Promoting the widespread access and integration of new energy generation into existing power markets is a key strategy for China to achieve peak carbon and carbon neutrality. A joint regulatory mechanism composed of government regulators, power generation enterprises, and third-party testing organizations has become an effective way to ensure the stable operation of the power market and safeguard the economic interest of all parties. In order to analyze the key factors affecting the mechanism and improve the regulatory efficiency, this paper constructs a three-party evolutionary game model, explores the motivations of the participants under different strategy choices, and establishes a set of indicator systems for evaluating producers. The evolutionary game model is numerically simulated using the unified dynamics method, and the evolutionary stable strategy analysis is used to reveal how the key parameters affect the outcome of the game and its dynamic process, so as to find out the potential driving factors affecting the strategy choices. The results of the study show that in the early stage of market development, it is crucial to improve the profitability of firms, and the government needs to impose strict penalties and high incentives. As the market gradually matures and becomes more transparent, the government can gradually reduce the level of penalties. At the same time, ensuring accountability mechanisms from higher authorities to the government is key to ensure the effectiveness of regulation. This study provides an important theoretical basis and policy recommendations for constructing a new regulatory structure for the electricity market.

AC

Government incentives for outstanding companies

AS

Government awards for outstanding organizations

CH

Cost of producing high quality electricity

CL

Cost of producing low quality electricity

CO

Corporate speculation costs

CR

Third-party testing agencies intend to find the cost of rent

CS

Cost of strict government regulation

CT

Enterprise rent-seeking costs

CZ

Government spending to rectify the market

PC

Government penalties for non-compliant companies

PS

Government penalties for non-compliant institutions

RH

Benefits of electricity sales

RT

Third-party testing agency gains

RS

The benefits of government regulation

SE

Punishment of the government by higher authorities

Under the current severe situation of continuous deterioration of the ecological environment, the energy industry, as one of the major sources of pollution, and its low-carbon transformation has become one of the major issues to be solved on a global scale (Hu , 2023a; 2023c; Miguel , 2010; Peyerl , 2022; and Tan , 2023). The power sector, in particular, accounts for a considerable share of China's total carbon emissions. Therefore, China has made a solemn commitment to the world to realize the goal of carbon neutrality. In this context, in-depth re-form and transformation of the power industry will undoubtedly become one of the effective ways to realize China's carbon neutral goal (McElroy, 2010; Yang , 2022; and Zou , 2022).

Historically, the monopolistic nature of the electricity industry, as a natural monopoly, although justified to a certain extent, has become a key factor impeding the transformation of the electricity market toward green and low-carbon (Bai , 2023; Han , 2024; Hu , 2023b; Hu and Zhang, 2023; and Zhu , 2024). In order to solve this problem, countries around the world have taken deregulation measures with a view to breaking through the established barriers in the power sector and promoting the liberalization and marketization of the power market (Bojnec and Krizaj, 2021; Streimikiene and Siksnelyte, 2014). China is no exception, as the government has created a series of incentives to promote the development of the renewable power generation industry and is committed to building an electricity supply and consumption system dominated by a high proportion of new energy sources. As of 2023, China's national installed renewable power capacity has reached 1.404 × 109 kW, a figure that underscores the country's tremendous progress in renewable energy (Hu, 2023; Hu , 2023a; and Hu , 2023c).

In order to further break down industry barriers, China has implemented a liberalization policy that has increased the diversity of electricity market players and attracted a large number of social resources to participate in electricity distribution and operation. However, this rapid market liberalization has also brought certain challenges; in particular, the existing regulatory system has struggled to meet the needs of the rapid development of the power industry in terms of regulatory efficiency and has even limited the progress of the industry in some aspects. To address this challenge, the government has begun to transfer some of its monitoring and regulatory functions to third-party testing organizations, with a view to building a new, more efficient regulatory system that will enhance the overall efficiency of regulation (Wu , 2024). Through these measures, China aims to ensure the sustainable development of its power sector while advancing its long-term goal of carbon neutrality.

A trend can be observed in regulatory practices in other industries: with the implementation of government measures to simplify administrative procedures and decentralization as well as the rapid development of the testing industry, third-party testing organizations are becoming a key gateway to assessing and listing the quality of products of power companies. Together with government regulators, these organizations share the important responsibility of ensuring the safety of electricity in society. However, the possible rent-seeking behavior of third-party testing organizations, driven by interest, may lead to market disorder (Feess , 2015; Liang , 2023; Wei , 2022; and Weng , 2023). The characteristics of the power industry include high research and development costs, difficult testing, long payback periods, stringent requirements for production processes, etc. These factors lead to higher costs and lower benefits in producing high-quality electricity. In contrast, the production of low-quality electricity is relatively more profitable (Alam and Bhattacharyya, 2016). In the context of an imperfect regulatory system and limited binding force of government regulation, power producers may be inclined to produce low-quality power and seek higher economic benefits by seeking rent from third-party testing organizations. Similarly, third-party testing organizations may intentionally engage in rent-seeking under the temptation of high benefits. Rent-seeking behavior not only leads to the inflow of low-quality electricity into the market, which is detrimental to consumers' rights and interest, but also may lead to electric power safety accidents, which threaten social security (Sadi and Arabkoohsar, 2020). The safety and stability of the power system is directly related to national security and the stability of people's lives; therefore, it is of great practical significance to study the rent-seeking phenomenon in power quality testing and formulate corresponding regulatory strategies. This requires regulatory agencies not only to improve the regulatory efficiency but also to ensure the fairness and transparency of the regulation, in order to prevent the occurrence of rent-seeking behavior and to protect the healthy development of the power market.

