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This article aims to provide an exposition of evolutionary game theory which can be used for pedagogical purposes.

The exposition is presented as a mathematical model in order to cover the formal underpinnings of evolutionary game theory. The paper aims to illustrate the theory using some simple examples.

The paper discusses population games and describes the notion of revision protocols that agents use to change strategies. As an example of an evolutionary dynamic, the paper discusses the replicator dynamic in detail. It shows convergence of this dynamic to Nash equilibrium in simple 2 strategy games. The paper then applies this dynamic to a particular class of 3 strategy games to establish the possibility on cyclical behavior around a Nash equilibrium.

The paper can serve as an educational briefing for students and researchers who are new to the field of evolutionary game theory.

The operation of water environment treatment Public-Private Partnership projects (WETP-PPP) is crucial to the project effectiveness. However, there are often problems in projects that attach importance to construction and neglect operation management, which seriously affect the project operation effect. To ensure the good operation effect of the WETP-PPP, an evolutionary game model of the regulation strategy during the operation period of WETP-PPP is constructed.

An evolutionary game model of regulation is established which considers the government, the project company and the public in water environment treatment Public-Private Partnership projects (WETP-PPP). Five scenarios of equilibriums and the game's evolutionary stable strategies are analyzed, and the corresponding stability conditions are then obtained. Finally, through the simulation, the influence of different factors on the choice of the three-party strategy is analyzed.

First, the key factors that affect the evolution game are the regulation costs and performance rewards of the government, the project company's operation costs and penalties for opportunism and the public supervision costs and rewards. Second, in order to ensure the operation effect, the government needs the performance incentive from the superior government. Third, the public's supervision enthusiasm needs to be mobilized by the government. Last, the penalty strength of speculative operation should be strong enough to play a deterrent role.

The theoretical research in this paper has some limitations. Initially, due to the large number of participants in WETP-PPP, in addition to the government department, the project company and the public studied in this paper, it also involves the consulting industry and financial institutions. In the future, more participants can be added to form four-party interest relationships and conduct four-party evolutionary game research. Second, the operation environment of WETP-PPP is complex and changeable, and various influencing factors are intertwined, the number of parameters involved in this paper is limited, and further detailed research is needed in the future.

Based on the evolutionary game theory, this article discusses the evolution law of the tripartite game behavior of the government department, the project company and the public, which is helpful to clarify the strategy evolution path of the tripartite in the WETP-PPP, and the generation condition and evolution mechanism of the equilibrium strategy of the tripartite game. The key parameters affecting the tripartite strategy selection are analyzed through simulation, which can provide reference for the government department to formulate relevant measures. At the same time, it broadens the application field of evolutionary games and supplements the research on the management mechanism of WETP-PPP during the operation period.

Based on the evolutionary game theory, this paper introduces the supervision behavior of the public, which can provide a new perspective for researchers to conduct relevant research. Secondly, for the regulation during the operation of WETP-PPP, this paper can provide reference for the government department to establish a scientific public supervision system, improve the government supervision mechanism and other relevant measures, which can help promote the public supervision willingness, improve the regulation efficiency of the government and guide the project company to reduce speculation, so as to ensure the effect of water environment management.

This paper focuses on the regulation of WETP-PPP during the operation period to research interactions among the government, the project company and the public. Based on the analysis of the evolutionary game, some suggestions are put forward, such as perfecting the government regulation mechanism, optimizing the reward and punishment system for the project company and broadening the channels of public supervision. The research results of this paper can provide support for the government's regulation of WETP-PPP and ensure the project operation effect.

This paper aims to propose the mechanism of cross-network effect embedded, which can help cross-border e-commerce (CBEC) platforms strengthen cooperative relationships with sellers more equitably and effectively by using the network structural characteristics of the platforms themselves.

A two-stage evolutionary game model has been used to confirm the influence factors. The mathematical derivation of evolutionary game analysis is combined with the simulation method to examine the role of cross-network effect in cooperation. The evolutionary game model based on the cross-network effect is proposed to achieve better adaptability to the study of cooperation strategy from the two-sided market perspective.

The evolutionary game model captures the interactions of cross-network effect and the influence factors from a dynamic perspective. The cross-network effect has a certain substitution on the revenue-sharing rate of SMEs. CBEC platforms can enhance the connection between consumers and the website by improving the level of construction, which is a good way to attract sellers more cost-effectively and efficiently.

This study provides a new method for the validation of the cross-network effect, especially when data collection is difficult. But this method is only a numerical simulation. So the conclusions still need to be further tested empirically. Besides, researchers are advised to explore the relationship between the added user scale and the cross-network effect in some specificCBEC platforms.

