides a subsidy $s$ for photovoltaic enterprises' on-grid electricity price; weak supervision means no subsidy.

1.2.4 Costs and revenues of power grid enterprises

1) Grid enterprises adopting active cooperation require grid upgrading costs $C_{\mathrm{b}}$, assumed to absorb all on-grid electricity. If photovoltaic enterprises choose active grid-connection, grid enterprises gain transmission revenue $t_{\mathrm{r}}{Q}_{\mathrm{1}}$ (with $t_{\mathrm{r}}$ as average transmission and distribution price) and, per "Document No. 136", price difference settlement fee $(P_{\mathrm{1}}-P_{\mathrm{0}})Q_{\mathrm{0}}$ for mechanism-included electricity. For passive grid-connection by photovoltaic enterprises, grid enterprises earn transmission revenue $t_{\mathrm{r}}{Q}_{\mathrm{0}}$ and price difference settlement fee $(P_{\mathrm{1}}-P_{\mathrm{0}})Q_{\mathrm{0}}$.

2) Grid enterprises adopting passive cooperation may face power absorption difficulties and on-grid quantity restrictions, with revenue limited to $t_{\mathrm{r}}{Q}_{\mathrm{0}}+$($P_{\mathrm{1}}-P_{\mathrm{0}}$)$Q_{\mathrm{0}}$; if photovoltaic enterprises also choose passive grid-connection, unstable electricity access may incur additional grid operation and maintenance costs $L_{\mathrm{b}}$.

3) Government strong supervision imposes annual penalty $d$ on grid enterprises adopting passive cooperation (e.g., missing renewable energy consumption share targets); weak supervision means no penalty.

1.2.5 Costs and revenues of government

1) Government revenue includes taxes from photovoltaic and grid enterprises at rates $t_{\mathrm{0}}$ and $t_{\mathrm{1}}$ respectively. Total tax revenue is $t_{\mathrm{0}}{R}_{\mathrm{a}}+t_{\mathrm{1}}{R}_{\mathrm{b}}$, with $R_{\mathrm{a}}$ and $R_{\mathrm{b}}$ representing the profits of photovoltaic enterprise and power grid enterprises, respectively.

2) Regardless of government strategy, grid enterprises' passive cooperation damages government credibility, with assumed $L_{\mathrm{g}}$.

3) Government strong supervision provides additional on-grid electricity price subsidy $s$ to regional photovoltaic enterprises; if grid enterprises passively cooperate (e.g., missing renewable energy consumption share targets), $d$ is imposed.

4) Government weak supervision cancels subsidies to photovoltaic enterprises and $d$ on grid enterprises for passive cooperation.

1.3 Establishment of the Game Payoff Matrix

Based on the above assumptions, a payoff matrix of the three-party evolutionary game subjects is constructed (Table 2).

1.4 Replication Dynamic Equations and Equilibrium Point Analysis

According to evolutionary game theory, the replication dynamic equations for photovoltaic enterprises, power grid enterprises, and government are constructed respectively.

The replication dynamic equation for photovoltaic enterprises is:

$F\left(x\right)=\mathrm{d}x/\mathrm{d}t=x\left(\mathrm{1}-x\right)\left[y\left(Q_{\mathrm{1}}-Q_{\mathrm{0}}\right)\left(P_{\mathrm{1}}+g+zs\right)-C_{\mathrm{a}}\right]$(1)

The replication dynamic equation for power grid enterprises is:

$F\left(y\right)=\mathrm{d}y/\mathrm{d}t=y\left(\mathrm{1}-y\right)\left[x\left(t_{\mathrm{r}}(Q_{\mathrm{1}}-Q_{\mathrm{0}})-L_{\mathrm{b}}\right)+zd-C_{\mathrm{b}}+L_{\mathrm{b}}\right]$(2)

The replication dynamic equation for government is:

$F\left(z\right)=\mathrm{d}z/\mathrm{d}t=z\left(\mathrm{1}-z\right)\left[xy{t}_{\mathrm{0}}s\left(Q_{\mathrm{0}}-Q_{\mathrm{1}}\right)+\left(y-\mathrm{1}\right)\left(t_{\mathrm{1}}-\mathrm{1}\right)d+t_{\mathrm{0}}s{Q}_{\mathrm{0}}-s\right]$(3)

By differentiating the above replication dynamic equations, we obtain:

$\{\begin{array}{c}\mathrm{d}F(x)/\mathrm{d}x=\left(\mathrm{1}-\mathrm{2}x\right)[y\left(Q_{\mathrm{1}}-Q_{\mathrm{0}}\right)\left(P_{\mathrm{1}}+g+zs\right)-C_{\mathrm{a}}],\\ \mathrm{d}F(y)/\mathrm{d}y=\left(\mathrm{1}-\mathrm{2}y\right)\left[x\left(t_{\mathrm{r}}(Q_{\mathrm{1}}-Q_{\mathrm{0}})-L_{\mathrm{b}}\right)+zd-C_{\mathrm{b}}+L_{\mathrm{b}}\right],\\ \mathrm{d}F(z)/\mathrm{d}z=\left(\mathrm{1}-\mathrm{2}z\right)\left[xy{t}_{\mathrm{0}}s\left(Q_{\mathrm{0}}-Q_{\mathrm{1}}\right)+\left(y-\mathrm{1}\right)\left(t_{\mathrm{1}}-\mathrm{1}\right)d+t_{\mathrm{0}}s{Q}_{\mathrm{0}}-s\right].\end{array}$(4)

Letting $F\left(x\right)$= $F\left(y\right)$= $F\left(z\right)$= 0, we can obtain 8 local stable equilibrium points, which are E₁(0,0,0), E₂(0,0,1), E₃(0,1,0), E₄(0,1,1), E₅(1,0,0), E₆(1,0,1), E₇(1,1,0), and E₈(1,1,1), respectively. According to evolutionary game theory, an ESS must satisfy the condition that all eigenvalues in the Jacobian matrix are negative.

Based on the above replication dynamic equations, the Jacobian matrix can be derived as Equation (5):

$\left(\begin{array}{ccc}\left(\mathrm{1}-\mathrm{2}x\right)[y\left(Q_{\mathrm{1}}-Q_{\mathrm{0}}\right)\left(P_{\mathrm{1}}+g+zs\right)-C_a]& x\left(\mathrm{1}-x\right)\left[\left(Q_{\mathrm{1}}-Q_{\mathrm{0}}\right)\left(P_{\mathrm{1}}+g+zs\right)\right]& x\left(\mathrm{1}-x\right)ys\left(Q_{\mathrm{1}}-Q_{\mathrm{0}}\right)\\ y\left(\mathrm{1}-y\right)\left(t_r(Q_{\mathrm{1}}-Q_{\mathrm{0}})-L_b\right)& \left(\mathrm{1}-\mathrm{2}y\right)\left[x\left(t_r(Q_{\mathrm{1}}-Q_{\mathrm{0}})-L_b\right)+zd-C_b+L_b\right]& y\left(\mathrm{1}-y\right)d\\ z\left(\mathrm{1}-z\right)y{t}_{\mathrm{0}}s\left(Q_{\mathrm{0}}-Q_{\mathrm{1}}\right)& z\left(\mathrm{1}-z\right)\left[x{t}_{\mathrm{0}}s\left(Q_{\mathrm{0}}-Q_{\mathrm{1}}\right)+\left(t_{\mathrm{1}}-\mathrm{1}\right)d\right]& \left(\mathrm{1}-\mathrm{2}z\right)\left[xy{t}_{\mathrm{0}}s\left(Q_{\mathrm{0}}-Q_{\mathrm{1}}\right)+\left(y-\mathrm{1}\right)\left(t_{\mathrm{1}}-\mathrm{1}\right)d+t_{\mathrm{0}}s{Q}_{\mathrm{0}}-s\right]\end{array}\right)$(5)

Substituting the 8 local stable equilibrium points into Equation (5) respectively, the eigenvalues of the corresponding Jacobian matrix can be obtained (Table 3).