In the existing academic research, the exploration of electricity regulation mostly focuses on the regulation of the access criteria of the electricity market (Huang , 2019), tariff-setting mechanism (Burinskiene and Rudzkis, 2010; Tostado-Véliz , 2023), power-related services (Taale and Kyeremeh, 2016; Thomas and Urpelainen, 2018), and management of electricity-related services. These studies provide theoretical basis and practical guidance for effective regulation of the electricity market. On the other hand, research on power quality mainly focuses on the improvement of power quality when grid-connected electricity is generated from unstable renewable energy sources such as wind and solar energy (Feng , 2021; Jin , 2020; and Nijhuis , 2015), and on the development of power quality standards and testing methods (Jasinski , 2020; Kapoor , 2021). These studies are of great significance in ensuring the stable operation of power systems and power quality. However, there are relatively few studies on regulatory strategies for power quality, which provides an important entry point for this study. The study of regulatory strategies for power quality not only helps to improve the operational efficiency of the power system but also protects the interest of consumers and prevents the erosion of the market by poor-quality power, thus ensuring the safe and stable operation of the power system. Therefore, this study has important theoretical and practical value for improving the regulatory system of the electric power market and promoting the sustainable development of the electric power industry.

This paper constructs a three-party evolutionary game model involving a government regulator, a third-party testing agency, and an electricity producer, aiming to analyze the strategic interactions and evolutionary stabilization strategies of these stakeholders in the electricity market. Several key factors are considered in the model, including the profitability of power enterprises, the incentives and penalties of government regulators for third-party testing organizations and power producers, the rent-seeking costs of power producers and third-party testing organizations as well as the supervision and penalties of government regulators by higher authorities. Through the analysis of the evolutionary game model, this paper aims to reveal how the strategic choices of the participants in the electricity market are affected by these factors and how they evolve over time to reach a steady state. This research not only helps to understand the complex dynamics of the electricity market but also provides policy makers with a theoretical basis for optimizing regulatory strategies and improving market efficiency and fairness.

Game theory as an analytical tool has significant advantages in assessing and predicting the benefits in strategic interactions, especially in considering the individual and social behavior of stakeholders, and it bridges the gap between traditional analytical approaches (Eissa , 2021; Su , 2018). Evolutionary game theory, on the other hand, further integrates the idea of biological evolution into the framework of game theory, explaining the phenomena of mutual learning, competition, and adaptation of different subjects in the process of strategy selection (Axelrod and Hamilton, 1981). In classical game theory, participants are assumed to be fully rational and able to have complete information on which to make optimal decisions. However, this assumption often does not hold true in the real world. Participants in the electricity market are neither fully aware of each other's decision-making process nor completely unaware of each other's intentions. Their strategic choices often do not find the optimal solution in a single attempt, and even the so-called optimal strategy changes with the social environment (Wu , 2024). Therefore, the behavioral strategies of electricity market participants are unpredictable.

Evolutionary game theory combines classical game theory with dynamic evolutionary theory, which emphasizes the concepts of finite rationality and dynamic equilibrium compared to traditional game theory. In the power market, power producers, third-party testing organizations, and the government all need to develop their own strategic choices, but the differences in their interest lead to conflicts in the development of the power market. Since these three parties are usually unequal in terms of status and information, they can only adjust their own strategies in constantly observing and adapting to the strategies of the other two parties, in order to seek to realize their respective optimal strategies. Thus, evolutionary game theory provides a framework suitable for analyzing the strategic choices of electricity market participants, enabling this paper to more accurately model and predict behavioral dynamics in electricity markets.

Third-party testing organizations and government regulation are the key to guarantee the quality and safety of electric energy. The logical relationship between the three evolved game subjects of power industry regulation constructed in this paper is shown in Fig. 1.

FIG. 1.

Logic relationship of the three-party evolutionary game model.

FIG. 1.

Logic relationship of the three-party evolutionary game model.

Close modal

In order to construct the game model, analyze the stability of each party's strategy and equilibrium point as well as the influence relationship of each element, the following assumptions are made.

  • Hypothesis 1: Electricity production enterprises are participant 1, third-party testing organizations are participant 2, and government regulators are participant 3, and all three parties are finite rational subjects; they all want to obtain the maximum benefit, and the strategy choice gradually evolves and stabilizes in the optimal strategy over time.

  • Hypothesis 2: Strategy Space for Power Producers, α = (α1, α2) = (Production of high quality electricity, Production of low quality electricity), and choose α1 with probability of x, choosing α2 with probability (1 − x), the strategic choice of the power producer affects its own benefits and costs. In this paper, we explore three different options:

    • Producing high-quality electricity: Electricity producers may choose to invest in advanced production technologies and equipment to ensure that the quality of electricity products meets high standards. This strategy may increase production costs, but at the same time, it can improve the market competitiveness of electricity products, increase consumer satisfaction, and potentially gain government incentives.

    • Producing low-quality electricity: In order to reduce costs or increase profits, some electricity producers may choose to produce low-quality electricity. This strategy may reduce production costs but may harm consumers and may result in government penalties.

    • Rent-seeking behavior: Electricity producers may try to collude with third-party testing organizations to gain an unfair advantage, for example, by paying kickbacks or bribes to ensure that their low-quality electricity passes testing.

