Sustainable Collaboration and Incentive Policies for the Integration of Professional Education and Innovation and Entrepreneurship Education (IPEIEE)

Abstract

The Integration of Professional Education and Innovation and Entrepreneurship Education (IPEIEE) has been recognized as an important direction for the development of higher education in enhancing the innovation and entrepreneurship awareness and ability of college students. However, universities and teachers are facing challenges while promoting IPEIEE, namely, various stakeholders, the unreasonable design of the curriculum system, and the lack of relevant incentive policies. In addition, IPEIEE in many universities has been placed on hold. Few studies have examined the innovation regime in IPEIEE, despite it being a dilemma that the field confronts. Thus, taking into account the roles of universities, teachers, and students in the evolutionary game model, this paper firstly constructs an evolutionary game model for teachers and students, in which the costs and parameters affecting the benefit matrix, as well as the stability strategy, are refined. Secondly, the behavior of universities is introduced to examine the effects of universities on strategic choices of teachers and students. Finally, a mechanism analysis is conducted in combination with the principal–agent model to gain a deeper understanding of the evolutionary stability of stakeholder strategies in the IPEIEE. The findings emphasize potential Evolutionary Stable Strategies (ESS) that universities, as promoters and guides, should take as measures concerning both economic encouragement and management encouragement to promote IPEIEE, so as that the ‘ideal state’ can be achieved. Furthermore, if specific incentives for different stakeholders are proposed and set at an appropriate intensity, this will encourage active cooperation among these stakeholders. This paper explores the evolution mechanism of innovation strategies in IPEIEE from the perspective of stakeholders, offering a better comprehension of the dynamic evolution of these strategies. The key findings also offer support for policymakers to promote the mutual development of agents in the IPEIEE, thus enhancing the overall sustainable collaborative capability of the IPEIEE.

1. Introduction

Since China’s reform and opening up, the university professional education has made considerable progress. However, with economic growth, the rapid development of new technologies, frequent innovation and entrepreneurship activities, such as the transformation of industries; the rise of new industries; the establishment of the concept of ecological civilization; and the great advances of science and technology, have resulted in a sharp increase in socio-economic demand for innovative and entrepreneurial talent [1,2]. As the central nexus of education, science and technology, and talent cultivation, China’s higher education system serves as the fundamental strategic pillar for comprehensively advancing the construction of a modern socialist nation [3]. The modernization of Chinese-style education encapsulates the developmental trajectory of China’s educational system, with innovation and entrepreneurship education serving as its foundational cornerstone. In the context of contemporary high-quality educational development, innovation and entrepreneurship education bear the critical responsibility of driving advancements in the modernization of Chinese-style education [4]. Innovation and entrepreneurship comprise the engine of sustainable socio-economic development, and the cultivation of innovative and entrepreneurial talents is the key to innovation activities [5]. Given the increasingly challenging university student employment landscape and the rising significance of innovation, since 2018, the State Council and relevant subordinate departments have released a series of policies such as “Guiding Opinions on Promoting High-Quality Development of Innovation and Entrepreneurship and Creating an Upgraded Version of ‘Double Creation’”, “Guiding Opinions on Further Supporting Innovation and Entrepreneurship of University Students”, and “Administrative Measures for State-level Innovation and Entrepreneurship Training Programme for University Students”, which clearly emphasized the necessity to enhance innovation and entrepreneurship education and training for university students, and to incorporate innovation and entrepreneurship education and practice programmes into the mandatory curriculum system of the university professional education. Although the performance of IPEIEE in curriculum integration, effective communication of practice, effective articulation of platforms between professional education and innovation, and entrepreneurship education has made strides in recent years, the current situation of IPEIEE in many universities is concerning. Universities and teachers are facing challenges while promoting IPEIEE, namely, the various stakeholders, the unreasonable design of the curriculum system, and the lack of relevant incentive policies. In addition, IPEIEE in many universities has been placed on hold. Hence, optimizing IPEIEE governance policies to ensure efficient management and sustainable collaboration poses a significant challenge in meeting talent development needs and advancing innovation and entrepreneurship education reforms in higher education today.