The analysis of eigenvalues in Table 3 indicates that three key conditions determine the evolutionary stability:1) $(Q_{\mathrm{1}}-Q_{\mathrm{0}})(P_{\mathrm{1}}+g)-C_{\mathrm{a}}$> 0 indicates positive net benefit for photovoltaic enterprises choosing active grid-connection; 2) $(t_{\mathrm{r}}{Q}_{\mathrm{1}}-t_{\mathrm{r}}{Q}_{\mathrm{0}})-C_{\mathrm{b}}$> 0 means grid enterprises' net benefit from active cooperation (after transformation costs) exceeds that from passive cooperation; 3) $t_{\mathrm{0}}s(\mathrm{2}{Q}_{\mathrm{0}}-Q_{\mathrm{1}})-s$> 0 reflects government revenue after tax adjustment exceeds subsidy expenditure. These three conditions (each >0 or not) yield 8 hypothetical scenario combinations (Table 4). After analyzing evolutionary game stable strategies, the results are presented in Table 5.

Table 5 shows distinct evolutionary equilibrium points across scenarios: Scenarios 1 and 3 have E₈(1,1,1) with strategy (active grid-connection, active cooperation, strong supervision); Scenario 2 has E₇(1,1,0) with (active grid-connection, active cooperation, weak supervision); Scenarios 5 and 7 have E₄(0,1,1) with (passive grid-connection, active cooperation, strong supervision); Scenarios 6 and 8 have E₃(0,1,0) with (passive grid-connection, active cooperation, weak supervision).

2 Parameter Assignment of Verification Case

This paper adopts actual data on photovoltaic industry in Jiangxi Province in 2024. Only the daily average market transaction electricity price ($P_{\mathrm{1}}$) is referenced from the 2024 Hubei Electricity Market White Paper, and the indicator values are generally consistent between the two provinces, reflecting the common characteristics of photovoltaic market electricity prices in central China. The initial values assigned to each parameter of the model are presented in Table 6. It should be noted that $P_{\mathrm{0}}$ and $L_{\mathrm{g}}$ are eliminated during the evolution process, and initial values are no longer assigned to them.

It should be noted that: (a) Under the new market-oriented mechanism for on-grid electricity prices of new energy specified in "Document No. 136", electricity price subsidies for new energy have been basically eliminated, except for 74 special regions. Accordingly, the electricity price subsidy $s$ adopted in this study is not a traditional high-intensity incentive subsidy, but a residual and symbolic average subsidy close to zero. The initial value of $s$ is 0.000 001 ten thousand yuan/MWh. (b) For core operational parameters, official local statistics of Jiangxi Province and announcements issued by power grid enterprises are adopted preferentially. For industrial standard and policy-related parameters, unified national norms and legal documents are applied to avoid inconsistencies caused by heterogeneous data sources. Meanwhile, this study focuses on the photovoltaic market in Central China, and the simulation results are mainly intended to provide policy references for central provinces, so as to further ensure regional applicability and persuasiveness.

3 Simulation Analysis and Verification

This paper uses Python for numerical simulation to analyze how key parameter variations affect the three subjects' strategy selection in the evolutionary game. The initial parameter settings of this simulation are shown in Table 6. It should be noted that: the initial values of the above parameters meet the conditions of Scenario 1 in Table 5; however, this simulation experiment will also examine the impact of fluctuations in the values of individual factors on the strategic choices of the three main bodies. Therefore, under the condition of fluctuations in certain parameters, conditions satisfying other cases may occur, and the correctness of the model will be verified one by one in this simulation.