  • Hypothesis 3: Strategy space for third-party testing organizations, γ = (γ1, γ2) = (Rejection of rent-seeking, intention to seek rent), and choose γ1 with probability of y and γ2 with probability of (1 − y). There are two choices of testing institutions as follows:

    • Government regulators need to invest considerable human and financial resources in adopting a strict regulatory strategy for the electricity market, including building a professional regulatory team, maintaining regulatory facilities, formulating and updating regulations to meet market dynamics, and establishing coordination and cooperation mechanisms with other agencies. In addition, the government needs to educate the public to enhance their understanding of the regulatory measures and deal with noncompliance to ensure enforcement. Nevertheless, these investments have resulted in significant benefits, such as improved power quality, maintenance of market order, advancement of sustainable development, increased public trust, enhanced international image, incentives for companies to innovate, and prevention of power accidents.

    • Rent-seeking behavior: Third-party testing organizations may choose to engage in rent-seeking activities by accepting bribes or kickbacks from power producers in exchange for qualified certification of low-quality power products. This strategy may bring short-term gains but may damage the credibility of the testing organization and the overall health of the market.

  • Hypothesis 4: The government regulator has a strategy space β = (β1, β2) = (strict regulation, lax regulation) and chooses β1 with probability z and β2 with probability (1 − z). Two options for the government are presented:

    • When the government chooses strict regulation; pays human, material, and financial resources and other costs; gets regulation, government, and social gains; need to make rewards for excellent enterprises and punishments for non-compliant enterprises and institutions.

    • In adopting lax regulatory policies, while government regulators can alleviate financial pressure and administrative burdens in the short term, they must at the same time be prepared to cope with multiple potential risks of reduced regulatory efficiency, loss of public trust, market disruption, and higher social costs in the long term. Lax regulation may further lead to poor enforcement of electricity quality standards, failure of the market self-regulation mechanism, and may invite accountability from higher authorities.

  • Hypothesis 5: In the electricity market, power producers choose to produce high-quality electricity and avoid rent-seeking behavior with third-party testing organizations, which is in line with not only the requirements of social stability and economic development but also the ultimate goal pursued by government regulators. While pursuing their own maximum returns, power producers and third-party testing organizations should ensure that their actions do not impede the fair competition and healthy development of the market.

In the process of power market development, government regulators, power producers, and third-party testing organizations all have their own behavioral strategy choices and interest needs. Any one of them makes a strategic choice will affect the other two parties, different strategic choices will have different degrees of impact on the development of the electricity market, and the development of the electricity market will present a dynamic process. In order to explore the benefits and costs of the three stakeholders making different behavioral strategies, this paper sets some relevant parameters and defines their meanings, as shown in the Nomenclature.

According to the aforementioned assumptions, the mixed strategy game matrix of power producers, third-party testing organizations, and government regulators are shown in Tables I and II.

TABLE I.

Tri-party mixed strategy game payoff matrix.

Electricity power production enterprise industry Third party testing organizations Government regulators
Strict regulation (z) Loose regulation (1-z)
Production of high-quality electricity (x)  Reject rent-seeking (y)  ME1  ME2 
Intentional rent seeking (1-y)  ME3  ME4 
Production of low-quality electrical energy (1-x)  Reject rent-seeking (y)  ME5  ME6 
Intentional rent seeking (1-y)  ME7  ME8 
Electricity power production enterprise industry Third party testing organizations Government regulators
Strict regulation (z) Loose regulation (1-z)
Production of high-quality electricity (x)  Reject rent-seeking (y)  ME1  ME2 
Intentional rent seeking (1-y)  ME3  ME4 
Production of low-quality electrical energy (1-x)  Reject rent-seeking (y)  ME5  ME6 
Intentional rent seeking (1-y)  ME7  ME8 
TABLE II.

Tri-party mixed strategy game payoff matrix.

Payoff Electricity power production enterprise industry Government regulators Third party testing organizations
ME1  RH − CH + AC  −CS − AC − AS + RS  RT + AS 
ME2  RH − CH  RS  RT 
ME3  RH − CH + AC  −CS − AC + PS + RS  RT − CR − PS 
ME4  RH − CH  RS  RT − CR 
ME5  −CL − CO − PC  −CS + PC − AS  RT + AS 
ME6  −CL − CO  RS 
ME7  RH − CL − CO − CT − PC  −CS + PC + PS − CZ  RT − CR + CT − PS 
ME8  RH − CL − CO − CT  −CZ − SE  RT − CR + CT 
Payoff Electricity power production enterprise industry Government regulators Third party testing organizations
ME1  RH − CH + AC  −CS − AC − AS + RS  RT + AS 
ME2  RH − CH  RS  RT 
ME3  RH − CH + AC  −CS − AC + PS + RS  RT − CR − PS 
ME4  RH − CH  RS  RT − CR 
ME5  −CL − CO − PC  −CS + PC − AS  RT + AS 
ME6  −CL − CO  RS 
ME7  RH − CL − CO − CT − PC  −CS + PC + PS − CZ  RT − CR + CT − PS 
ME8  RH − CL − CO − CT  −CZ − SE  RT − CR + CT 
Expected return of electricity producers to produce high or low quality electricity and the average expected return (E11, E12, E 1 ¯),
{ E 11 = y z ( R H C H + A C ) + ( 1 y ) z ( R H C H + A C ) + y ( 1 z ) ( R H C H ) + ( 1 y ) ( 1 z ) ( R H C H ) , E 12 = y z ( C L C O P C ) + ( 1 y ) z ( R H C L C O C T P C ) + y ( 1 z ) ( C L C O ) + ( 1 y ) ( 1 z ) ( R H C L C O C T ) , E 1 ¯ = x E 11 + ( 1 x ) E 12 .
(1)
The replication dynamic equation for the strategy choice of the power producer is
F ( x ) = d x d t = x ( E 11 E 1 ¯ ) = x [ E 11 x E 11 ( 1 x ) E 12 ] = x ( 1 x ) ( E 11 E 12 ) = x ( 1 x ) [ C L C H + C O + C T + z ( A C + P C ) y ( C T R H ) ] .
(2)
Find the first order derivative of F(x) and obtain F ( x ),
F ( x ) = ( 1 2 x ) [ C L C H + C O + C T + z ( A C + P C ) y ( C T R H ) ] .
(3)

