Qing YU; Ying LIU; Fangyuan SU; Muran YU; Zhen WANG; Xueyao YUAN

doi:10.21078/JSSI-2024-0069

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系统科学与信息学报(英文) ›› 2025, Vol. 13 ›› Issue (1) : 1-22. DOI: 10.21078/JSSI-2024-0069

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Evolutionary Game Analysis of Profit Distribution Between Government and Enterprises in Public Data Authorization Operations

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Abstract

To address the issue of revenue distribution between government departments and enterprises in the operation of public data authorization, an evolutionary game model was constructed for both government and enterprise parties. The impacts of different incentive levels and revenue distribution ratios on the strategic choices and evolutionary trends of both government and enterprise were analyzed. It was found that when the government chose a strategy of weak authorization and strong regulation, enterprises showed a higher tendency to actively participate in public data sharing. In addition, when the revenue distribution ratio between government and enterprise was 3:7, the game evolution of both parties tended to be stable, reaching a balanced state that is beneficial and sustainable for both parties.

Key words

public data / authorized operation / income distribution / evolutionary game model

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Qing YU , Ying LIU , Fangyuan SU , Muran YU , Zhen WANG , Xueyao YUAN. . 系统科学与信息学报(英文), 2025, 13(1): 1-22 https://doi.org/10.21078/JSSI-2024-0069

Qing YU , Ying LIU , Fangyuan SU , Muran YU , Zhen WANG , Xueyao YUAN. Evolutionary Game Analysis of Profit Distribution Between Government and Enterprises in Public Data Authorization Operations. Journal of Systems Science and Information, 2025, 13(1): 1-22 https://doi.org/10.21078/JSSI-2024-0069

1 Introduction

Driven by the wave of the digital age, public data has become a key factor in driving innovation and economic growth. As an important element of data resources, public data accounts for up to 70%

\sim

80% of the entire data, and is crucial to all aspects of national economic development. It is also an important foundation for the digital transformation of the economy. China currently adopts a government-led data openness model, under which local governments have established provincial and municipal public data open platforms. The "China Local Government Data Openness and Utilization Report — Provincial Index (2023)" shows that as of August 2023, 226 provincial and local governments in China have launched data open platforms. The number of regional data open platforms over the past years is shown in Figure 1.

Figure 1 Growth in the number of open data platforms at the prefecture level and above over the past years

Full size|PPT slide

However, it remains challenging to promote data sharing. In the context of governments adopting different levels of authorization for public data, the attitudes and decisions of enterprises to participate in data sharing are particularly complex. On the one hand, as the controller of huge amounts of public data, the government aims to promote the effective circulation of data under the premise of ensuring data security and compliant use. This relies on means of strong authorization and weak regulation or weak authorization and strong regulation, through which reasonable monetization of data assets can be achieved. Eventually, it will in turn contribute to the improvement of the data governance system, the upgrade of security technology, and the leap in the quality of public services. On the other hand, enterprises possessing a large amount of data are eager to unlock new economic value-added space and promote product innovation and market expansion through the integration of public data. However, they have to face the potential increase in data acquisition costs and strict restrictions of cooperation under the mode of weak authorization and strong regulation. Alternatively, under the mode of strong authorization and weak regulation, enterprises also suffer from the uncertainty in data quality and potential market risks, which undoubtedly affects their cost-benefit considerations and uncertainty assessment of future benefits in data-sharing decisions. These two different orientations have a significant impact on the willingness of enterprises with large amounts of data to participate, which constitutes a dynamic evolutionary game process.

The authorization operation process of public data mainly involves the government providing public data to specific market entities (i.e., government authorized entities), which are often large and well-known enterprises. Current research focuses on two aspects of the authorization and operation of public data: The construction and effective-ness evaluation of cooperation model between government departments and enterprises. On the one hand, prior studies explored the specific processes and cooperation mechanisms of government-enterprise cooperation in data authorization operations^{[1, 2]}, as well as the innovative characteristics compared to traditional data management models. The focus was on analyzing how the government and enterprises could promote effective integration and value release of data resources through different mechanisms, including con-tract design, benefit distribution^{[3, 4]}, and risk sharing. On the other hand, the academia also studied the impact of such cooperation model on improving government efficiency, incentivizing corporate innovation, and overall social welfare^[5]. Some scholars pointed out that the operation of public data authorization through government's strong or weak authorization strategies^[6] not only examines the government's regulatory ability for data security and privacy protection^[7], but also directly affects enterprises' innovation initiatives and market's response speed. It may even raise disputes over data monopoly and market fairness.

Therefore, government-enterprise cooperation is essential in the field of public data authorization and operation. This cooperation model aims to efficiently unleash the potential of public data through collaboration between the government and enterprises, thereby promoting the maximum utilization of data value and ensuring data security and public welfare. However, the open questions are 1) how to allocate the benefits under the framework of government enterprise cooperation, and 2) how to balance government regulatory responsibility, public interest protection, and corporate innovation incentives? Prior studies in the literature exhibit some limitations. Firstly, there is a lack of in-depth analysis from the perspective of game theory on the dynamic interaction relationship between the government and enterprises in data authorization operation cooperation. This is especially true when it comes to the investigations of the strategic choices of both parties when pursuing their optimal interests and reasons for potential cooperation difficulties. Secondly, very few works analyzed the role and strategic choices of the government in data governance, especially in terms of balancing regulation and incentives and promoting a subtle balance between data openness and protection. In addition, there is also a need for a systematic analysis of the impact of the strict-ness of government authorization on the participation enthusiasm of enterprises, data utilization efficiency, and innovation achievements.

The aim of this study is to construct a game model to comprehensively analyze the strategic choices and dynamic evolution of profit distribution mechanisms between government and enterprises in the process of data authorization operation, as well as their impact on the stability of cooperation models. By examining the distribution of benefits for both parties under different strategy combinations, this study aims to explore profit distribution schemes that can not only incentivize data openness and utilization, but also maximize overall social welfare. Mechanism designs that can promote fair sharing of public data value and long-term cooperation are also studied.

2 Analysis of Evolutionary Game Behavior Between Government and Enterprises

2.1 Concept of Public Data

Public data refers to data generated or obtained by the government, public institutions, enterprises, etc. when fulfilling their public management and service responsibilities. These data have public attributes and can be widely shared and used to promote economic and social developments. The sharing and openness of public data are of great significance for promoting the development of the digital economy, improving government governance capabilities, and promoting social equity. In the Beijing-Tianjin-Hebei region, the sharing of public data can promote the coordinated development of industries and improve the overall competitiveness of the region.