Parameters $t_{\mathrm{r}}$, $t_{\mathrm{0}}$, $t_{\mathrm{1}}$, $L_{\mathrm{b}}$ are usually verified by government departments, with relatively stable values; moreover, there is a proportional relationship $q$ between $Q_{\mathrm{1}}$ and $Q_{\mathrm{0}}$. Thus, this simulation only discusses parameters such as $P_{\mathrm{1}}$, $s$, $q$, $C_{\mathrm{a}}$, $d$, $g$, which may have large value fluctuations and are closely related to the grid connection of photovoltaic energy.

3.1 Impact of Daily Average Market Transaction Electricity Price (${\mathit{P}}_{\mathrm{1}}$)

Under the market-oriented pricing mechanism for new energy grid connection, all energy sources affect market prices, so photovoltaic energy may face significant price fluctuations when entering the market. P₁ takes 10 values in [0.001 0, 0.070 0] ten thousand yuan/MWh, with 100 replicator dynamics equation evolution results cyclically plotted over time (Fig. 2). The threshold of $P_{\mathrm{1}}$ is in [0.001 0, 0.008 7]; as $P_{\mathrm{1}}$ rises within this range, the equilibrium shifts from ESS₂(0,1,1) to ESS₁(1,1,1), where ESS₂ means passive grid connection by photovoltaic enterprises, detrimental to industry sustainability. When $P_{\mathrm{1}}$ is below the threshold value, the model satisfies Scenario 5 in Table 5; on the contrary, it satisfies Scenario 1. Simulation shows: 1) Above the threshold, higher $P_{\mathrm{1}}$ increases enterprises' expected profit, raising active grid-connection probability; below it, profit lags expenditure, favoring passive strategies. 2) Rising $P_{\mathrm{1}}$ reduces power grid enterprises' active cooperation probability, as higher prices increase purchase costs, curbing enthusiasm and prompting preference for existing models to lower prices. However, it will still choose to active cooperation under the influence of photovoltaic enterprises and the government in the end. 3) As shown in Fig. 2, changes in the value of $P_{\mathrm{1}}$ have a significantly weaker impact on the willingness of power grid enterprises than on that of photovoltaic enterprises. With price fluctuations, the government tends to supervise the settlement of new energy transaction price, guiding both enterprises to adopt active strategies and avoid the adverse impacts caused by market fluctuations.

Fig. 2 Impact of different ${\mathit{P}}_{\mathrm{1}}$ (Note: the unit of ${\mathit{P}}_{\mathrm{1}}$ is ten thousand yuan/MWh)

3.2 Impact of Electricity Price Subsidy ($\mathit{s}$)

Under the policy background of "Document No. 136", which has substantially phased out subsidies, the subsidy $s$ adopted in this paper is not a traditional high-intensity incentive subsidy, but a residual and symbolic average subsidy close to zero. Considering the price volatility in the photovoltaic market, we set $P_{\mathrm{1}}$ at three levels: 0.006, 0.046 7, and 0.07 ten thousand yuan/MWh. For each level of $P_{\mathrm{1}}$, five values of $s$ within the interval [0.000 001,0.060 000] ten thousand yuan/MWh are selected. Simulation results of the replicator dynamic equations over 100 evolutionary iterations are plotted cyclically. As can be seen from Fig. 3, the evolutionary outcome converges to ESS₂(0,1,1) only when $P_{\mathrm{1}}$= 0.006 and $s$= 0.000 001, while all other scenarios converge to ESS₁(1,1,1). In particular, when $P_{\mathrm{1}}$> 0.006 ten thousand yuan/MWh, $s$ exerts no significant influence on the evolutionary results, and the equilibrium point remains ESS₁(1,1,1). This indicates that: When $P_{\mathrm{1}}$ is excessively low, it will negatively affect the grid-connection decisions of photovoltaic enterprises, which is consistent with the conclusion in Section 3.1. When $P_{\mathrm{1}}$ exceeds the threshold value, the strategic choices of the three stakeholders in central China (represented by Jiangxi) are insensitive to adjustments in $s$. In this case, the model consistently conforms to Scenario 1 in Table 5, further validating the model's effectiveness. Simulation results: 1) The photovoltaic industry in central regions such as Jiangxi (medium-to-high penetration areas) has formed a relatively mature market-oriented profit model. Photovoltaic enterprises in these regions have now adapted to policies with reduced or even eliminated subsidies. Their revenue mainly derives from electricity market transactions, guaranteed power accommodation, and weak policy incentives, rather than traditional subsidies. Although a slight increase in s can raise the expected returns of PV enterprises, its share in total revenue has declined significantly. Even when s approaches zero, enterprises can still cover costs and achieve reasonable returns relying on market-based revenue, thus exhibiting weak sensitivity to subsidy changes. 2) Smaller $s$ strengthens power grid enterprises' active cooperation, as subsidy cancellation promotes energy competition fairness and their willingness to accept new energy grid-connection. 3) The smaller $s$ is, the weaker the government's supervisory tendency. Cancelling subsidies can also cut the government's fiscal burden, restrict the obstacles special subsidies create for the rational development of other energy forms, and facilitate the government's shift from a "direct intervenor" to a "rule-maker and supervisor".