China has implemented IPEIEE as a means to drive the reform of innovation and entrepreneurship education in universities. Educational resources related to the IPEIEE should be provided by universities. Teachers should be responsible for improving teaching ability, participating in curriculum reform, and guiding students according to the actual conditions. Students need to work hard to improve their knowledge and innovation and entrepreneurship skills [6]. Whether universities, teachers and students can achieve great communication and cooperation directly affects the implementation effect of IPEIEE. However, the goals and interests of universities, teachers, and students in promoting IPEIEE are not fully aligned. Universities are more focused on improving their academic reputation and rankings, attracting excellent students and faculty, and aiming to win more financial support. Teachers pay more attention to teaching and research outputs due to academic status and competition for promotion, while students focus more on acquiring knowledge and skills to enhance their employability and personal development. Especially with the severe employment environment, and the increasing prominence of reform of innovation and entrepreneurship education in undergraduate education, universities are increasingly focusing on the collaborative and sustainable development of IPEIEE. They engage in the game of strategy with teachers and students in the field of IPEIEE, within the context of an imperfect system. The main reason for this phenomenon is the flawed incentive mechanism within IPEIEE [7]. University incentive mechanisms do not effectively align the behavioral motivations of teachers and students with public interests, like advancing IPEIEE. When teachers and students’ interests are not satisfied in the collaborative and sustainable development actions of IPEIEE, the inadequacy in their enforcement becomes particularly evident. As “stakeholders”, teachers and students, following the principle of maximizing their own interests, are unwilling to implement IPEIEE if the actual outcomes do not meet expectations or if the implementation costs are excessively high. When the incentives of universities are relatively loose, teachers may choose to continuously adhere to the traditional way of teaching, due to the large cost of changing the teaching mode or the implementation effect of IPEIEE. Students may choose to ignore IPEIEE due to a lack of initiative for self-directed learning. When universities implement a sound incentive management system for IPEIEE, the cost of teachers and students implementing the IPEIEE will be reduced. If the incentive benefits of teachers and students does not cover the implementation cost of IPEIEE, teachers and students will lack the incentive to seriously promote the collaborative and sustainable development of IPEIEE. In summary, fostering collaborative and sustainable development in IPEIEE necessitates alignment not just of university objectives but also the cooperation among diverse stakeholders, including teachers and students. To efficiently govern IPEIEE, it is crucial to clarify the needs and expectations of stakeholders.

Evolutionary game theory is a method for analyzing the intricate interactions among independent and rational stakeholders. It has been widely used in the field of educational administration. Building on the concept of bounded rationality, evolutionary game theory extends classical game theory by incorporating dynamic evolution into its comprehensive approach. Initially, it was used to analyze conflict and cooperation in biological evolution. In the 1980s, economists introduced evolutionary game theory to analyze institutional change, industrial evolution, environmental governance, and other issues in economic and social development [8,9]. Recently, evolutionary game theory has been extensively applied in education system reform to uncover the interactive relationships and behaviors among educational entities. The game players primarily consist of the government, universities, enterprises, teachers, and students. The games are categorized based on the number of participants, including two-party evolutionary games and three-party evolutionary games. A three-party evolutionary game, compared to a two-party game, more comprehensively reflects the diversity and complexity of players. It proves to be an effective method for analyzing the evolving strategies of multiple agents with bounded rationality in long-term repeated games [10]. Therefore, the application of three-party evolutionary game theory in education reform research has been extensive, with a primary focus on the following two aspects. One aspect involves constructing a cooperative evolutionary game model involving the government, universities, and enterprises to investigate their respective interests in the reform of innovation and entrepreneurship education. The second aspect involves constructing a tripartite evolutionary game model involving universities, students, and enterprises to examine the impact of innovation and entrepreneurship education on enhancing employment prospects [11]. In these games, innovation and entrepreneurship capabilities, as well as implementation costs, are crucial considerations for stakeholders deciding whether to cooperate in reforming innovation and entrepreneurship education. Indeed, incentives serve as an effective tool for universities to implement Innovation and Entrepreneurship Education, as they can enhance stakeholders’ willingness to cooperate.