In December 2022, the "Opinions of the Central Committee of the Communist Party of China and the State Council on Building a Data Infrastructure System to Better Play the Role of Data Elements" (i.e., "20 Data Elements") proposed 20 policy measures to build a data infrastructure system from the aspects of data property rights, circulation and transactions, income distribution, and security governance. In February 2023, the Central Committee of the Communist Party of China and the State Council issued the "Overall Layout Plan for Digital China Construction", in which the "2522" framework layout was clarified, and the data element was added to the blue-sky picture of "Digital China". It also proposed that by 2035, the level of digital development in China should be world-leading. In March 2023, the first session of the 14th National People's Congress proposed the establishment of the National Data Bureau to coordinate the planning and construction of digital China, digital economy, and digital society. This clearly indicates China's determination to activate data elements and their potentials.

At present, research on public data mainly focuses on the technical, policy, and governance aspects of public data openness. Firstly, the feasibility of achieving interoperability and data sharing amongst different data sources through establishing unified data formats, data encoding standards, and data exchange protocols has been explored. Wang, et al.^[8] proposed to establish an e-GRMS (Electronic Government Information Resource metadata standard) which includes 25 core elements. Huang and Wang^[9] proposed to refer to foreign experiences and build an open-data platform based on CKAN. Bertot, et al.^[10] proposed that open-data management institutions need to establish appropriate data standard formats, realize data-level interoperability in different fields, as well as encourage the establishment of effective data sharing and interoperability frameworks between governments and departments. Secondly, the open sharing of public data also requires strong policy support. Chen, et al.^[11] sorted out the policy guidance and strategic planning of China's data element market, which revealed six major trends in the development of data element market. These included 1) gradual improvement of the policy system; 2) prioritization of public data governance; 3) obvious trend of data re-source assetization; 4) diversified data governance; 5) emphasis on data security and privacy protection; and 6) active exploration of cross-border data transactions. Fang Jincheng's research found that public data openness is capable of significantly narrowing the gap in regional development levels, promoting coordinated regional development, breaking down regional information barriers, and bridging the gap in regional re-source endowments^[12]. Tang and Ma^[13] proposed that data regulation can guarantee the maximization of data elements' value, and is an important innovation of the modernized regulation of digital economy. The government's role needs to be scientifically positioned, so as to establish an efficient regulatory system. Li and Wu^[14] analyzed the background and mechanism of data elements from the perspective of political economy. It was pointed out that with the vigorous development of the digital economy, data, as the core element for driving the operation of the digital economy, plays an increasingly important role in the overall operation and development of the economy and society. Finally, scholars have explored the contribution and construction path of public data elements to the development of digital economy. Liu, et al.^[15] conducted empirical re-search about the impact of data element market construction on the development of urban digital economy. It has been found that the construction of data element market significantly promotes the development of urban digital economy. Cui and Peng^[16] conducted a comprehensive study on the value dimension, practical difficulties, and path exploration of data element participation in profit distribution from three aspects. Zhang^[17] proposed to explore the construction path of data elements from the perspective of the realistic movement of Chinese path to modernization. Based on the analysis of the mechanism of data element value formation and the impact factors of data element value creation, Yang and Xia^[18] proposed a path to realize the value of data elements, including strengthening the main capacity of data elements, emphasizing the construction of data element resources, and regulating the circulation environment of data elements.

Generally speaking, the current research on open sharing of public data is at the forefront, but the perspective is relatively narrow. Compared to traditional production factors, public data factors have unique technical and economic characteristics. These include virtuality, non-competitiveness, positive externality, value uncertainty, specificity, increasing marginal output, and near-zero marginal cost. These characteristics play a key role in improving social operation efficiency and enterprise production and operation efficiency, realizing doubled capability of value creation, and ultimately affecting the micro foundation of economic development transmission mechanisms^[19].

2.2 Analysis of Government Department Behavior

The government department serves as both the maker of authorization rules and the regulator in the operation of public data authorization. The difference in authorization strength among government departments reflects the different regulatory strategies of the government, as well as the distribution ratio of benefits between government and enterprises. These will impose different impacts on the willingness of enterprises with a large amount of data to participate in data sharing^[20-22].

On the one hand, strong authorization is accompanied by relatively weak regulation. The government adopts strict standards when authorizing, and provides detailed regulations on the use, processing, and dissemination of data, which gives enterprises a clear framework of rights and obligations. Once authorized, enterprises only need to follow relatively relaxed regulations on data usage, allowing them to freely explore the value of data within the prescribed framework. The government largely relies on corporate self-discipline and market mechanisms for self-adjustment and is less involved in daily operational monitoring, which encourages enterprises to participate in data sharing and promotes innovation vitality.

On the other hand, weak authorization complements relatively strong regulation. The government has relatively loose rules and standards when performing authorization. This gives enterprises enough freedom and encourages more enterprises to use public data and actively participate in data sharing. However, in order to ensure the legitimate use of data and protect public interests, the government will then implement strong regulatory measures, including but not limited to regular audits, tracking of data use, and violation penalties. This strategy attempts to expand data circulation while relying on post regulatory measures to correct market failures, protect data security and user privacy. Therefore, this article categorizes the strategies of government departments into 1) strong authorization and weak regulation, and 2) weak authorization and strong regulation.

2.3 Analysis of Corporate Behavior

In this study, enterprises specifically refer to those with a large amount of public data. Under the government's authorized operation model, enterprises' responses may include 1) using data and participating in sharing, 2) not using data but participating in sharing, 3) using data without participating in sharing, and 4) not using data and also not participating in sharing. The latter two normally happen to companies that have a large amount of data and can get profits from the data. Due to the unsatisfied setting of government revenue distribution ratios, they hold a cautious or even resistant attitude towards authorized operation of public data and are unwilling to share their data with public attributes^{[23, 24]}. Therefore, this article divides the strategies of enterprises into positive sharing and negative sharing.