This study provides a new method for the validation of the cross-network effect, especially when data collection is difficult. But this method is only a numerical simulation. So the conclusions still need to be further tested empirically. Besides, researchers are advised to explore the relationship between the added user scale and the cross-network effect in some specific CBEC platforms.

Investigations that study cooperation strategy from the cross-network effect perspective in CBEC are limited. The research figured out which influence factors are affected by the cross-network effect in cooperation. A two-stage evolutionary game model was proposed to explain the interaction of the factors. The evolutionary game analysis with a simulation method was combined to highlight the role of cross-network effect on cooperation strategy to give a deeper investigation into the sustainable cooperation ofCBEC.

Recently, the concept of financial technology (FinTech) has attracted extensive attention from international organisations and regulators, in particular, how to achieve a “win–win” situation between financial institutions' FinTech innovation and effective regulation has become a hot topic. This study purposes to explore the evolutionary game relationship between FinTech innovation and regulation by constructing both static and dynamic earmarking game models.

A simulation experiment was conducted using primary data obtained from a commercial bank in China.

The results of the theoretical analysis of evolutionary game models were consistent with the corresponding simulation results, proving the validity of the proposed evolutionary game models. It was also found that the dynamic earmarking game model was more stable and effective than the static earmarking game model in promoting FinTech innovation and regulation. Furthermore, when the regulators utilised a dynamic earmarking mechanism, the evolutionary path of financial institutions and regulators' behaviour strategies took the shape of a spiral and eventually converged to a central point, indicating the existence of an evolutionary stable strategy and Nash equilibrium. Finally, because the behaviour strategies of financial institutions were mainly influenced by the regulators' policies, the regulators were inspired to adjust the corresponding regulation policies on FinTech innovation.

This study bridges the knowledge gap in the existing literature on financial innovation and regulation, in particular by establishing evolutionary game models from the perspective of financial earmarking policies. Also, the case study for simulation experiments can gain a more intuitive insight into FinTech innovation and financial earmarking policies.

The paper aims to elucidate effective strategies for promoting the adoption of green technology innovation within the private sector, thereby enhancing the value of public–private partnership (PPP) projects during the operational phase.

Utilizing prospect theory, the paper considers the government and the public as external driving forces. It establishes a tripartite evolutionary game model composed of government regulators, the private sector and the public. The paper uses numerical simulations to explore the evolutionary stable equilibrium strategies and the determinants influencing each stakeholder.

The paper demonstrates that government intervention and public participation substantially promote green technology innovation within the private sector. Major influencing factors encompass the intensity of pollution taxation, governmental information disclosure and public attention. However, an optimal threshold exists for environmental publicity and innovation subsidies, as excessive levels might inhibit technological innovation. Furthermore, within government intervention strategies, compensating the public for their participation costs is essential to circumvent the public's “free-rider” tendencies and encourage active public collaboration in PPP project innovation.

By constructing a tripartite evolutionary game model, the paper comprehensively examines the roles of government intervention and public participation in promoting green technology innovation within the private sector, offering fresh perspectives and strategies for the operational phase of PPP projects.

This paper aims to show that evolutionary game theory not only provides a general and unified theory of political philosophy and strategic management theories but also a positive theory of interactive behavior.

This study suggests a way of the evolutionary game-theoretical model.

The model presented in this paper demonstrates coopetition is derived from balance points in multi-actor games. As the political–philosophical address of those strategic games will of all becomes convention in this balance point at which common knowledge occurs global optimum.

This study explores the connections between several streams in philosophy and strategic management. What does a particular philosophy contribute to strategic management with respect to game theory? When addressing this question in historical or exploratory terms, or in a combination of both, the end result is similar: particular philosophical issues, properly explained, are discussed in relation to important questions in strategic management.

What are the psychological and behavioral underpinnings of strategic decisions of this kind? What type of cognitive frames and managerial mental models, such as the game-theoretical model, might enable or hinder the integration of real-world problems in strategic decision-making?

What explains the evolution of such mental models, as well as the development of philosophical ideas, in informing the origins? How does the evolution of social and political contexts influence change in the cognitive and behavioral underpinnings of strategic decision-making?

This study highlights the overt power of strategic management ideas – competition, cooperation and coopetition – which have historically been built on the foundations of organizational theory, while also underlying the potential of philosophies, collective wisdom and Condorcet’s jury theorem and Rousseau’s (1998) correctness theory in games of evaluation. This study investigates whether the many produce better decisions than the wise few.

As an effective measure for reducing energy consumption and achieving carbon neutrality, prefabricated building projects (PBPs) have attracted considerable attention in China. Although the Chinese Government has vigorously promoted PBPs, neither developers nor consumers have high recognition of PBPs. This study aimed to explore the decision-making behaviour of governments, developers and consumers in promoting the development of prefabricated buildings in China and to better optimise the incentive strategies for prefabricated buildings in China.