Most existing studies primarily concentrate on innovation and entrepreneurship behavior and how to promote it. There is limited and incomplete research on incentive policies that foster collaborative and sustainable development of Innovation and Entrepreneurship Education from the evolutionary game perspective. Given this, this paper focuses on the implementation of universities, considering their goal of promoting IPEIEE and the teachers’ aim of maximizing teaching outcomes. It establishes a dynamic evolutionary game model with universities, teachers, and students as the main participants. Then, using the principal–agent model, universities’ incentive behaviors are introduced for simulation analysis to explore how relevant policies affect the strategic stability of evolutionary games. This paper seeks to offer an approach for universities to manage teachers and students, enabling collaborative and sustainable development of IPEIEE, while meeting talent training needs and implementing innovation and entrepreneurship education reforms. It not only uncovers current issues in IPEIEE from a stakeholder perspective and offers a dynamic mechanism for universities to influence teacher and student behavior, but also presents evidence on the status of innovation and entrepreneurship education reform implementation for evolutionary game research, which provides references for enhancing the curriculum system and advancing collaborative and sustainable development in IPEIEE. In this study, the theories of IPEIEE and GT are further developed and elaborated on. This study aims to close the research gap. It constructs a multi-party dynamic game model of teachers, students and universities based on GT, which mirrors the degree of realization of IPPEIEE as a result of the game between teachers and students. IPEIEE and GT theories are developed and deepened in this study. Moreover, it provides theoretical support and policy recommendations for the continued development of IPEIEE, so that education departments and universities can promote the collaboration of IPEIEE work through relevant incentives.

2. Literature Review

2.1. Integration of Professional Education and Innovation and Entrepreneurship Education (IPEIEE)

IPEIEE is an educational model, which combines professional education and innovation and entrepreneurship education in order to enrich the vocational education system and content, and to guide universities to cultivate more comprehensive talents with professional skills and knowledge. In general, IPEIEE occurs from higher education and vocational education, including the reform of teaching methods, the development of a curriculum system, the training of faculty, and the creation of a practice platform, etc., which has a great potential for development. Since the Middle Ages, professional education has emerged in a certain form, which is a three-dimensional and multi-level concept, including two stages, namely, basic professional education in the preparatory stage and professional education in the advanced stage [12,13]. Entrepreneurship education is an effective vehicle for students’ divergent creative thinking cultivation and technical classroom activity evaluation [14]. Jeffrey Timmons, the father of entrepreneurship education, has conducted a systematic study in his book “Entrepreneurship” [15], and Harvard professors have also proposed that entrepreneurship education is like an “onion of wisdom” [16], and the application of entrepreneurship education to professional teaching has an irreplaceable role in cultivating students with key skills in the 21st century [17]. Thus, IPEIEE has been widely used in tertiary education in order to stimulate students’ entrepreneurial thinking, develop their entrepreneurial skills, and facilitate the transformation of developing graduates into unique human capital [18].

A growing number of studies have been conducted on the IPEIEE. In terms of the content setting of entrepreneurship education courses in universities, most focus on the purpose of the program, the division of content, the inclusion of content, and educational methods. Some scholars examine the curriculum involved from the perspective of the skills required by society [19]; some scholar divide the college entrepreneurship education curriculum into three categories, namely, opportunity identification, integration of resources, and establishment of operational business organizations [20], while others propose that the college entrepreneurship education curriculum system should include entrepreneurial awareness, entrepreneurial knowledge, entrepreneurial ability, and entrepreneurial operation [21]. Some also propose business plans and case-based pedagogy from the perspective of popularity with students [22] as well as experiential and evaluative teaching from the perspective of wide application [23].