3 Game Model Construction

3.1 Game Model Assumptions

The government and enterprises are assumed to be the game entities in this model, and they can choose any strategy as the initial strategy before the evolutionary game begins. They will try different strategies to obtain higher profits during the game. In this continuous game process, the strategies of the government and enterprises will gradually converge to a stable optimal strategy over time. In order to make the cooperative game model more reasonable, it is assumed that the game entities exhibit limited rationality, and each entity will follow its own behavior logic to maximize its profits. Other assumptions are as follows:

Assumption 1 As aforementioned, the government's game strategy is either strong authorization and weak regulation or weak authorization and strong regulation. The probability of the government choosing a strong authorization and weak regulation strategy is

x

(0 \leq x \leq 1)

, under which the government adopts strict standards during authorization and grants clear rights and obligations to enterprises. Once an enterprise is authorized, the government's regulation on data usage is relatively relaxed, allowing it to freely explore the value of data within the prescribed framework. On the other hand, the probability of the government choosing a weak authorization and strong regulatory strategy is

1 - x

. This corresponds to the case in which the government's rules and standards during authorization are relatively loose, giving enterprises enough freedom and encourage more enterprises to use public data and actively participate in data sharing. However, in order to ensure the legitimate use of data and protect public interests, strong regulatory measures will be implemented afterwards.

Assumption 2 The game strategy of the enterprise is either positive sharing or negative sharing. The probability of an enterprise choosing an positive sharing strategy is given by

y

(0 \leq y \leq 1)

. This means that the enterprise will actively seek and fully utilize open data resources, and also actively share its data with public attributes to create social welfare value. The probability of choosing a negative sharing strategy is therefore

1 - y

, under which that companies have a low willingness and investment in utilizing public data. Although they might use open data to a limited extent when necessary, they are generally unwilling to share their own data.

Assumption 3 When government departments formulate and implement public data authorization operation rules, they need to pay a certain cost

C_{g 1}

, including but not limited to data organization and regulatory maintenance fees. After the adoption of public data authorization operation, promoting enterprises to actively use and share data will bring various reputation benefits

R_{R 1}

to government departments. This may include improvements of social welfare, constructions of innovative ecosystems, and stimulations for economic vitality. If enterprises adopt a negative sharing strategy, it may lead to problems such as idle data resources, intensified information cocoons, and damage to public trust. This will lead to hidden losses

N_{g}

to the government.

Assumption 4 In the process of data authorization and operation, government departments encourage enterprises to legally and efficiently use open data and actively share their own data by establishing incentive mechanisms such as financial subsidies, tax cuts, and technical supports. The incentive cost is recorded as

C_{g i}

, and in the meantime, the distribution ratio of operational benefits between government and enterprises is set as

ε

. Enterprises can receive certain incentive benefits, which helps enhance their enthusiasm of data utilization, thereby bringing indirect reputation benefits

R_{R 2}

to the government. These includes improvements of social and economic benefits, accelerations of industrial innovation, and deliveries of policy goals.

Assumption 5 Enterprises can obtain direct economic benefits

I_{p}

after using public data and actively sharing it. When adopting a negative sharing strategy, enterprises will face certain reputation losses

L_{R}

. Under government's authorized operation strategies and incentive measures, enterprises need to undertake the cost

C_{e 1}

for compliant uses of data when choosing collaboration strategies (i.e., positive sharing). This cost includes investments in data protection technology, compliance training, etc. Collaboration strategies help companies establish a good market profile, enhance consumer trust, and expand business development space, which lead to long-term reputation benefits

I_{R}

Assumption 6 It is assumed that both the government and the enterprise can freely choose a certain strategy as the initial strategy before the game begins. In order to maximize their own interests, both parties will dynamically adjust their strategies during the game process based on the behavior of the other party, market feedbacks, and policy changes. As the game continues, the strategies of both parties will gradually converge to a stable optimal strategy combination, which results in an evolutionary equilibrium state of stable and mutually beneficial distribution of benefits between government and enterprises under the public data authorization operation.

The specific parameter design in the game model is shown in Table 1.

Table 1 Model parameter design

Definition	Symbols
Goverment costs under strong authorization and weak regulation	$C_{g 1}$
Goverment costs under weak authorization and strong regulation	$C_{g 2}$
Reputation benefits of the government	$R_{R 1}$
Goverment reputation loss	$N_{g}$
The cost of government incentives for companies to share data	$C_{g i}$
Indirect reputation benefits obtained by the government	$R_{R 2}$
Government incentive coefficient	$α$
Penalty under strong government regulation	$L_{g}$
The cost of actively sharing data among enterprises	$C_{e 1}$
The benefits of actively sharing data among enterprises	$I_{p}$
Reputation losses of enterprises	$L_{R}$
Reputation benefits of enterprises	$I_{R}$
Government incentive value received by enterprises	$I_{g}$
Distribution ratio of the revenue	$ε$
Goverment authorization intensity coefficient	$β$
Public data authorization operation revenue	$E$

3.2 Strategy Selection of Game Players

3.2.1 Model Construction

Based on the above assumptions and the design of model parameters, the evolutionary game model between government and enterprise is constructed. First, the payment income matrix of government departments and enterprises can be calculated, as shown in Table 2.

Table 2 Profit matrix of both parties in the game

Enterprise	Government
	Strong authorization and weak regulation ( $x$ )	Weak authorization and strong regulation ( $1 - x$ )
	Actively sharing ( $y$ )	$ε E - C_{g 1} + R_{R 1} - C_{g i}$	$ε E - C_{g 2} + R_{R 1} - N_{g}$
$I_{p} + (1 - ε) E + I_{g} + l_{g} + C_{g}^{\cdot}$	Actively sharing ( $y$ )	$I_{p} + (1 - ε) E + I_{g} - C_{e 1}$
Negative sharing ( $1 - y$ )	$ε E - C_{g 1} - N_{g}$	$ε E - C_{g 2}$
Negative sharing ( $1 - y$ )	$- L_{g}$	$0$

If the government chooses a weak authorization and strong regulation strategy, and enterprises actively participate in data sharing, they will receive incentive values from the government. However, if enterprises actively share data but engage in illegal operations, they will suffer certain losses, and government departments will receive benefits through punitive measures. On the other hand, if the government adopts a strategy of strong authorization and weak regulation, and enterprises do not share data (i.e., negative sharing), they will not gain profits. Accordingly, the government will have to take the implicit reputation loss.

3.2.2 Model Solving

Replicator dynamic differential equations acts as the core of evolutionary games. By solving the replicator dynamic differential equations, stable states and evolutionary trends of participating entities' strategy choices can be obtained, which lay a theoretical foundation for analyzing the behavior and decision-making of participating entities in the game process. The calculations of the replicator dynamic equations for government departments and enterprises are presented below.

