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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.

With the growing demand for infrastructure and public services in recent years, PPP-UP have attracted a great deal of attention. However, while the user focuses on the payment for use and the private sector is concerned with its return on investment, the public sector pays more attention to the efficient utilization of public funds. In order to analyze the willingness of each stakeholder to join PPP-UP, an evolutionary game model involving the three parties is constructed.

An evolutionary game model is established that considers the users and the public and private sectors in user-pay public-private-partnership projects (PPP-UP). Eight scenarios of equilibriums and the game's evolutionary stable strategies are analyzed, and the corresponding stability conditions are then obtained. A situation where all three players are willing to cooperate in theory is also examined. The key influencing parameters that affect cooperation behaviors are further discussed.

First, the results illustrate that by properly adjusting the influencing factors, the cooperation status among the three parties can be changed along with certain evolutionary trends. Second, it is hard to modify unsatisfactory evolutionary stability by small changes in both the price compensation of and the construction and operation compensation. Third, it is necessary to involve the users in the decision-making process in PPP-UP and take their demands regarding benefits and payments into account.

In this paper, we focus on PPP-UP to research interactions among the public and private sectors and the users. Based on the analysis of the evolutionary game, to facilitate the successful implementation and development of a project, several conditions are needed to ensure tripartite cooperation. Several recommendations are then proposed for decision-makers in PPP-UP.

The equipment manufacturing industry, as a strategic industry of China, is experiencing a transition from imitative innovation to independent innovation. The achievements of independent innovation have not been as good as could have been expected. Based on evolutionary economics, the purpose of this paper is to explore the evolutionary path of the two innovation modes, respectively, and analyze the internal and external factors that hinder the mutation from imitative innovation routine to independent innovation routine. According to the results of the evolutionary game model, several policy suggestions are proposed to promote the transition from imitative innovation to independent innovation.

This paper is based on the concepts of evolutionary economics. Routine, mutation, path dependence and selection are included in the analysis of the evolutionary path of the two innovation modes. Especially, the evolutionary game model of innovation modes selection is established to explain how internal and external conditions work in the transition.

The paper explores the evolutionary path of the transition from imitative innovation to independent innovation in the equipment manufacturing industry of China, and analyses the obstacles and factors (internal path dependence, and the lack of benefit incentive and external mutation conditions such as fiscal support and intellectual property protection) that hinder the mutation from imitative innovation routine to independent innovation routine. The results of the evolutionary game model show that the pursuit of the benefit (innovation return or the profit), as an internal mutation condition, is the most fundamental motivation for independent innovation, while policy incentives, as the external mutation conditions, have a significant impact on the evolutionary transition. According to the results, several policy suggestions are proposed to promote the transition from imitative innovation to independent innovation.

Taking the equipment manufacturing industry as a particular object, this paper tries to explain the evolutionary path and the obstacle factors of the transition from imitative innovation to independent innovation from the perspective of evolutionary economics, involving routine, mutation, path dependence, selection, and so on. The evolutionary game model of innovation modes selection is established to investigate the influence of these factors.

This paper aims to recognize whether government policy supervision or social network platform supervision can effectively promote the control of misconducts of web celebrity brand eWOM marketing and to identify the key factors influencing the unhealthy web celebrity marketing environment.

Theoretical research was employed to develop a practical approach for applying evolutionary game theory to eWOM marketing controlling strategies modeling via dynamic visualization, systematic simulation experiments.

Evolutionary game theory combined with dynamic simulation modeling can provide a formal approach to understanding web celebrity brand eWOM marketing decision-making in social media, which can thus support the control of unhealthy web celebrity marketing environment. The results demonstrate that the reasonable control of social platform control costs may be more effective than the government policy on web celebrity fake brand eWOM marketing behaviors.

The study enriches the research on the management and control of eWOM marketing as well as provides guidance for the sustainable development of the web celebrity economy in social media.

Knowledge sharing in a master-apprentice pattern is the process of transferring tacit knowledge from masters to apprentices. In addition, 90 per cent of knowledge required for organizational innovation is tacit knowledge in the master-apprentice pattern. The purpose of this paper is to analyze the evolution of knowledge sharing in master-apprentice pattern and explore the consequences of how to improve the knowledge sharing in the master-apprentice pattern.

This paper uses asymmetric evolutionary game theory to study the evolutionary track of knowledge sharing in master-apprentice pattern of innovative organizations by analyzing the utility of masters and apprentices during the process of knowledge sharing in master-apprentice pattern of the innovative organization.

The results reveal that when the masters obtained utility from sharing knowledge is greater than that from hoarding knowledge, and the apprentices obtained utility from studying hard is greater than the costs, the innovative organization can get the largest utility from the knowledge sharing in the mater-apprentice pattern.

The limitation of the research is that this paper mainly studies knowledge sharing among individuals and does not research knowledge sharing between individuals and organizations.

This research has extended the understanding of knowledge sharing in master-apprentice and its evolution path. Also, the obtained findings are conducive to promoting knowledge sharing in master-apprentice and improving human resource management in innovative organizations.

This paper attempts to construct the evolution path of knowledge sharing in master-apprentice pattern, which is a useful exploration of the dynamics of knowledge sharing in master-apprentice pattern and makes up for the shortcomings of the existing research.