In addition, the entrepreneurship education model is expanded in foreign universities. Entrepreneurship educator Timmons, in Entrepreneurship [15], proposed an integrated model and a composite model of entrepreneurship education universities, and Streeter, Jaquette, and Hovis put forward the famous focusing, magnetizing, radiating, and hybrid classical models of entrepreneurship education in universities [24,25,26]. Meanwhile, the evaluation of entrepreneurship education in universities is also studied. Most foreign scholars’ research on entrepreneurship education evaluation in universities is based on the subject of entrepreneurship education evaluation, evaluation indexes, evaluation methods, evaluation times, and so on, such as the seven-factor evaluation method [27] and the six-indicator evaluation system for entrepreneurship education [28]. Furthermore, some foreign experts and scholars have proposed an independent system of entrepreneurship education, but it is also a new concept of education. It should integrate innovation and entrepreneurship education into mainstream education [29] and integrate the methods and knowledge of innovation and entrepreneurship education into all fields [30]. Such as, Gibb emphasizes that the focus of entrepreneurship and innovation education in the future is how to better integrate with the profession [31]. How to integrate innovative ideas, entrepreneurial awareness, and entrepreneurial technology into professional education is an important issue in cultivating professional talents with innovative ability and entrepreneurial ability [16]. Overall, the study concludes that entrepreneurship education and professional education must be integrated for the educational benefits of entrepreneurship education to emerge, develop, and even be born. In entrepreneurship and professional education, there are different modes of integration.

In the new era of innovation-driven development, it is particularly necessary for college students to carry out integrated education combining professional theory and practice, innovation and entrepreneurship knowledge and skills. There is a large volume of published studies describing the use of IPEIEE in the curriculum. For example, Erjuan Cui and colleagues examined how IPEIEE courses in marketing majors could be taught more effectively [32], Yuxue Wei et al. explored the construction of the course system of “industrial catalysis” in the context of IPEIEE [33], and Jinling Gao et al. set up a teaching module based on the concept of IPEIEE for the automotive CAD course with strong practicability, which is different from the traditional classroom teaching [34].

In short, there are many studies that focus on the necessity and application of the IPEIEE. However, few efforts have been made to address the reluctance of many professionals to leave their original specialties to specialize in entrepreneurship education [35]. Faced with this situation, it is necessary for us to carry out institutional innovation. On the one hand, we should establish the corresponding incentive mechanism; on the other hand, we need to raise the profile of entrepreneurship education and make it a key part of college education.

2.2. Game Theory (GT)

GT studies strategic interactions between individuals and organizations, penetrating into various fields of social science due to its rigorous mathematical analysis, often referred to as the physics of social science [36,37,38]. GT was proposed by Von Neumann and Morgenstem in 1944 in the book “Game Theory and Economic Behavior”, which marked the initial formation of systematic game theory [39,40]. In the field of GT, the term ‘game’ denotes an abstract mathematical representation of decision making among multiple agents, with the primary objective being the comprehensive inclusion of relevant decision-making factors. GT has contributed numerous solution concepts aimed at guiding rational decision making within the game-theoretic framework [41,42,43]. Unlike other mathematical models, GT focuses on the study of interactions and strategic choices among decision makers and the outcomes of decisions under such interactions and strategic choices [44,45,46], which plays a key role in designing next-generation networks [47,48]. Different research areas have used it. In stakeholder interaction studies, for instance, GT is used to perform a rigorous mathematical analysis approach to evaluate and predict stakeholder interactions [49], mathematical modeling is accomplished in strategic interactions between intelligent decision makers [50], and scholars propose a perspective to study the problem of interference-resistant communication from game-theoretic learning [51].

More studies expand GT by collaborative and non-collaborative models [52,53,54]. GT has also been applied to psychology and policy making [55,56]. As topics such as the sharing economy and circular supply chain continue to emerge in production research and operation management, we need to have a full understanding of the strategic behavior of decision makers and the application of complex analytical methods such as GT, in order to explore these issues and solve related challenges [57]. In addition, some scholars have used GT to construct a supply chain game-theoretic network framework of labor constraints under three different scenarios to analyze the state of labor shortage in the context of the new crown epidemic [58].