1) According to the established mutual benefit matrix above, it can be seen that the expected benefit

E_{x 1}

for government departments to choose strong authorization and weak regulation strategies is:

\begin{aligned} E_{x 1} = y (R_{R 1} - C_{g i} + N_{g}) + ε E - C_{g 1} - N_{g} . \end{aligned}

(1)

The expected benefit of government departments choosing a weak authorization and strong regulation strategy,

E_{x 2}

is:

\begin{aligned} E_{x 2} = ε E - C_{g 2} - y (R_{R 1} + N_{g}) . \end{aligned}

(2)

The average revenue of government departments

{\bar{E}}_{x}

is:

\begin{aligned} {\bar{E}}_{x} = x E_{x 1} + (1 - x) E_{x 2} . \end{aligned}

(3)

Therefore, the replicator dynamic differential equation of the government sector is:

\begin{aligned} F (x) = x (1 - x) (E_{x 1} - E_{x 2}) = x (1 - x) [y (2 R_{R 1} - C_{g i} + 2 N_{g}) - C_{g 1} - N_{g} + C_{g 2}] . \end{aligned}

(4)

2) According to the benefit matrix, the expected benefit

E_{y 1}

for enterprises to choose an active data sharing strategy is:

\begin{aligned} E_{y 1} = x I_{g} + I_{p} + I_{R} + E - ε E - C_{e 1} . \end{aligned}

(5)

The expected benefit of enterprises choosing a negative data sharing strategy,

E_{y 2}

is:

\begin{aligned} E_{y 2} = - x L_{R} . \end{aligned}

(6)

The average income of the enterprise

{\bar{E}}_{y}

is:

\begin{aligned} {\bar{E}}_{y} = y E_{y 1} + (1 - y) E_{y 2} . \end{aligned}

(7)

Therefore, the replicator dynamic differential equation of the enterprise is:

\begin{aligned} F (y) = y (1 - y) (E_{y 1} - E_{y 2}) = y (1 - y) [x (I_{g} + L_{R}) + (1 - ε) E + I_{p} + I_{R} - C_{e 1}] . \end{aligned}

(8)

3.3 Stability Analysis of Government Enterprise Game Strategies

3.3.1 Stability Analysis of Government Department Strategy Evolution

Let

F (x) = \frac{d x}{d t} = 0

, that is, the government departments choose the strategy of strong authorization and weak regulation. When the evolution converges to stabilization, we have

x_{1} = 0, x_{2} = 1

y_{0} = \frac{(C_{g 1} + N_{g} - C_{g 2})}{(2 R_{R 1} - C_{g i} + 2 N_{g})}

. The corresponding different cases are discussed below.

1) When

y = \frac{C_{g 1} + N_{g} - C_{g 2}}{2 R_{R 1} - C_{g i} + 2 N_{g}}

, all

0 \leq x \leq 1

are in a stable state. In other words, when the probability of government departments choosing strong authorization and weak regulation strategies is

y = \frac{C_{g 1} + N_{g} - C_{g 2}}{2 R_{R 1} - C_{g i} + 2 N_{g}}

, the strategies that enterprises choose active sharing are stable.

2) When

y \neq \frac{C_{g 1} + N_{g} - C_{g 2}}{2 R_{R 1} - C_{g i} + 2 N_{g}}

x_{1} = 0, x_{2} = 1

are two stable state points. According to the stability theorem of replicator dynamic differential equations and the characteristics of evolutionary stability strategies,

F^{'} (x) < 0

is required. In this regard, there are two situations:

① When

y > \frac{C_{g 1} + N_{g} - C_{g 2}}{2 R_{R 1} - C_{g i} + 2 N_{g}}

and

F^{'} (0) > 0

F^{'} (1) < 0

, that is,

x = 1

is the stable state point of game evolution. After a long-term repeated game between the two parties at this stable point, when the system is in equilibrium, the enterprise will choose active sharing strategies. They will actively acquire and use open data from government departments to enhance the value of its products and services.

② When

y < \frac{C_{g 1} + N_{g} - C_{g 2}}{2 R_{R 1} - C_{g i} + 2 N_{g}}

and

F^{'} (0) < 0

F^{'} (1) > 0

, that is,

x = 0

is the steady state point of the game evolution. At this stable state point, enterprises usually choose the strategy of actively sharing data in order to enhance market competitiveness. However, government departments will reduce the probability of encouraging enterprises to do so due to the cost problem.

3.3.2 Analysis of the Stability of Enterprise Strategy Evolution

Let

F (y) = \frac{d y}{d t} = 0

, that is, the probability of the enterprise choosing an active data sharing strategy tends to stabilize, it can be obtained that

y_{1} = 0, y_{2} = 1

x_{0} = \frac{C_{e 1} - (1 - ε) E - I_{p} - I_{R}}{I_{g} + L_{R}}

. The corresponding scenarios are discussed in the following.

1) When

x = \frac{C_{e 1} - (1 - ε) E - I_{p} - I_{R}}{I_{g} + L_{R}}

, for all

0 \leq y \leq 1

, it is a stable state. This means that when the probability of enterprises choosing to actively share data is

x = \frac{C_{e 1} - (1 - ε) E - I_{p} - I_{R}}{I_{g} + L_{R}}

, any probability of government departments choosing weak authorization and strong regulation is considered stable.

2) When

x \neq \frac{C_{e 1} - (1 - ε) E - I_{p} - I_{R}}{I_{g} + L_{R}}

y_{1} = 0, y_{2} = 1

are two stable state points. According to the stability theorem of replicator dynamic differential equations and the characteristics of evolutionary stability strategy,

F^{'} (y) < 0

is required. Therefore, there exist the following two cases:

① When

x > \frac{C_{e 1} - (1 - ε) E - I_{p} - I_{R}}{I_{g} + L_{R}}

F^{'} (0) < 0

F^{'} (1) > 0

y = 0

is the stable state point of the game evolution. Under this stable point, after long-term repeated games between the two parties, the government departments will tend to choose the strategy of strong authorization and weak regulation, and will not take incentive measures for enterprises.

② When

x < \frac{C_{e 1} - (1 - ε) E - I_{p} - I_{R}}{I_{g} + L_{R}}

F^{'} (0) > 0

F^{'} (1) < 0

y = 1

is the stable state point of the game evolution. At this stable point, government departments generally choose weak authorization and strong regulation strategies. Such strategies are adopted to improve social welfare, as well as incentivize enterprises when their enthusiasm of participating in data sharing is not high.