Fig. 3 Impact of different $\mathit{s}$ and ${\mathit{P}}_{\mathrm{1}}$ (Note: the unit of $\mathit{s}$ and ${\mathit{P}}_{\mathrm{1}}$ are ten thousand yuan/MWh)

3.3 Impact of Annual Innovation Costs Invested by Photovoltaic Enterprises (${\mathit{C}}_{\mathbf{a}}$)

Annual innovation costs $C_{\mathrm{a}}$ take 10 values in [500,8 000] ten thousand yuan, with 100 replicator dynamics equation evolutions simulated and plotted cyclically over time. Figure 4 shows $C_{\mathrm{a}}$'s threshold is 7 167-8 000 ten thousand yuan; as $C_{\mathrm{a}}$ rises within this range, equilibrium shifts from ESS₁(1,1,1) to ESS₂(0,1,1), where ESS₂ means photovoltaic enterprises choose passive grid-connection. When $C_{\mathrm{a}}$> 7 167, the model satisfies Scenario 5 in Table 5; on the contrary, it satisfies Scenario 1. Simulation shows: 1) Below the threshold, photovoltaic enterprises choose active grid-connection under other parties' influence, but their willingness to maintain the status quo grows with $C_{\mathrm{a}}$; when $C_{\mathrm{a}}$ exceeds the threshold, revenue fails to cover expenses, leading to passive grid-connection. 2) Higher $C_{\mathrm{a}}$ increases power grid enterprises' active cooperation probability, as photovoltaic enterprises' innovations may improve price prediction and energy storage configuration, boosting photovoltaic energy's value to the grid and thus grid enterprises' cooperation willingness. 3) As shown in Fig. 4, changes in the value of $C_{\mathrm{a}}$ have a significantly weaker impact on the willingness of power grid enterprises than on that of photovoltaic enterprises. To correctly guide the strategic choices and continuous innovation of photovoltaic enterprises, the government chooses to supervise photovoltaic enterprises' innovation cost investment.

Fig. 4 Impact of different ${\mathit{C}}_{\mathbf{a}}$ (Note: the unit of ${\mathit{C}}_{\mathbf{a}}$ is ten thousand yuan)

Photovoltaic energy may face price fluctuations in market electricity transactions; examining only single innovation cost changes cannot reveal such fluctuations' impact on their innovation. Thus, under three market prices $P_{\mathrm{1}}$= 0.02, 0.046 7, 0.07, $C_{\mathrm{a}}$ take 3 values in [500, 7 000] ten thousand yuan respectively, with 100 replicator dynamics equation evolutions simulated and plotted cyclically over time for further analysis. Figure 5 shows: With the same $C_{\mathrm{a}}$, higher $P_{\mathrm{1}}$ raises photovoltaic enterprises' active grid-connection likelihood; conversely, if $P_{\mathrm{1}}$ remains depressed for a long time, the higher the probability that photovoltaic enterprises will choose the passive grid-connection strategy. This indicates that the higher the average market transaction price, the more motivated photovoltaic enterprises are to secure higher prices by optimizing energy storage, forecasting demand, and timing grid connections, thus gaining excess profits. The new market price settlement mechanism obviously incentivizes these enterprises to boost innovation.