Applications in pedagogy have been explored based on GT. In 1979, Hamburger. H first applied game theory to the analysis of teacher–student interactions [59], based on which, Hector Correa conducted a series of theoretical analyses of the game phenomenon between teachers and students [60], after which, he innovatively introduced two variables of personal competence and perception of professional ethics to existing teacher–student game models to further improve them [61,62,63,64]. Charles F. Eiszler investigated the relationship between student assessment and the trend of course grade growth through regression analysis and found that the assessment system led to inflation and devaluation of course grades [65]. Some scholars have argued that the direct link between the evaluation system and the promotion process for faculty members is a direct cause of grade inflation, which in turn spawns a host of problems [66]. According to the issues raised by the former, Hans Bonesrønnin employed an adaptive game theory model based on statistical analysis to analyze the causes and consequences of teachers’ different practice scores [67]. Similarly, Hector Correa et al. have initially analyzed the impact that classroom interaction behaviors between teachers and students have on the teaching and learning process based on GT [64].

Using GT, some researchers have also investigated the concept of teachers and students as the main body of each other, and the construction of course teacher–student interaction teaching models and mechanisms [68]. Despite these studies enriching GT in different ways, little attention has been paid to its application in IPEIEE. Accordingly, no previous studies have taken into account the game between teachers, students, and universities in the ongoing collaborative development of IPEIEE from the perspective of GT. Also, few have tried to study which incentives can promote the continuous collaborative development of IPEIEE.

3. Materials and Methods

The study was conducted in two steps. In the first step, we construct an evolutionary game model for teachers and students, in which the costs and parameters affecting the benefit matrix are refined, as well as the stability strategy.

In the early stage of IPEIEE, innovation and entrepreneurship education efforts are often divorced from professional education, resulting in the lack of a high-quality innovation and entrepreneurship curriculum system. Where the work of IPEIEE remains only on the surface, the sustainable collaboration for IPEIEE will be inefficient or even ineffective. Therefore, the necessary incentives for teachers and students are required in universities. In the second step, the behavior of universities is introduced to examine the effects of universities on strategies of teachers and students. Finally, a principal–agent model is established to study how to motivate.

3.1. Socio-Ecosystem Framework of the Sustainable Development of the IPEIEE

According to the current situation of higher education in China, which draws together Ostrom’s social-ecological system framework, the basic structure for the IPEIEE social-ecological system is deconstructed as four core subsystems of “Resource system”, “Resource units”, “Users”, and “Governance system”, as shown in Figure 1. The research framework demonstrates the core subsystems, system contexts, linked systems, and interactive relationship among these three types of variables in the social-ecological system of the IPEIEE by simple and integrated forms [69]. The system contexts include society, economy, and policy context, which provide a favorable environment for IPEIEE activities, while teachers and students participate in the process as system users.

In actual teaching, teachers can increase the proportion of practical teaching, with the help of effective practice to deepen the integration of professional education and innovation education [70]. As the main body of the teaching practice of the IPEIEE, students can exercise the ability to find problems and solve problems during the process of participating in practical projects, and continuously improve their theoretical application ability and innovation and entrepreneurship ability [71]. Also, universities engage in the IPEIEE as important actors in the sustainable collaboration for the IPEIEE by policymaking, financial support, publicity, and education, etc.

The interaction and outcome in this system are influenced by direct causality and feedback from core subsystems at a particular time. Universities, teachers, and students, as the core stakeholders in the sustainable collaboration for the IPEIEE, have certain differences in their goals. Based on the goals, the three main actors coevolve and inspire innovation activity, and develop each other’s strategies and behaviors for the “IPEIEE” teaching model, thereby realizing value creation.