3.3.3 Stability Analysis of the Game Evolution Between Government and Enterprise

The mixed evolution of games between government departments and enterprises can be described by replicating a system of dynamic differential equations. Firstly, let

F (x) = 0, F (y) = 0

, five results, i.e.,

E_{1} (0, 0), E_{2} (0, 1), E_{3} (1, 0), E_{4} (1, 1), E_{5} (x_{0}, y_{0})

, can be derived, which correspond to the equilibrium points of the game model, where

x_{0} = \frac{C_{e 1} - (1 - ε) E - I_{p} - I_{R}}{I_{g} + L_{R}}

y_{0} = \frac{(C_{g 1} + N_{g} - C_{g 2})}{(2 R_{R 1} - C_{g i} + 2 N_{g})}

. According to the stability theorem of differential equations, strategy stability analysis is conducted on government departments and enterprises, respectively, to find the optimal strategy. The Jacobian matrix of the system is solved as follows:

\begin{matrix} J = [\begin{matrix} \frac{\partial F (x)}{\partial x} & \frac{\partial F (x)}{\partial y} \\ \frac{\partial F (y)}{\partial x} & \frac{\partial F (y)}{\partial y} \end{matrix}], \end{matrix}

(9)

\begin{matrix} J = [\begin{matrix} (1 - 2 x) [y (2 R_{R 1} - C_{g i} + 2 N_{g}) - C_{g 1} - N_{g} + C_{g 2}] & x (1 - x) (2 R_{R 1} - C_{g i} + 2 N_{g}) \\ y (1 - y) (I_{g} + L_{R}) & (1 - 2 y) [x (I_{g} + L_{R}) + (1 - ε) E + I_{p} + I_{R} - C_{e 1} \end{matrix}] . \end{matrix}

(10)

For the Jacobian matrix of an equilibrium point, if its determinant value is greater than zero and its trace value is less than zero, then this equilibrium point is considered as an evolutionarily stable strategy. Specifically, the expression for the determinant value can be derived as:

\begin{aligned} det J & = (1 - 2 x) (1 - 2 y) [y (2 R_{R 1} - C_{g i} + 2 N_{g}) - C_{g 1} - N_{g} + C_{g 2}] \times [(I_{g} + L_{R}) + (1 - ε) E \\ + I_{p} + I_{R} - C_{e 1}] - x y (1 - x) (1 - y) (R_{R 1} - C_{g i} + 2 N_{g}) (I_{g} + L_{R}), \end{aligned}

(11)

\begin{aligned} tr J & = (1 - 2 x) [y (2 R_{R 1} - C_{g i} + 2 N_{g}) - C_{g 1} - N_{g} + C_{g 2}] \\ + (1 - 2 y) [x (I_{g} + L_{R}) + (1 - ε) E + I_{p} + I_{R} - C_{e 1}] . \end{aligned}

(12)

The corresponding calculation results of the five equilibrium point are shown in Table 3.

Table 3 Determinants and traces of the Jacobian matrices of the five equilibrium points

Equalization	Determinant (det $J$ )	Trace (tr $J$ )
(0, 0)	$(C_{g 2} - C_{g 1} - N_{g}) [(1 - ε) E + I_{p} + I_{R} - C_{e 1}]$	$C_{g 2} - C_{g 1} - N_{g} + (1 - ε) E + I_{p} + I_{R} - C_{e 1}$
(0, 1)	$C_{g i} - 2 R_{R 1} - N_{g} - C_{g 2} + C_{g 1} + (1 - ε) E + I_{p} + I_{R} - C_{e 1}$	$2 R_{R 1} - C_{g i} - C_{g 1} + C_{g 2} + N_{g} - (1 - ε) E - I_{p} - I_{R} + C_{e 1}$
(1, 0)	$(C_{g 1} - C_{g 2} + N_{g}) [I_{g} + L_{R} + (1 - ε) E + I_{p} + I_{R} - C_{e 1}]$	$(C_{g 1} - C_{g 2} + N_{g}) [x (I_{g} + L_{R}) + (1 - ε) E + I_{p} + I_{R} - C_{e 1}]$
(1, 1)	$(2 R_{R 1} - C_{g i} + N_{g} + C_{g 2} - C_{g 1}) [I_{g} + L_{R} + (1 - ε) E + I_{p} + I_{R} - C_{e 1}]$	$C_{g i} - 2 R_{R 1} - N_{g} + C_{g 1} - C_{g 2} - I_{g} - L_{R} + (ε - 1) E - I_{p} - I_{R} + C_{e 1}$
$(x_{0}, y_{0})$	$(1 - x_{0}) (1 - y_{0}) [C_{g 2} - C_{g 1} - N_{g} + (1 - ε) E + I_{p} + I_{R} - C_{e 1}]$	$0$

Table 4 summarizes the stability results of the five equilibrium points based on the calculated determinant and trace values. It can be seen that two equilibrium points, i.e.,

E_{1} (0, 0)

and

E_{2} (0, 1)

, are considered as stable points. The central point represents the boundary of game evolution under different strategies. The unstable point corresponds to the strategy combination that is unstable, whereas the strategy combination of the saddle point is the equilibrium point of the mixed strategy. By analyzing the parameters that affect system evolution one by one, we can gain a deeper understanding of the evolution mechanism and stability of the system, and further optimize the game strategies. According to the parameter settings, phase diagrams that illustrate the trends of the interaction between government departments and enterprises can be drawn, and the results are shown in Figure 2. Analyzing the trends of the game in the phase diagrams can lead to:

Table 4 Stability analysis of equilibrium points

Equilibrium point	Determinant	Trace	Result
$E_{1} (0, 0)$	$-$	$+$	Stable Point
$E_{2} (0, 1)$	$+$	$-$	Stable Point
$E_{3} (1, 0)$	$+$	$+$	Unstable Point
$E_{4} (1, 1)$	$-$	$-$	Saddle Point
$E_{5} (x_{0}, y_{0})$	$+$	0	Central Point

Figure 2 Figures showing different evolution trends. (a) Evolution trend under changes changes of corporate profits. (b) Evolution trend under of enterprise costs. (c) Evolution trend of changes changes of enterprise loss values. (d) Evolution trend under of government costs. (e) Evolutionary trends under changes of incentive values and penalty values

Full size|PPT slide

I_{p}

refers to the benefits obtained when the enterprise chooses to actively share data. When

I_{p}

continues to increase, the system converges to

E_{2} (0, 1)

. This means that the probability of the game evolution between the government and the enterprise converging to the ideal mode increases, as shown in Figure 2(a). This will gradually make the system evolve towards the ideal situation.