Based on prospect and evolutionary game theories, an evolutionary game model of three stakeholders in the development of PBPs – government, developers and consumers – was constructed. Combined with the system dynamics theory, the incentive policy behaviour and influencing factors of the three parties in the evolutionary game model were analysed.

The results showed that the initial probability of the three parties affects the decision-making behaviour of each party and that of other stakeholders. Government subsidies to developers are more sensitive than developers themselves. There is a certain threshold for the scope of government subsidies to consumers, and exceeding this threshold does not promote the development of PBPs. Based on the results, policy recommendations to the government, developers and consumers were proposed to enhance PBP development.

This study provides suggestions for governments to formulate reasonable incentive policies for prefabricated buildings and a specific theoretical basis for the sound development of prefabricated buildings.

Owing to multiple superiorities to traditional counterparts, prefabricated construction (PC) has gained increasing attention worldwide. The development of PC projects reflects the effects of both policy supervision and PC practice, which aids the government in reasonably identifying the key issues of PC's promotion and rationally improving the policy deployment. However, existing studies fail to address this aspect, especially lacking quantitative exploration. This study explores the micro mechanism of PC's promotion, from the perspective of developing PC projects.

A tripartite evolutionary game model based on prospect theory of the government, developers and contractors is constructed. After rigorous theoretical deduction, this study adopts Changchun in China as a case city and collects the data using the Delphi technique, policy documents and literature analysis.

Results indicate that contractors are generally willing to implement PC projects and the government chooses to actively supervise PC's promotion. The negative investment behavior of developers is the main obstacle to promote PC in Changchun currently.

The conclusions are applicable to other comparable regions. This study is of value to promote PC with high efficiency and effect.

The tripartite evolutionary game model based on prospect theory proposed in this study is conducive to reveal the essence of PC's promotion. This is an important breakthrough in extant studies, with a broad applicability in the PC domain beyond China.

This paper constructs a tripartite evolutionary game model between the government, the core enterprises of film copyright export and imports and uses the system dynamics model to simulate and find the optimal selection results of single and mixed government incentives under dynamic changes, aiming to promote the development of foreign trade of film copyright and innovation and development of the film industry so as to improve the overall social benefits of the film industry and provide policy enlightenment for enhancing the import power of foreign core enterprises to introduce domestic film copyrights.

In this paper, a tripartite evolutionary game model of the government, the core enterprises of film copyright export and imports is constructed, the evolution process of cooperation strategy is derived, the impact of innovation income coefficient, mixed incentive policy and single incentive policy on the evolution results is analyzed, and the system dynamic model is used to simulate to find the optimal selection results of single and mixed government incentives under dynamic changes, so as to provide reference for the government’s dynamic incentive decision-making.

The results show that export-oriented core firms are more sensitive to mixed incentives, while import-oriented core firms respond more quickly to single incentives. The large innovation income coefficient has a negative impact on the willingness of import-oriented core enterprises to cooperate. The study proposes measures to increase the willingness of core companies to participate.

Due to the fact that numerical simulation is based on simulation, there may be a certain gap between it and the actual situation. Therefore, it is necessary to further use actual data to conduct empirical analysis on the theoretical model.

This article mainly focuses on analyzing the impact of strategy choices and related parameters of various entities on the incentive mechanism and studying the foreign trade cooperation strategies of film copyright export enterprises under policy support from a theoretical model perspective. Furthermore, research has proven that in order to effectively enhance the willingness of foreign import core enterprises to participate in the foreign trade of domestic film copyrights, the government needs to coordinate the use of single incentive policies and mixed incentive policies. This study provides a major contribution for policymaker to develop film copyright import and export trade.

Based on the research conclusions, this paper puts forward management countermeasures to further improve the development of the film copyright import and export trade. The first is to enrich government incentive methods and stimulate the vitality of film copyright and foreign trade market entities. The second is to guide the core enterprises of film copyright export to increase investment in innovation and stimulate the endogenous driving force of industrial development. Finally, lengthen the foreign trade industry chain of film copyright and increase the income of film derivatives.

Firstly, this paper applies the research methods of evolutionary game and system dynamics simulation to the field of foreign trade research on film copyright and expands the research perspectives and methods of the film industry. Secondly, by analyzing the “cost-benefit incentive” relationship of the evolutionary game of government export-oriented core enterprises and importing core enterprises, an evolutionary game model is constructed, the quantitative point of tripartite interest decision-making is solved and the research object of the evolutionary game method is expanded. Finally, the system dynamics model is used to simulate and find the optimal selection results of single and mixed government incentives under dynamic changes, so as to provide reference for the government’s dynamic incentive decision-making.