3.2. Defining Synthetic Value of IPEIEE

The comprehensive value of IPEIEE is the real value of the sustainable development of IPEIEE throughout the course construction of IPEIEE lifecycle. The value of the curriculum system of ‘IPEIEE’ is reflected at its effectiveness and function. Thus, the program function of the sustainable collaboration of IPEIEE is analyzed in this subsection. Firstly, professional education and innovation and entrepreneurship education is one of the important links to cultivate individuals capable of shouldering the responsibility of national rejuvenation. The integration of these two aspects is essential for universities aiming to build a high-quality professional teaching environment, guiding students to connect society demands with their individual professions and fostering innovative and entrepreneurial talents [72]. Secondly, IPEIEE is an urgent need to allow universities to serve the country, and it has the attribute of public goods. IPEIEE can effectively alleviate the problem of difficult employment of graduates and play a positive role in socio-economic development in China.

On the basis of the above analysis, the composition of the comprehensive value of IPEIEE is further elaborated. The Net Present Value (NPV) of IPEIEE reflects its general value from building double first-class majors and cultivating versatile talents perspective. The external value is evident in the project’s social service functions, such as easing graduate employment challenges and positively impacting socio-economic development in China. Thus, the comprehensive value of the project encompasses both general and external value.

The best view of the general, external value of the IPEIEE project is as shown in Figure 2.

3.3. Dynamic Game Modeling of Teachers and Students

3.3.1. Fundamental Assumption

• Two players

Teachers and students are involved as stakeholders in the IPEIEE. In the process of the sustainable collaboration for the IPEIEE, teachers are mainly responsible for providing teaching mode of the IPEIEE; students are accountable for transforming innovative achievements and enhancing their entrepreneurial skills. Teachers and students, as limited rational groups, adapt their strategies in an iterative manner in pursuit of optimal outcomes, until both of the parties reach the stable strategy in the process of learning and imitation.

2.

Strategy sets

In the process of the sustainable collaboration for the IPEIEE, teachers can choose between Support and Nonsupport strategies (S, NS); students mostly play a role in this process, so they can adapt their behaviors accordingly, and thus, students can choose either Cooperation or Noncooperation (C, NC).

3.

Cost

Teachers and students, as the subjects of the IPEIEE, put time and energy into the IPEIEE. If teachers choose “S”, the additional cost of choosing a satisfactory teaching programme for teachers is $\mathrm{q}’$; the cost for students to cooperate with teachers in the IPEIEE can be represented as $\mathrm{q}$.

4.

Income

Assuming teachers choose the strategy “S”, ${\mathrm{n}}_0$ represents students’ income; the income for teachers is represented as ${\mathrm{m}}_0$ if students choose “C”. Also, the income for students is defined as ${\mathrm{n}}_1$ when teachers choose the strategy “S”; the income for teachers is denoted by ${\mathrm{m}}_1$ when students choose “C”. When teachers and students choose “S” and “C”, the extra income for teachers is represented as ${\mathrm{m}}_2$; likewise, students’ extra income is ${\mathrm{n}}_2$.

5.

Probability

As in the model, Students and teachers choose their strategies based on their own interests. If the proportion of teachers choosing “S” is represented as $\mathrm{x}$, then $1 - \mathrm{x}$ is the proportion of teachers choosing “NS”. Similarly, if y represents the proportion of students choosing “C”, then the proportion of students choosing “NC” is denoted by 1 − y (x, y ∈ [0, 1]).

3.3.2. Constructing an Evolutionary Game Model of Students and Teachers

As shown in

Table 1. Game income matrix for Students and Teachers.

	Students	$\mathbf{C} (\mathbf{y}$)	$\mathbf{NC} (1-\mathbf{y}$)
Teachers
S ($\mathrm{x})$		${\mathrm{m}}_1+{\mathrm{m}}_2- \mathrm{q},{\mathrm{n}}_1+{\mathrm{n}}_2- \mathrm{q}$	${\mathrm{m}}_0- \mathrm{q},{\mathrm{n}}_0$
NS ($1 - \mathrm{x})$		${\mathrm{m}}_1,{\mathrm{n}}_0- \mathrm{q}$	${\mathrm{m}}_0,{\mathrm{n}}_0$

, the game payoff matrix can be derived between the teachers and students by defining the relevant parameters and assumptions.