Settings H ( y ) = C L C H + C O + C T + z ( A C + P C ) y ( C T R H ).

According to the stability theorem of the replication dynamics equation and the evolutionary stability strategy, when F x = 0 and F x < 0, then we get y = ( C L C H + C O + C T y ( C T R H ) ) / ( A C + P C ) = y * Since H ( y ) / y > 0. Therefore, H(y) is a decreasing function with respect to y. The evolutionary phase diagram of the power producer strategy is obtained.

Expected benefits of refusal or intentional rent-seeking by third-party testing organizations and average expected benefits (E21, E22, E 2 q ¯),
{ E 21 = x z ( R T + A S ) + x ( 1 z ) × R T + ( 1 x ) z ( R T + A S ) + ( 1 x ) ( 1 z ) × 0 , E 22 = x z ( R T C R P S ) + x ( 1 z ) ( R T C R ) + ( 1 x ) z ( R T C R + C T P S ) + ( 1 x ) ( 1 z ) ( R T C R + C T ) , E 1 ¯ = y E 21 + ( 1 y ) E 22 .
(4)
The replication dynamic equation for the strategy selection of third-party testing organizations is
F ( y ) = d y d t = y ( E 21 E 2 ¯ ) = y ( 1 y ) ( E 21 E 22 ) = y ( 1 y ) ( C R C T R T + z ( A S + P S + R T ) + x ( C T + R T ) xzR T ) .
(5)
Find the first order derivative of F(y) and obtain F ( y ),
d ( F ( y ) ) y = ( 1 2 y ) ( C R C T R T + z ( A S + P S + R T ) + x ( C T + R T ) xzR T ) .
(6)

Settings G ( x ) = C R C T R T + z ( A S + P S + R T ) + x ( C T + R T ) xzR T.

Stability theorem and evolutionary stabilization strategy according to replication dynamics equation, when F(y) = 0 and F′(y) < 0, then we get x = CR − CT − RT + z(AS + PS + RT)/(−CT − RT + zRT) = x*. Since G ( x ) / x > 0, therefore G(x) is an increasing function about x. The phase diagram of the evolution of the third-party testing organization's strategy is obtained.

Expected return with strict or lenient government regulators and average expected return (E31, E32, E 3 ¯),
{ E 31 = x y ( C S A C A S + R S ) + x ( 1 y ) ( C S A C + P S + R S ) + ( 1 x ) y ( C S + P C A S ) + ( 1 x ) ( 1 y ) ( C S + P C + P S C Z ) , E 32 = x y R S + x ( 1 y ) R S + ( 1 x ) y R S + ( 1 x ) ( 1 y ) ( C Z S E ) , E 3 ¯ = z E 31 + ( 1 z ) E 32 .
(7)
The replication dynamic equation for the government regulator's strategy choice is
F ( z ) = d z d t = z ( E 31 E 3 ¯ ) = z ( 1 z ) ( E 31 E 32 ) = z ( z 1 ) ( C S P C P S S E + x ( A C + P C + S E ) + y ( A S + P S + R S + S E ) xy ( R S + S E ) ) .
(8)
Finding the first-order derivative of F(z) and obtain F ( z ),
d ( F ( z ) ) z = ( 2 z 1 ) ( C S P C P S S E + x ( A C + P C + S E ) + y ( A S + P S + R S + S E ) xy ( R S + S E ) ) .
(9)

Settings J ( y ) = C S P C P S S E + x ( A C + P C + S E ) + y ( A S + P S + R S + S E ) xy ( R S + S E ).

According to the stability theorem of the replication dynamics equation and the evolutionary stabilization strategy, when F(z) = 0 and F′(z) < 0, then we get y = CS − PC − PS − SE + x(AC + PC + SE)/−(AS + PS + RS + SE) + x(RS + SE) = y*. Since J ( y ) / y > 0, so J(y) is an increasing function about y, and the government strategy evolution phase diagram is obtained.

When making F(x) = 0, F(y) = 0, and F(z) = 0, we can get the equilibrium points of the system: (0,0,0), (1,0,0), (0,1,0), (0,0,1), and (1,1,1). In order to ensure that the study is meaningful, the values considered need to ensure that the benefits outweigh the costs, that the benefits to firms that produce low-quality electricity but succeed in rent-seeking are greater than the benefits of producing high-quality electricity, and that the benefits to third-party testing organizations that intend to rent-seek are greater than the benefits of refusing to rent-seek. According to Lyapunov stability theory, a stable point is asymptotically stable if and only if all the eigenvalues are less than 0. Otherwise, the point is unstable, i.e., a source or saddle point (Ma , 2016).