Fig. 5 The impact of different ${\mathit{C}}_{\mathbf{a}}$ and ${\mathit{P}}_{\mathrm{1}}$ (Note: the unit of ${\mathit{C}}_{\mathbf{a}}$ is ten thousand yuan; the unit of ${\mathit{P}}_{\mathrm{1}}$ is ten thousand yuan/MWh)

3.4 Impact of Mechanism-Based Electricity Quantity Proportion ($\mathit{q}$)

"Document No. 136" stipulates "mechanism-included electricity can be lower than total generation", so $Q_{\mathrm{0}}$<$Q_{\mathrm{1}}$. Thus, by setting the proportion of mechanism electricity $q$= $Q_{\mathrm{0}}$/$Q_{\mathrm{1}}$ (0<$q$<1), the impact of mechanism electricity and actual grid-connected electricity on the evolutionary results can be analyzed indirectly through this proportion. $q$ takes 10 values in [0.10, 0.95], with 100 replicator dynamics equation evolutions simulated and plotted cyclically over time. Figure 6 shows $q$'s threshold is 0.478-0.572; as $q$ drops from 0.572 to 0.478, equilibrium shifts from ESS₁(1,1,1) to ESS₂(1,1,0) (government "weak supervision"). When $q<$ 0.572, the model satisfies Scenario 2 in Table 5; on the contrary, it satisfies Scenario 1. Simulation results: higher $q$ reduces photovoltaic enterprises' active grid-connection willingness but raises power grid enterprises' "active cooperation" probability. Higher proportion means more $Q_{\mathrm{0}}$ and less market-transacted electricity ($Q_{\mathrm{1}}$$-$$Q_{\mathrm{0}}$): photovoltaic enterprises gain less from flexible transactions (lower enthusiasm), while grid enterprises face smaller price fluctuation risks (stronger cooperation willingness). However, "Document No. 136" emphasizes guiding new energy like photovoltaics in market transactions. Higher $q$ means lower photovoltaic market participation, prompting stronger government supervision. Figure 6 shows that when $q$ is higher than the threshold, the government will choose "strong supervision"; when $q$ further decreases, the government tends to choose "weak supervision". The government is highly sensitive to q.

Fig. 6 Impact of different $\mathit{q}$

To sum up, the value of $q$ does not affect the strategic choices of photovoltaic enterprises and power grid enterprises, but it does influence their willingness to choose. As shown in Fig. 6, changes in the value of q have a significantly weaker impact on the willingness of power grid enterprises than on that of photovoltaic enterprises. Meanwhile, a gradual decrease in $q$ indicates further stabilization of the power market transactions, reflecting the government's shift from a "direct intervener" to a "rule-maker and supervisor".

3.5 Impact of Green Certificate Spillover Value ($\mathit{g}$)

Green certificate spillover value $g$ takes 10 values in [0.000 1, 0.100 0] ten thousand yuan/MWh, with 100 replicator dynamics equation iterations simulated and plotted cyclically over time. Figure 7 shows that $g$ does not affect the equilibrium point from always being ESS(1,1,1). In this case, the model consistently conforms to Scenario 1 in Table 5, further validating the model's effectiveness. Simulation results: 1) Higher $g$ boosts photovoltaic enterprises' expected market revenue, enhancing their participation willingness and active grid-connection probability. 2) Higher $g$ increases photovoltaic electricity in transactions, raising grid enterprises' absorption burden; they prefer the status quo, but still cooperate under others' influence. 3) As shown in Fig. 7, changes in the value of g exert roughly equivalent effects on the willingness of both photovoltaic enterprises and power grid enterprises. Government will monitor grid-connected electricity's green certificate value in transactions to ensure supply-demand stability.