3.3.3. Analyzing Stability Strategies of Teachers

Based on a game profit matrix between teachers and students, the income of the teachers choosing strategy “S” or “NS” is denoted by ${\mathrm{U}}_{11}$ and ${\mathrm{U}}_{12}$, respectively, while their average income is denoted by ${\mathrm{U}}_1$. Therefore,

$${\mathrm{U}}_{11}=\mathrm{y}\left({\mathrm{m}}_1+{\mathrm{m}}_2-\mathrm{q}\right)+\left(1-\mathrm{y}\right)\left({\mathrm{m}}_0-\mathrm{q}\right)$$

(1)

$${\mathrm{U}}_{12}=\mathrm{y}{\mathrm{m}}_1+\left(1 - \mathrm{y}\right){\mathrm{m}}_0$$

(2)

$${\mathrm{U}}_1={\mathrm{xU}}_{11}+\left(1 - \mathrm{x}\right){\mathrm{U}}_{12}$$

(3)

Based on (1)–(3), the replication dynamic equation of teachers choosing strategy “S” is shown as

$$\mathrm{F}\left(\mathrm{x}\right)={\displaystyle \frac{\mathrm{dx}}{\mathrm{dt}}}=\mathrm{x}\left({\mathrm{U}}_{11} - {\mathrm{U}}_1\right)=\mathrm{x}\left(1 - \mathrm{x}\right)\left({\mathrm{m}}_2\mathrm{y} - \mathrm{q}’\right)$$

(4)

Let ${\displaystyle \frac{\mathrm{dx}}{\mathrm{dt}}}=0, {\mathrm{x}}_1^{*}=0$, ${\mathrm{x}}_2^{*}=1$, and ${\mathrm{y}}^{*}={\displaystyle \frac{\mathrm{q}}{{\mathrm{m}}_2}}$ can be obtained.

When ${\mathrm{y}=\mathrm{y}}^{*}$, then ∀$\mathrm{x}$, F($\mathrm{x}$)$\equiv 0$, F’$\left(\mathrm{x}\right)\equiv 0$, the proportion of teachers reaches equilibrium, regarding the choice of strategies “S” and “NS”, when the proportion of students choosing “C” is ${\mathrm{y}}^{*}={\displaystyle \frac{\mathrm{q}}{{\mathrm{m}}_2}}$.

When ${\mathrm{y}>\mathrm{y}}^{*}$, the evolutionary Stable Strategies for teachers is $\mathrm{F}’\left(0\right)>0,\mathrm{F}’\left(1\right)<0,{\mathrm{x}}_2^{*}=1$, which means that the students and the teachers form a good interaction about IPEIEE and both reach an optimal equilibrium state of Pareto.

When ${y<y}^{\mathrm{*}}$, the evolutionary Stable Strategies for teachers is $\mathrm{F}’\left(0\right)<0, \mathrm{F}’\left(1\right)>0, {\mathrm{x}}_1^{*}=0$, which means that teachers’ strategy changes from “S” to “NS” when the proportion of students choosing “C” fails to reach the equilibrium point.

3.3.4. Analyzing Student Stability Strategies

Likewise, the income of the students choosing strategy “C” or “NC” is denoted by ${\mathrm{U}}_{21}$ and ${\mathrm{U}}_{22}$ respectively; their average income is denoted by ${\mathrm{U}}_1$. Thus,

$${\mathrm{U}}_{21}=\mathrm{x}\left({\mathrm{n}}_1+{\mathrm{n}}_2 - \mathrm{q}\right)+\left(1 - \mathrm{x}\right)$$

(5)

$${\mathrm{U}}_{22}=\mathrm{x}{\mathrm{n}}_0+\left(1- \mathrm{x}\right){\mathrm{n}}_0$$