Construction of Jacobian matrices for three-party evolutionary games,
J = [ J 1 J 2 J 3 J 4 J 5 J 6 J 7 J 8 J 9 ] = [ F ( x ) x F ( x ) y F ( x ) z F ( y ) x F ( y ) y F ( y ) z F ( z ) x F ( z ) y F ( z ) z ] = [ A 11 A 12 A 13 A 21 A 22 A 23 A 31 A 32 A 33 ] .
(10)
In Eq. (10)
A 11 = ( 1 2 x ) ( C L C H + C O + C T + z ( A C + P C ) y ( C T R H ) ) ,
A 12 = x ( x 1 ) ( C T R H ) ,
A 13 = x ( x 1 ) ( A C + P C ) ,
A 21 = y ( y 1 ) ( ( C T + R T ) R T ) z ) ,
A 22 = ( 1 2 y ) ( C R C T R T + ( A S + P S + R T ) z + ( C T + R T ) x R T xz ) ,
A 23 = y ( y 1 ) ( ( A S + P S + R T ) R T x ) ,
A 31 = z ( z 1 ) ( ( A C + P C + S E ) y ( R S + S E ) ) ,
A 32 = z ( z 1 ) ( ( A S + P S + R S + S E ) x ( R S + S E ) ) ,
A 33 = ( 1 2 z ) ( C S P C P S S E + x ( A C + P C + S E ) + y ( A S + P S + R S + S E ) xy ( R S + S E ) ) .

As can be seen from Table III, there are two evolutionary stability points (0,0,1) and (1,1,0) in the system, which correspond to the combination of the strategy where the power producer chooses to produce low-quality electricity, the third-party testing agency chooses to intend rent-seeking, and the government regulator chooses to strictly regulate, and the strategy combination where the power producer chooses to produce high-quality electricity, the third-party testing agency chooses to reject rent-seeking, and the government regulator chooses to loosely regulate. In order to avoid the development of the electricity market to the stable point (0,0,1), there is a rent-seeking behavior of electricity producers and third-party testing agencies, which makes low-quality electricity constituting the electricity market and disrupting the social development, and the government regulators need to make the correct strategy choice and appropriate punishment. The strategy combination of stabilization points (1,1,0) meets the national and social needs and achieves the highest economic and social benefits, which is the direction we need to study.

TABLE III.

Equilibrium points of the system and its characteristic values.

Equilibrium points (x,y,z) Eigenvalues λ 1, λ 2 , λ 3 Symbol of eigenvalues Local stability
(0,0,0)  CR − CT − RT, CL − CH + CO + CT, PC − CS + PS + SE  (−, −, +)  Unstable point 
(1,0,0)  CR, PS − CS − AC, CH − CL − CO − CT  (+, −, +)  Unstable point 
(0,1,0)  CT − CR + RT, PC − CS − AS − RS, CL − CH + CO + RH  (+, +, N)  Unstable point 
(0,0,1)  CS − PC − PS − SE, AS + CR − CT + PS, AC − CH + CL + CO + CT + PC  (−, −, −)  Evolutionary stable strategy (ESS) 
(1,1,0)  −CR, −AC − AS − CSCH − CL − CO − RH  (−, −, −)  ESS 
(1,0,1)  AS + CR + PS, AC + CS −PS, CH − AC − CL − CO − CT − PC  (N, +, N)  Unstable point 
(0,1,1)  CT − CR − AS − PS, AS + CS − PC + RS, AC − CH + CL + CO + PC + RH  (+, N, N)  Unstable point 
(1,1,1)  AC + AS + CS, −AS − CR − PS, CH − AC − CL − CO − PC − RH  (−, −, +)  Unstable point 
Equilibrium points (x,y,z) Eigenvalues λ 1, λ 2 , λ 3 Symbol of eigenvalues Local stability
(0,0,0)  CR − CT − RT, CL − CH + CO + CT, PC − CS + PS + SE  (−, −, +)  Unstable point 
(1,0,0)  CR, PS − CS − AC, CH − CL − CO − CT  (+, −, +)  Unstable point 
(0,1,0)  CT − CR + RT, PC − CS − AS − RS, CL − CH + CO + RH  (+, +, N)  Unstable point 
(0,0,1)  CS − PC − PS − SE, AS + CR − CT + PS, AC − CH + CL + CO + CT + PC  (−, −, −)  Evolutionary stable strategy (ESS) 
(1,1,0)  −CR, −AC − AS − CSCH − CL − CO − RH  (−, −, −)  ESS 
(1,0,1)  AS + CR + PS, AC + CS −PS, CH − AC − CL − CO − CT − PC  (N, +, N)  Unstable point 
(0,1,1)  CT − CR − AS − PS, AS + CS − PC + RS, AC − CH + CL + CO + PC + RH  (+, N, N)  Unstable point 
(1,1,1)  AC + AS + CS, −AS − CR − PS, CH − AC − CL − CO − PC − RH  (−, −, +)  Unstable point 

In the process of rewarding and punishing production enterprises, government regulators need to assess and score power production enterprises to obtain reward and punishment standards. Enterprises are examined in terms of the level of power quality, the level of low-carbon emission reduction, the level of economic returns, the level of energy utilization, the level of intelligent operation, and the level of environmental impact. As shown in Fig. 2.