National student loans help solve the problem of tuition fees for students from poor families to a great extent. This paper aims to study the behavior of three main players involved in university student loans, namely, universities, banks and students and explores necessary conditions for promoting the steady development of student loans, as well as the sustainability of cooperation and coordination among players, thus promoting the further development of student loans.

First, from the perspectives of the three related players of banks, students and universities and their behavior, this paper establishes a three-player behavioral evolutionary game model, conducts a sustainable game analysis among the different players, and by replicating the dynamic equations with the Jacobian matrix solve the evolutionarily stable strategy. Finally, applying MATLAB tools, a sensitivity analysis of relevant impacting factors is carried out to explore the influencing mechanism of the sustainable development of student loans.

To achieve the mechanism of mutual coordination and cooperation between participants, banks need to be guided to actively issue student loans and conduct strict loan review. College students should be encouraged to establish good credit and strengthen penalties should be implemented for violations of regulations. Universities should be encouraged to help banks reduce information asymmetry, promote financial knowledge and student integrity education and promote the sustainable development of national student loans.

This research will help scholars better understand the interaction mechanism among universities, banks and students, and promote the sustainable development of national student loans.

The purpose of this paper is to elaborate on the interactive conflicts between business and governmental authorities in the regulatory process of an emerging business model: sharing economy. Focusing on bike sharing system, the study also investigates the conflict-handling strategy of bike sharing companies and government regulation.

An evolutionary game model is introduced to illustrate the interactive conflict between bike sharing companies and government regulation, combined with system dynamics (SD) to simulate the evolutionary conflict-handling strategies between the two players.

The dynamic strategies of the two players are observed, and under five conditions the conflict outcomes are evolutionary stable states. Simulations show that each party sacrifices part of its interest and adjust its strategy according to that of the other, indicating the conflict-handling strategy as a compromising mode. Furthermore, the strategies of bike sharing companies are sensitive to additional operation and maintenance costs for producing low-quality bicycles and costs of positive regulation, which provides theoretical guidance for regulatory authorities.

The station-less bike sharing come up in China recently, and it is an important research field of entrepreneurship. Owing to the uniqueness and novelty of the phenomenon, conflicts and challenges exist during the regulation process. Thus, the study practically contributes to the conflict-handling strategies of businesses and government under the context of sharing economy. Methodologically, as a novel issue with less available data to carry out empirical research, this study combines evolutionary game theory with SD to shed light on the complex interactions between businesses and government. The research method can be applied to other entrepreneurial studies.

The purpose of this paper is to investigate the dynamics and evolution of trust in organizational cross alliances.

In alliances between corporations and nonprofit organizations, trust in decision-making is a dynamic process. Using the replicated dynamics model of evolutionary game theory, this paper provides a trust decision model and analyzes four scenarios under different parameters. A numerical simulation is developed to present an intuitive interpretation of the dynamic development of trust decisions and the effects of incentive and punishment mechanisms.

Under different parameters, bounded rationality and utilities result in different but stable evolutionary strategies; the initial probability of adopting a trust strategy leads directly to whether participants adopt the strategy when the system reaches stability after continued games; and incentive and punishment mechanisms can significantly reduce the initial probability of adopting a trust strategy where the system evolves to meet stable state needs.

The establishment of trust relationships is an important influence on the stable and coordinated development of an alliance. The proposed model can help the alliance build closer trust relationships and provide a theoretical basis for the design of the trust mechanism.

Incentive and punishment bound by some degree of trust are introduced to address the problems of trust decisions and their dynamics; the model created reflects the bounded rationality and utility of each game stage. Useful evolutionary stable strategies using different variables are proposed to address the decision-making problems of trust in cross alliances.

When disasters occur, the Chinese national or local government and their relevant departments (hereinafter referred to as the government) probably need to acquire emergency supplies from suppliers. Before concluding a transaction, the public officials usually negotiate the quality and price of the emergency supplies with the suppliers. They expect to achieve the best relief effect while the suppliers want to maximize their own interests. Therefore, in order to help the government acquire inexpensive emergency supplies with high quality in a short time, the purpose of this paper is to examine the negotiation process and proposes a negotiation principle for the staff.

This paper first elaborates the characteristics and impact factors of emergency supplies requisition negotiation. Then it establishes a model describing the negotiation on price and quality of emergency supplies between the public officials and suppliers. Afterwards, it proposes an algorithm which can estimate the success rate of the negotiation. Finally, the paper employs the conclusion of the model and algorithm to analyze the emergency supplies requisition negotiation process during the China Lushan earthquake.

This paper proposes a “WRAD” principle of emergency supplies requisition negotiation of public officials in disasters. First, they should ensure the requisition price is not too low. Second, they would widen the difference between the high price and low price. Third, it is best for them to follow the principle of “ascending negotiation and descending choice” while selecting multiple suppliers to negotiate.

This paper establishes a model to study the emergency supplies requisition negotiation process between the public officials and suppliers based on evolutionary game theory. The model assumes that both the public officials and suppliers are not fully rational individuals, and they need time to consult with each other to find out the optimal solution. This paper proposes an innovative action principle of the public officials during the negotiation process which can help it to acquire inexpensive, high-quality, emergency supplies within a short period from the suppliers.