C_{e 1}

refers to the total cost that an enterprise needs to pay when it chooses an active data sharing strategy. When

C_{e 1}

increases, the cost of acquiring data and sharing its own data will gradually increase. As such, the enterprise will tend to choose a negative data sharing strategy, and both parties of the game will eventually converge to the worst strategy in the evolution process. As shown in Figure 2(b), this scenario makes the system evolve towards a chaotic state, i.e., an equilibrium cannot be reached.

L_{R}

refers to the reputation loss of enterprises. If the enterprise still chooses the strategy of negative data sharing under the government's weak authorization and strong regulation, it will result in the loss of social reputation value. When

L_{R}

increases, as shown in Figure 2(c), the game between the two parties will eventually move forward to the ideal situation according to the evolution trend.

C_{g i}

refers to the incentive cost paid by the government to encourage enterprises to use data. When

C_{g i}

increases, the cost of government departments increases. However, it is uncertain whether enterprises will choose the strategy of active data sharing and whether government departments' own income can cover the cost. Therefore, government departments tend to choose the strategy of strong authorization and weak regulation to save costs. As shown in Figure 2(d), the probability that the strategy evolution of both sides converges to the ideal model will decrease, which is not beneficial to the overall evolution of the system.

I_{g}

and

L_{g}

are incentives and punishments for enterprises by government departments, respectively. When the reward and punishment values gradually increase,

E_{5}

moves to the upper right, and the area of

E_{2} E_{3} E_{4} E_{5}

increases, as shown in Figure 2(e). The system evolution gradually converges to

E_{1} (0, 0)

and

E_{2} (0, 1)

4 Analysis of the Simulation Experiments

4.1 Experimental Purpose and Environment

To verify the effectiveness of the proposed cooperative game model and the accuracy of the derived equations, we have conducted extensive simulation experiments. The equilibrium points

E_{1}

and

E_{2}

, as well as the effectiveness of the game model under different initial strategies have been validated. The simulation environment for this experiment is summarized as follows. CPU is the 11th Gen Intel (R) Core (TM) i5-1155G7 @ 2.50 GHz. The memory size is 16.00 GB. The operation system is Windows 11, and Matlab R2019b simulation platform is used.

4.2 Evolution Results of the Game Between the Two Sides Under Parameter Changes

4.2.1 Parameter Sensitivity Analysis

In order to better simulate the impact of parameter changes on the evolution trend of the game between the two parties, a parameter sensitivity analysis is carried out using the government and enterprise benefit equation established in Section 3.3.2.

1) Government departments

The replicator dynamic equation of government departments is as follows:

F (x) = x (1 - x) (E_{x 1} - E_{x 2}) = x (1 - x) [y (2 R_{R 1} - C_{g i} + 2 N_{g}) - C_{g 1} - N_{g} + C_{g 2}]

. The corresponding sensitivities of parameters

C_{g i}

C_{g 1}

R_{R 1}

C_{g 2}

N_{g}

are shown in Figure 3. By analyzing the curve trend of each parameter, it can be obtained that for the revenue equation of government departments,

C_{g i}

(government incentive enterprise cost) and

C_{g 1}

(government cost) are more sensitive than other parameters. In other words, these two parameters have relatively greater impact on the strategy selection of government departments. Therefore, we can consider regularly changing these two parameters to observe their influences on the evolution trend of the game between the two sides.

Figure 3 Parameter sensitivity analysis for government sector replicator dynamic equation

Full size|PPT slide

2) Enterprises

The replicator dynamic equation of enterprise is as follows:

F (y) = y (1 - y) (E_{y 1} - E_{y 2}) = y (1 - y) [x (I_{g} + L_{R}) + (1 - ε) E + I_{p} + I_{R} - C_{e 1}]

. The sensitivities of the parameters in this equation are shown in Figure 4. It can be seen that for the replicator dynamic equation of enterprises,

ε

(government-enterprise income distribution ratio) and

I_{R}

(corporate reputation income) are more sensitive than other parameters, indicating that these two parameters exhibit greater impacts on the strategy selection of enterprises. Therefore, the two parameters should be changed regularly as well to observe their influences on the evolution trend of the game between the two sides.

Figure 4 Parameter sensitivity analysis for enterprise replicator dynamic equation

Full size|PPT slide

4.2.2 Evolution Results of the Game Between the Two Sides Under Parameter Changes

In order to simulate the evolution path of strategic choices between government departments and enterprises, combined with the management methods and operation rules of public data authorization operations in nine cities including Shanghai, Ningbo, and Hangzhou, as well as the description of the "revenue distribution" section in the "National Public Data Operation Annual Development Report (2023)", most of the revenue from public data authorization operations is turned over to the government at an average rate of 7%

\sim

14%. The government's own revenue is not high, and there is an average cost of 2.7% to encourage enterprises to participate in sharing. Therefore, the parameters of the model are assigned values based on the actual openness and rule design of public data authorization operations. The parameter assignment rules are as follows:

The cost paid by the government (

C_{g 1}

) is generally twice that of the enterprise (

C_{e 1}

), the cost of incentivizing enterprises by the government (

C_{g i}

) is 3% of the total cost, and after 10% of the revenue from public data authorization operation is turned over, and then distributed between the government and enterprises (

ε

), the government's revenue (

R_{R 1} + R_{R 2}

) is generally 1.5 times its cost. The experimental parameters were set according to this rule. The initial values of the experimental parameters are shown in Table 5.

Table 5 Parameter design

Parameter symbols	Numerical value	Parameter symbols	Numerical value
$C_{g 1}$	100	$C_{e 1}$	50
$R_{R 1}$	110	$I_{p}$	200
$N_{g}$	20	$L_{g}$	50
$C_{g i}$	30	$E$	500
$R_{R 2}$	16	$I_{R}$	220
$α$	1.5	$ε$	0.4

The simulation results show that when the initial selection strategy probability of both sides is 0.5, the system evolves towards two equilibrium stable state points, i.e.,

E_{1} (0, 0)

and

E_{2} (0, 1

). This is consistent with the mathematical derivations presented in Section 3.