Fig. 7 Impact of different $\mathit{g}$ (Note: the unit of $\mathit{g}$ is ten thousand yuan/MWh)

This indicates that adjustment of $g$ may not impact the final strategic choices of the three parties, but they significantly influence the intensity of choice willingness (between "passive selection" and "active preference") for photovoltaic enterprises and power grid enterprises.

3.6 Impact of Assessment penalties ($\mathit{d}$)

Annual penalties $d$ take 10 values in [0, 20 000] ten thousand yuan, with 100 evolutions of the replicator dynamics equation simulated and plotted over time. Figure 8 shows d does not affect the equilibrium point from always being ESS(1,1,1). In this case, the model consistently conforms to Scenario 1 in Table 5, further validating the model's effectiveness. Simulation results: 1) Higher $d$ raises grid enterprises' active cooperation probability. 2) Higher $d$ reduces photovoltaic enterprises' active grid-connection probability; they may shift innovation responsibility to grid enterprises, lowering their own requirements but eventually choosing grid-connection under others' influence. 3) As shown in Fig. 8, changes in the value of $d$ have a significantly greater impact on the willingness of power grid enterprises than on that of photovoltaic enterprises. Meanwhile, a smaller penalty $d$ corresponds to a weaker regulatory tendency of the government, reflecting the trend in government regulatory strategy and its transition from a "direct intervener" to a "rule-maker and supervisor".

Fig. 8 Impact of different $\mathit{d}$ (Note: the unit of $\mathit{d}$ is ten thousand yuan)

This indicates that consumption responsibility assessment penalties may not influence the final choice of photovoltaic and power grid enterprises to adopt active grid connection strategies, but significantly impact their willingness intensity in strategy selection. Meanwhile, the reduction of assessment penalties reflects the government's role transition from a "direct intervenor" to a "rule maker and supervisor".

4 Conclusions and Suggestions

4.1 Conclusions

1) Photovoltaic enterprises are highly sensitive to electricity prices. Sustained electricity prices below the critical threshold will curb new energy investment in the central and western regions abundant in wind and solar resources yet with underdeveloped economies, calling for precautions against vicious competition featured by "bad money driving out good".

2) Full subsidy phase-out still brings transitional risks. While New energy industry in central China can sustain sound operation without substantial subsidies, such a situation cannot be replicated in the central and western regions plagued by high wind and solar curtailment.

3) Due to the nature of state-owned enterprises, grid enterprises prioritize administrative objectives over profit maximization in decision-making and generally choose cooperative strategies, with their willingness to cooperate subject to electricity prices fluctuations, subsidies and consumption assessment.

4) Limitations: Based on bounded rationality, this paper only analyzes Photovoltaic grid connection. Restricted by the public welfare attribute of electricity, the model assumes grid companies gain revenue merely from power transmission excluding end-user retail proceeds, which conforms to China's recent policy to set up independent power retailers serving end consumers. Future research can bring in demand-side participants and explore risk control strategies covering adjustable loads and energy storage to reduce industrial dependence on administrative measures.

4.2 Suggestions

Based on the conclusions of the evolutionary game discussed earlier, the following suggestions are put forward for the three levels of government, photovoltaic enterprises, and power grid enterprises:

1) Government level: (a) Under the market-oriented mechanism specified in "Document No. 136", photovoltaic generation enterprises in medium-to-high penetration regions of central China can maintain their willingness to actively connect to the grid without relying on substantial subsidies. Nevertheless, the regional disparities among China's provinces cannot be overlooked. Instead, policy implementation should take into account the characteristics of different regions, adopt appropriately flexible regulation, and apply policy tools in a differentiated manner. (b) Second, establish strategic thresholds to stabilize the market. Taking Jiangxi Province as an example, when the market transaction price of photovoltaic energy continues to be lower than 0.006 ten thousand yuan/MWh, the government should activate a temporary price intervention mechanism. It is advisable to set a ceiling for the innovation costs of photovoltaic generation enterprises (for example, with reference to RMB 7 167 ten thousand yuan), and the excess part may be eligible for additional pre-tax deductions for R&D expenses. In addition, the ratio $q$ of supervisory mechanism electricity to grid-connected photovoltaic electricity may be monitored. When $q$ exceeds 0.572, the government should further strengthen the supervision and guidance of photovoltaic enterprises' participation in the market transactions.