FIG. 2.

Evaluation indicators.

FIG. 2.

Evaluation indicators.

Close modal
When renewable energy accounts for a high percentage of the power generation system, due to its own stochasticity and volatility, which makes the quality of the electricity produced vary, in order to ensure the safety and rights of the users of electricity, the selection of the voltage, voltage flicker, frequency, and distortion are four major parameters used to evaluate the power quality (Liang, 2017). The primary task of power producers is to provide society with stable and high-quality electricity, so government regulators strictly control this indicator as a high-weighted evaluation indicator,
A = T = 0 T = n ( U S U T ) U S + T = 0 T = n ( U F S U F T ) U F S + T = 0 T = n ( F S F T ) F S + T = 0 T = n ( D S D T ) D S ,
(11)
where U stands for voltage, UF stands for voltage flicker, F for frequency, D for distortion, and S for national standard.

Power production enterprises need to assume social responsibility, such as better use of renewable energy to reduce the waste of renewable energy, so this paper is based on renewable energy in the power production enterprises out of the proportion, utilization rate, etc. to evaluate the level of energy utilization of the enterprise.

  1. Share of renewable energy output D1

    The greater the proportion of electricity generated by renewable energy in the enterprise's energy, it means that the enterprise is more fully utilized when renewable energy in the region, but due to the uneven distribution of the natural resources themselves or the development of the difficulty is too large, does not comply with the proceeds of the revenue, so the addition of two correction coefficients, so as to make it more scientific,
    D 1 = α β ( n = 1 n = a E W + n = 1 n = b E p v + n = 1 n = c E H + n = 1 n = d E ESS ) E T ,
    (12)

    where EW denotes wind power generation, EPV denotes photovoltaic power generation, EH denotes hydroelectric power generation, EESS denotes energy storage power generation, ET denotes total power generation, α is the correction coefficient for resource occupancy, and β is the correction coefficient for the ratio of development difficulty to revenue.

  2. Renewable energy utilization D2

    Due to the wind and water and other clean energy is more difficult to control, volatility and prediction difficulties prone to error, power production enterprises may be the future to improve the quality of power supply and give up this part of the energy, but this behavior does not meet the national situation and social needs, so this paper will be included in the evaluation indicators,
    D 2 = n = 1 n = a ( P W W W P W ) + n = 1 n = b ( P P V W P V P P V ) + n = 1 n = c ( P H W H P H ) ,
    (13)

    where PW denotes wind availability, WW denotes wind abandonment, PPV denotes photovoltaic availability, WPV denotes light abandonment, PH denotes hydro availability, and WH denotes water abandonment.

Evaluation methods are mainly divided into subjective and objective two kinds, and the advantage of subjective weighting method is that it can determine the weights more reasonably according to the actual problems and subjective experience, to avoid the weights do not match the actual situation, but it will also make the results of the subjectivity increase, detached from the actual data; objective weighting method is to analyze and organize the original data to find out the law and then use mathematical methods to calculate the weights, so its objectivity is stronger, but at the same time, it cannot reflect the tendency of decision-makers, and it is easy for the results to be contrary to the reality. Stronger, but at the same time cannot reflect the tendency of decision makers, easy to appear the results, and the reality of the situation.

As a kind of official reward and punishment standard, it should be realistic and have data to rely on at the same time, so the evaluation method can be a combination of subjective hierarchical analysis and objective entropy value method as a new evaluation method. The entropy value method is used to analyze the entropy value of the data, and the weights are determined by the expert scores of the hierarchical analysis method, and the final reward and punishment scores are obtained comprehensively.

In order to explore the relationship between the changes of key parameters and the evolution process, numerical simulation is carried out using MATLAB software to analyze the strategies to effectively improve the regulatory efficiency. The relative values after the recommendations of the actual situation and relevant experts are set as the initial values of each parameter, array 1: CH − CL = 85, CO = 10, CT = 40, CR = 30, CS = 15, RH = 100, AC = 20, AS = 10, PC = 40, PS = 20, SE = 40.

In the game modeling analysis in this paper, we first explore the specific effects of increasing electricity sales revenue on the evolutionary game process and its outcomes. By setting a baseline revenue value of 100, we used the replicated dynamic equation system to conduct 50 simulations of evolution over time, and in each simulation, the electricity sales revenue was increased by 10. According to the simulation results shown in Fig. 3, we can find that in the process of the system that tends to a steady state, the increase in the electricity sales revenue has a significant impact on the strategic choices of power generation enterprises; with the increase in revenue, power generation enterprises are more inclined to produce high-quality electricity, which is because higher revenue can compensate for the increased cost of producing high-quality electricity, thus incentivizing enterprises to improve the quality of electricity. Meanwhile, the probability that government regulators need to strictly regulate decreases with increasing revenues, probably because higher revenues imply that firms have more resources to devote to quality control, thus reducing regulatory pressure on regulators. In addition, the probability of rent-seeking behavior by firms and third-party testing organizations also decreases with increasing revenues, possibly because higher revenues reduce the incentives for firms to make additional profits through illegal means.

FIG. 3.

Impact of electricity sales revenue.

FIG. 3.

Impact of electricity sales revenue.