1) When the parameters

C_{g 1}

and

ε

gradually increase in steps of 0.1 and 10, respectively, enterprises will get more benefits from active data sharing. Therefore, the percentage of enterprises choosing active data sharing strategies will gradually increase in the process of the evolutionary game. However, when the cost of government departments gradually increases, government departments will inevitably choose the strategy that can reduce costs. This means that the government will adopt the strategy of weak authorization and strong regulation, as well as increase the distribution ratio of the revenue to increase its income. However, this will lead to the significant decrease in the gains of enterprises, because of which the enterprises may eventually choose the strategy of negative sharing. As shown in Figure 5, this corresponds to the stable point of (0, 0) between government departments and enterprises, i.e., enterprises choose the negative data sharing strategy, and government departments choose weak authorization with easier rules and strong regulation to actively open public data to enterprises. This is not the optimal stable strategy of the game evolution, as it is not beneficial to the regular operation between government and enterprises, and will also compromise the advancement of the use of public data.

Figure 5 Stable point (0, 0)

Full size|PPT slide

2) When the parameters

C_{g i}

I_{R}

increase in steps of 1 or 10, the percentage of enterprises adopting an active data sharing strategy gradually increases during the evolution process, and they ultimately will choose an active data sharing strategy. In the meanwhile, the percentage of government departments choosing a weak authorization and strong regulation strategy will gradually increase. As such, government departments will ultimately choose a weak authorization and strong regulation strategy. This means that the authorization rules will be relatively simple, which encourages more enterprises to participate in data sharing, as shown in Figure 6. Consequently, this corresponds to the final stable point of (0, 1) of the game evolution between government departments and enterprises. This evolutionary stable strategy is beneficial for both government and enterprises, since it can further promote the circulation of public data as well as attract more enterprises to participate in the sharing of data with social attributes. Eventually, this will advance the contribution of public data to the society.

Figure 6 Stable point (0, 1)

Full size|PPT slide

4.3 Changes of Game Trends Under Different Reward Coefficients and Profit Distribution Ratios

1) Change of reward coefficient

The reward coefficient (i.e., incentive value) is one of the important means used by government departments to encourage enterprises to actively use data. In the initial state, the reward given by the government is not sufficient to encourage enterprises to choose the active sharing strategy. As a result, the game system eventually converges to the stable equilibrium point (0, 0), which is not beneficial to the long-term development of public data, and will lead to increased losses and waste of resources. In order to avoid this, we vary the government reward coefficient while keeping the profit distribution ratio unchanged. Generally speaking, adjusting the reward coefficient can affect the strategy choice of the enterprise, which results in the change of the evolution path of the system, and thereby makes it closer to the ideal state. Figure 7 shows the impact of reward coefficient on the trend of evolutionary stability of both parties in the game.

Figure 7 Stability trends of strategy evolution for both parties under different reward coefficients

Full size|PPT slide

In Figure 7, while keeping the profit distribution ratio unchanged, the reward coefficients given by government departments to enterprises are set as 0.1, 0.5 and 0.9, respectively. It can be seen that all three reward values cannot change the final strategy choice of both parties in the game, and the stable equilibrium trend of the system evolution is consistent with the initial state. This means that the government departments and enterprises do not change their strategies during the game process, and the evolutionary trend still gradually converges to the point (0, 0). Therefore, when the profit distribution ratio between government departments and enterprise is fixed, despite the increase in the reward coefficient, the revenue of enterprise will be relatively low under any strategy. In fact, enterprises may face heavy fine for their misconducts. As a result, it is difficult to stimulate enterprises to choose the active sharing strategy by simply increasing the reward coefficient.

2) Change of profit distribution ratio

The profit distribution ratio set by government departments has a significant impact on the choice of enterprises. In the initial state, the profit that government departments can obtain is relatively high, whereas the enterprises' profit is negligible. Therefore, the system will converge to a stable equilibrium point (0, 0) during the evolution process, which is not beneficial to the sustainable development of government departments. In order to improve this, the reward coefficient is kept unchanged, i.e., the strategic choice of enterprises will not affect its rewards. We then investigate the impact of reducing the profit distribution ratio on the evolutionary stability of both parties in the game. The results of the simulation experiment are shown in Figure 8.

Figure 8 The evolutionary stability trend of the strategies of both parties under different profit distribution ratios

Full size|PPT slide

According to the evolution results of Figure 8, when the profit distribution ratio of government departments varies from 0.3 to 0.9, the final strategy choices of both government departments and enterprises will change. The system gradually converges to the point (0, 1) in the process of evolution. It is seen that when the government departments reduce the profit distribution ratio, namely a higher revenue can be gained by enterprises through the same behavior, the system will eventually converge to the ideal state after multiple rounds of games. This helps better constrain the enterprise' behavior, i.e., while actively sharing data, enterprises will also comply with data sharing rules to ensure the open sharing of public data. As shown in Figure 8, when profit distribution ratio is 0.3, both parties in the game exhibit a faster trend to reach the ideal state.

5 Conclusion

5.1 Research Conclusion

By building a two-party game model, this paper deeply analyzes the strategy choice of government and enterprise in the process of data authorization operation, the dynamic evolution of income distribution mechanism and its impact on the stability of cooperation mode. Experimental verification shows that on the one hand, the best strategy of government and enterprise is weak authorization and strong supervision; Active data sharing, that is, the rules and standards of the government at the time of authorization are relatively loose, giving enterprises enough freedom to encourage more enterprises to use public data and actively participate in data sharing, and the government will then implement strong regulatory measures. At the same time, enterprises choose the strategy of actively sharing data, actively seek and make full use of open data re-sources, and actively share internal data with public attributes. On the other hand, the optimal set value of the revenue distribution ratio between the government and enterprises is 3:7, which can further promote enterprises to actively share internal data with public attributes and actively use public data that is open and shared by the government, which helps to ensure the security and compliance of data sharing, and the government and enterprises can jointly promote the healthy development of data element market. To maximize the value of data and improve the overall social economy. Finally, the management enlightenment of this paper is as follows:

The government should take a series of measures to optimize the open sharing of public data. First, governments need to streamline the process of authorizing public data and lower the threshold for businesses to obtain and use public data. By establishing clear and transparent authorization guidelines and reducing unnecessary administrative procedures, enterprises can be more motivated to participate. In addition, the government can set up a dedicated data service center to provide one-stop data acquisition and support services for enterprises, further reducing the operating costs of enterprises. Second, while ensuring data openness, the government needs to strengthen supervision, regulate the use of data, and establish a complete set of data use norms and standards to ensure that data is effectively used under the premise of legal compliance. At the same time, the government also needs to increase penalties for violations of laws and regulations and maintain a good environment for data use.