2) Photovoltaic enterprises level: (a) To address market fluctuations, enterprises should enhance their ability to identify and capture trading opportunities through technological innovation. By investing an appropriate level of costs in innovation, they can achieve high returns from transactions executed during periods of elevated electricity prices. (b) Additionally, they should explore medium- and long-term contract opportunities with large industrial and commercial users to lock in long-term returns, so as to avoid the revenue risk arising from market electricity prices falling below $P_{\mathrm{1}}$≤ 0.006 ten thousand yuan/MWh. (c) Furthermore, enterprises can develop collaborative distributed energy models by building "photovoltaic+energy storage+microgrid" systems in industrial parks to enable partial on-site self-consumption, thereby alleviating operational pressure when electricity price $P_{\mathrm{1}}$ fluctuates below the threshold. (d) Finally, active participation in the green certificate market can yield premium revenues and support long-term sustainability.

3) Grid level: Based on their state-owned attributes, a dual incentive and restraint mechanism that combines administrative goal orientation and reasonable return guarantee should be established. The assessment requirements for new energy accommodation shall be closely integrated with investment cost compensation. It is proposed that when power grid enterprises achieve the new energy accommodation targets, the government may provide special fiscal subsidies or additional deductions for investment costs. This not only strongly supports the institutional logic of "priority to state-owned attributes", but also prevents irrational expansion caused solely by assessment pressure. (b) State-owned grid enterprises should strengthen their social responsibilities. Their state-owned attributes determine that they must cooperate and undertake the administrative responsibilities of coordinating regional energy balance and removing barriers to new energy accommodation. They are also obliged to promote the implementation of policies for cross-provincial and cross-regional electricity transactions. Such responsibilities take precedence over the pursuit of profit maximization within individual regions.

1. 三峡大学 经济与管理学院, 湖北 宜昌 443002

2. 武汉商学院 人工智能与大数据学院, 湖北 武汉 430056

References

All Tables

All Figures

	Fig. 1 Important influencing factors screened by the four LLMs
In the text

	Fig. 2 Impact of different ${\mathit{P}}_{\mathrm{1}}$ (Note: the unit of ${\mathit{P}}_{\mathrm{1}}$ is ten thousand yuan/MWh)
In the text

	Fig. 3 Impact of different $\mathit{s}$ and ${\mathit{P}}_{\mathrm{1}}$ (Note: the unit of $\mathit{s}$ and ${\mathit{P}}_{\mathrm{1}}$ are ten thousand yuan/MWh)
In the text

	Fig. 4 Impact of different ${\mathit{C}}_{\mathbf{a}}$ (Note: the unit of ${\mathit{C}}_{\mathbf{a}}$ is ten thousand yuan)
In the text

	Fig. 5 The impact of different ${\mathit{C}}_{\mathbf{a}}$ and ${\mathit{P}}_{\mathrm{1}}$ (Note: the unit of ${\mathit{C}}_{\mathbf{a}}$ is ten thousand yuan; the unit of ${\mathit{P}}_{\mathrm{1}}$ is ten thousand yuan/MWh)
In the text

	Fig. 6 Impact of different $\mathit{q}$
In the text

	Fig. 7 Impact of different $\mathit{g}$ (Note: the unit of $\mathit{g}$ is ten thousand yuan/MWh)
In the text

	Fig. 8 Impact of different $\mathit{d}$ (Note: the unit of $\mathit{d}$ is ten thousand yuan)
In the text