Close modal

Based on these findings, we suggest that government regulators can appropriately relax tariff regulation for firms with unstable quality and instead focus their regulatory efforts on power quality. Such a regulatory strategy can ensure the stable development of the electricity market as well as effectively improve the overall quality of electricity, thereby protecting the interest of consumers and the safe operation of the power system. In addition, reducing production costs is also an effective way to improve the profitability of enterprises. Therefore, enterprises should increase their investment in green development measures such as technological innovation, infrastructure improvement, and industrial structure upgrading. Government departments can make these conditions one of the assessment criteria for rewards and punishments of production enterprises in order to promote the development of enterprises and, at the same time, effectively stimulate market competition. In this way, it can not only promote enterprises to improve their operational efficiency and quality control ability but also promote the healthy development and sustainability of the whole power industry.

In order to gain a deeper understanding of the impact of the government incentive policy on the fair and orderly development of the market, and to explore the possibility of eliminating the incentive policy after the market has matured, we conducted simulations of two scenarios based on Array 1: one in which the incentive is increased by 10 at a time, and the other in which the government does not make any incentives. With the simulation of these two scenarios, we obtained the results shown in Figs. 4 and 5. From these results, it can be observed that the government's incentive policy has a significant impact on the behavior of market participants. Specifically, the probability that the government needs to strictly regulate decreases more quickly when the government provides higher incentives. This is because high incentives are effective in motivating firms to spontaneously improve the quality of their products, thus reducing the need for strict regulation. In contrast, in the absence of incentives, the government needs stricter regulation to ensure that market participants comply with quality standards. This suggests that government incentive policies are necessary to guide firms' behavior and promote healthy market development in the early stages of market development.

FIG. 4.

Impact of government incentives to producers.

FIG. 4.

Impact of government incentives to producers.

Close modal
FIG. 5.

Impact of government incentives to third-party institutions.

FIG. 5.

Impact of government incentives to third-party institutions.

Close modal

Therefore, we suggest that the government should formulate a high incentive policy within a reasonable range. Such a policy not only reduces the probability of strict government regulation and reduces the government's regulatory expenditures, but also incentivizes firms to devote more resources and energy to high-quality production. Over time, as the market matures and enterprises regulate themselves, the government can gradually reduce the intensity of incentives or even eventually abolish the incentive policy, and instead rely on the market's self-regulation mechanism to maintain a fair and orderly market environment. Such a strategy will help achieve long-term stability and sustainable development of the market.

In the electricity market, incentive and penalty mechanisms are one of the most important means of promoting good market development. However, the strength of punishment must be carefully considered to ensure that it can effectively guide the behavior of enterprises without excessively suppressing their innovation and development. In order to explore the impact of the punishment strength on market development, this paper starts with the simulation analysis of the evolution process of the government's punishment strength on power enterprises and third-party testing organizations. Based on the setting of array 1, we consider a scenario in which the penalty strength increases by 10 each time and obtain the results shown in Figs. 6 and 7. These results reveal several key points: first, the effect brought by strict government regulation gradually decreases as the penalty increases, even have a negative effect in the later stages of market development. This may be due to the fact that excessive penalties may lead firms to adopt defensive strategies, thus reducing the flexibility of government regulation. On the other hand, as penalties increase, the probability that an electric utility chooses to produce high-quality electricity and the probability that a third-party testing organization chooses to reject rent-seeking increase. This suggests that, to a certain extent, heavier penalties can effectively curb the illegal behavior of enterprises and prompt them to pay more attention to the quality of products as well as improve the integrity of testing organizations. However, the government's adoption of harsher penalties and strict regulation are complementary and can be combined to achieve the best results. The government should ensure that penalties are strong enough to not only deter unlawful behavior but also avoid excessive punishment, so as not to adversely affect the normal operation of enterprises and the healthy development of the market. In this way, the government can more effectively guide market participants to comply with the rules and promote fair competition and high-quality development of the electricity market.

FIG. 6.

Impact of the strength of government penalties on producers.

FIG. 6.

Impact of the strength of government penalties on producers.

Close modal
FIG. 7.

Impact of the strength of government penalties on third institutions.

FIG. 7.

Impact of the strength of government penalties on third institutions.

Close modal

In the evolutionary game analysis of the electricity market, changes in rent-seeking costs have a significant impact on the strategic choices of market participants. As shown in Fig. 8, an increase in the cost of rent-seeking during the evolutionary process increases the probability of electric power enterprises to produce high-quality electricity while decreasing the probability of third-party testing organizations to reject rent-seeking. This finding suggests that when the cost of rent-seeking behavior increases, firms are more inclined to improve the quality of their products through legal means, and third-party testing organizations are more likely to resist the temptation of illegal benefits.

FIG. 8.

Impact of rent-seeking costs.

FIG. 8.

Impact of rent-seeking costs.

Close modal

Therefore, when the government formulates its regulatory strategy, it should take into account both the level of punishment and the monitoring measures. On the one hand, the government should strictly punish rent-seeking behaviors to serve as a deterrent; on the other hand, the government should also supervise and appropriately increase the rent-seeking costs of enterprises, so that the costs of illegal behaviors are much higher than the costs of legal operations, thus prompting enterprises to consciously comply with regulations and improve product quality.

In further simulations, we set different punishment strengths (SE = 40, 50, 60, and 70) of the higher authorities and obtained the simulation results shown in Fig. 9. These results show that the imposition of severe penalties by the higher authority helps to maintain a high rate of strict regulation by the government regulator. This high regulatory rate is a key factor in ensuring the stable and orderly development of the electricity market, which can effectively prevent market disorder and protect consumers' interest while promoting the healthy and sustainable development of the electricity industry. Therefore, in carrying out its regulatory duties, the government should make full use of the punitive mechanism of the higher authorities to ensure the effectiveness and enforcement of its regulatory policies.