As an enterprise with a large amount of data, it should enhance the spirit of public service and actively participate in data sharing. Enterprises should actively contribute data with public attributes, such as geospatial, cultural history, transportation, environment, etc., to promote the open sharing of public data. Through this active participation, it can not only improve the social image and brand value of the enterprise, but also promote the healthy development of the data ecology of the whole society. To this end, companies can work with governments to explore best practices and technical solutions for data openness to ensure efficient and sustainable use of data.

To sum up, the government and enterprises should work together to promote the effective opening and sharing of public data resources through reasonable policy guidance, technical support, incentive mechanism and enhancement of social responsibility.

5.2 Research Limitation

This paper provides an in-depth analysis of the strategy selection and revenue distribution mechanism in public data authorization operation. However, there are still some limitations. Firstly, the finite rationality of game players and the dynamic adjustment of strategy choices in this paper are based on some assumptions, which may be deviated from the complex situation in practical scenarios. This may affect the explanatory power of the model. Secondly, the model does not take into account all factors that may affect the game between government and enterprise, such as market changes, technological progresses, updates of policies and regulations, etc. These factors, however, may have non-negligible impacts on the game results. Finally, although this paper puts forward some policy recommendations, the implementation outcome and long-term impact of these recommendations need to be further verified by practice. When policy-makers apply these recommendations, they need to adjust and optimize the policy accordingly for different circumstances.

In summary, this study provides a framework for analyzing the government-enterprise game in the operation of public data authorization. We anticipate that by addressing the aforementioned limitations in future studies, the accuracy of the model and the practicability of policy recommendations can be further improved.

参考文献

原文顺序 | 文献年度倒序 | 文中引用次数倒序

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Abstract
Key words
引用本文
1 Introduction
Figure 1 Growth in the number of open data platforms at the prefecture level and above over the past years
2 Analysis of Evolutionary Game Behavior Between Government and Enterprises
2.1 Concept of Public Data
2.2 Analysis of Government Department Behavior
2.3 Analysis of Corporate Behavior
3 Game Model Construction
3.1 Game Model Assumptions
Table 1 Model parameter design
3.2 Strategy Selection of Game Players
3.2.1 Model Construction
Table 2 Profit matrix of both parties in the game
3.2.2 Model Solving
3.3 Stability Analysis of Government Enterprise Game Strategies
3.3.1 Stability Analysis of Government Department Strategy Evolution
3.3.2 Analysis of the Stability of Enterprise Strategy Evolution
3.3.3 Stability Analysis of the Game Evolution Between Government and Enterprise
Table 3 Determinants and traces of the Jacobian matrices of the five equilibrium points
Table 4 Stability analysis of equilibrium points
Figure 2 Figures showing different evolution trends. (a) Evolution trend under changes changes of corporate profits. (b) Evolution trend under of enterprise costs. (c) Evolution trend of changes changes of enterprise loss values. (d) Evolution trend under of government costs. (e) Evolutionary trends under changes of incentive values and penalty values
4 Analysis of the Simulation Experiments
4.1 Experimental Purpose and Environment
4.2 Evolution Results of the Game Between the Two Sides Under Parameter Changes
4.2.1 Parameter Sensitivity Analysis
Figure 3 Parameter sensitivity analysis for government sector replicator dynamic equation
Figure 4 Parameter sensitivity analysis for enterprise replicator dynamic equation
4.2.2 Evolution Results of the Game Between the Two Sides Under Parameter Changes
Table 5 Parameter design
Figure 5 Stable point (0, 0)
Figure 6 Stable point (0, 1)
4.3 Changes of Game Trends Under Different Reward Coefficients and Profit Distribution Ratios
Figure 7 Stability trends of strategy evolution for both parties under different reward coefficients
Figure 8 The evolutionary stability trend of the strategies of both parties under different profit distribution ratios
5 Conclusion
5.1 Research Conclusion
5.2 Research Limitation
参考文献

收稿日期	接受日期	出版日期
2024-06-19	2024-10-23	2025-02-25
发布日期
2025-02-25

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Abstract

Key words

引用本文

1 Introduction

Figure 1 Growth in the number of open data platforms at the prefecture level and above over the past years

2 Analysis of Evolutionary Game Behavior Between Government and Enterprises

2.1 Concept of Public Data

2.2 Analysis of Government Department Behavior

2.3 Analysis of Corporate Behavior

3 Game Model Construction

3.1 Game Model Assumptions

Table 1 Model parameter design

3.2 Strategy Selection of Game Players

3.2.1 Model Construction

Table 2 Profit matrix of both parties in the game

3.2.2 Model Solving

3.3 Stability Analysis of Government Enterprise Game Strategies

3.3.1 Stability Analysis of Government Department Strategy Evolution

3.3.2 Analysis of the Stability of Enterprise Strategy Evolution

3.3.3 Stability Analysis of the Game Evolution Between Government and Enterprise

Table 3 Determinants and traces of the Jacobian matrices of the five equilibrium points

Table 4 Stability analysis of equilibrium points

4 Analysis of the Simulation Experiments

4.1 Experimental Purpose and Environment

4.2 Evolution Results of the Game Between the Two Sides Under Parameter Changes

4.2.1 Parameter Sensitivity Analysis

Figure 3 Parameter sensitivity analysis for government sector replicator dynamic equation

Figure 4 Parameter sensitivity analysis for enterprise replicator dynamic equation

4.2.2 Evolution Results of the Game Between the Two Sides Under Parameter Changes

Table 5 Parameter design

Figure 5 Stable point (0, 0)

Figure 6 Stable point (0, 1)

4.3 Changes of Game Trends Under Different Reward Coefficients and Profit Distribution Ratios

Figure 7 Stability trends of strategy evolution for both parties under different reward coefficients

Figure 8 The evolutionary stability trend of the strategies of both parties under different profit distribution ratios

5 Conclusion

5.1 Research Conclusion

5.2 Research Limitation

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参考文献

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