FIG. 9.

Impact of government being punished with intensity.

FIG. 9.

Impact of government being punished with intensity.

Close modal

Under the assumption that all market participants have limited rationality, this paper constructs a three-party evolutionary game revenue model, including power producers, third-party testing organizations, and government regulators. By systematically analyzing the evolutionary process of the three parties under different strategy choices, this paper reveals the interdependence of the strategy choices of market participants. In the absence of effective regulation, power companies and third-party testing organizations may tend to choose non-compliant strategies due to less constraints on rent-seeking behavior. This will lead to chaos in the electricity market and may even have an impact on social stability. Therefore, appropriate regulation is necessary to guide the strategy choices of each participant to evolve in a direction favorable to the healthy development of the market.

The operation of the simulation system allows us to visualize the evolution of the behavior of the participants in the electricity market as well as the specific impact of different parameters on the evolution of the system. These simulation results provide participants with references for strategy selection and provide practical guidance for regulators in managing their behavior. By adjusting the model parameters, we can predict the market response under different policies, thus helping to formulate more effective regulatory strategies, and the specific analysis leads to the following key conclusions and recommendations:

  1. Improving the profitability of enterprises can promote the production of high-quality electricity; on the one hand, by increasing the sales price, it is necessary to pay attention to whether the price of electricity is compatible with social development, which needs to be strictly controlled by the government. On the other hand, it is to reduce production costs. Actively investing in scientific research can not only improve profitability but also stimulate industrial upgrading. Therefore, the government must urge enterprises to form close ties with relevant research institutions and schools, publicize scientific research information, and share scientific research results, in order to promote the continuous innovation of power production equipment and strengthen the sustainable development of the power industry.

  2. When comparing the evolutionary process after an increase in revenue from electricity sales by power firms and an increase in incentives and penalties by all parties by 10 units each time, it is found that the government's increase in incentives for power firms and third-party testing organizations has the most significant effect on the evolutionary stabilization process. This finding suggests that positive rewards may be an effective means of driving firms to comply with rules and improve service quality in electricity markets. Rewards can directly increase firms' profitability expectations, thus motivating them to adopt compliance and high quality production strategies. In contrast, increasing penalties has opposite effects on the market in the early and late stages of evolution. In the early stages of market development, higher penalties may help to quickly establish a sense of rules and regulate market behavior; however, as the market matures, excessive penalties may lead firms to adopt defensive strategies, thereby inhibiting market innovation and development. Therefore, when formulating and improving regulatory policies, the government should consider appropriately increasing the level of penalties in the early stage of market development in order to establish a standardized market environment. As the market matures, the government can gradually reduce the level of penalties while increasing incentives to encourage enterprises to spontaneously improve product quality and service standards. Such policy adjustments can help to achieve long-term stability and sustainable development of the market and, at the same time, can also promote innovation and efficient operation of the power industry.

  3. In regulating the electricity market, the government should take into account the different stages of market development and the characteristics of corporate behavior and formulate appropriate regulatory strategies. In the early stage of the market, rent-seeking behavior should be prevented by increasing the cost of rent-seeking; after the market matures, it should focus on strict regulation and punishment mechanisms, combined with media publicity, in order to maintain the fairness and stability of the market.

  4. In the regulatory framework for electricity markets, accountability mechanisms for regulatory failures by higher levels of government are an important incentive for regulators to enforce their regulatory duties more rigorously. When regulators are aware that they may be held accountable for their regulatory failures, they are more likely to take proactive measures to ensure compliance by market participants, thereby enhancing the robustness of firms in producing quality electricity. Thus, the accountability mechanism of higher levels of government is not only a form of oversight of regulators but also a form of protection for market participants. It helps establish a level playing field in the market and encourages enterprises to invest in technological innovation and quality management, thereby promoting the long-term healthy development of the electricity sector. Through such a mechanism, it can ensure that regulators, enterprises, and third-party testing organizations can all perform optimally in their roles and work together to promote the development of the electricity market in a greener, more efficient and sustainable direction.

At the current stage, the new electricity market is still in the initial construction and development phase, and data collection faces significant challenges. In view of this, this study adopts a prudent relative value estimation approach in data selection, which is based on actual market conditions and incorporates advice from experts in the field. Although the dataset used is not directly derived from actual market transactions, it still maintains considerable reference value and lays the foundation for subsequent studies. As the new electricity market gradually matures, the relevant data will gradually be made available to the public, and our group plans to use these real market data to update the model in future work, with a view to obtaining more accurate simulation results. In addition, we will propose more specific and targeted strategic recommendations based on these data to promote the healthy development and efficient operation of the electricity market.

The authors appreciate the financial support by the National Natural Science Foundation of China (Nos. 52069010 and 51966005).

The authors have no conflicts to disclose.

Menglin Hou: Conceptualization (equal); Methodology (equal); Software (equal); Visualization (equal); Writing – original draft (equal); Writing – review & editing (equal). Zhumei Luo: Funding acquisition (equal); Project administration (equal); Resources (equal); Supervision (equal); Writing – review & editing (equal). Shan Qing: Funding acquisition (equal); Supervision (equal). Xiaoxu Zhang: Funding acquisition (equal); Supervision (equal).

Data sharing is not applicable to this article as no new data were created or analyzed in this study.

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