(6)

$${\mathrm{U}}_2={\mathrm{yU}}_{21}+\left(1- \mathrm{y}\right){\mathrm{U}}_{22}$$

(7)

Based on (5) and (6), the replication dynamic equation of students choosing strategy “C” is shown as

$$\mathrm{F}\left(\mathrm{y}\right)={\displaystyle \frac{\mathrm{dy}}{\mathrm{dt}}}=\mathrm{y}\left({\mathrm{U}}_{21}-{\mathrm{U}}_2\right)=\mathrm{y}\left(1-\mathrm{y}\right)\left[\mathrm{x}\left({\mathrm{n}}_1+{\mathrm{n}}_2-{\mathrm{n}}_0\right)-\mathrm{q}\right]$$

(8)

Let ${\displaystyle \frac{\mathrm{dy}}{\mathrm{dt}}}=0$, ${\mathrm{y}}_1^{*}=0$, ${\mathrm{y}}_2^{*}=1$, and ${\mathrm{x}}^{*}={\displaystyle \frac{\mathrm{q}}{{\mathrm{n}}_1+{\mathrm{n}}_2-{\mathrm{n}}_0}}$ can be obtained.

When ${\mathrm{x}=\mathrm{x}}^{*}$, then $\forall \mathrm{y}, \mathrm{F}\left(\mathrm{y}\right)\equiv 0, \mathrm{F}’\left(\mathrm{y}\right)\equiv 0,$ the proportion of students reaches equilibrium, regarding the choice of strategies “C” and “NC”, when the proportion of choosing “S” for teachers is ${\mathrm{x}}^{*}={\displaystyle \frac{\mathrm{q}}{{\mathrm{n}}_1+{\mathrm{n}}_2-{\mathrm{n}}_0}}$.

When ${\mathrm{x}>\mathrm{x}}^{*}$, the evolutionary Stable Strategies for students is $\mathrm{F}’\left(0\right)>0, \mathrm{F}’\left(1\right)<0, {\mathrm{y}}_2^{*}=1$, which means that there is a good interaction about IPEIEE between the students and the teachers and both reach an optimal equilibrium state of Pareto.

When ${\mathrm{x}<\mathrm{x}}^{*}$, the evolutionary Stable Strategies for students is $\mathrm{F}’\left(0\right)<0, \mathrm{F}’\left(1\right)>0, {\mathrm{y}}_1^{*}=0$, which means that students’ strategy changes from “C” to “NC” when the proportion of choosing “S” for teachers fails to reach the equilibrium point.

3.4. Introducing University Behavior

During undergraduate education in higher education, teachers require effective teaching methods and learning platforms to implement talent cultivation model of IPEIEE for students. The way may increase the teaching costs and initial investment risks for teachers. In the absence of an effective teaching model for IPEIEE, teachers may exhibit negative behaviors, resulting in a lack of motivation on the supply side. Students, as passive recipients of theoretical knowledge, lack initiative knowledge due to the traditional teaching method of teaching book-based theoretical knowledge. As a result, students often lack the necessary attention towards the IPEIEE teaching mode, and likewise, they do not take the initiative to learn about IPEIEE for the enhancement of their skills in terms of specialization and ways of thinking.

Incentives for universities are an important means of promoting the sustainable collaboration for the IPEIEE and play a significant role in the advancement of higher education in China. Therefore, considering the current state of development of higher education in China, the incentive mechanisms for universities, which include positive incentives and negative incentives, are introduced in this subsection, to study how university behavior affects the development paths of students and teachers.

If we assume that ${\mathsf{\pi }}_1$ is a positive incentive of choosing strategy “S” for teachers from the universities and $\mathrm{a}$ is a penalty of choosing strategy “NS” for teachers; ${\mathsf{\pi }}_2$ is a positive incentive of choosing strategy “C” for students from the universities and$\mathrm{b}$ is a penalty of choosing strategy “NC” for students. The profit matrices of teachers and students after adding the universities’ incentives are shown in

Table 2. Introducing the income matrix of teachers and students game with economic incentive in Universities.

	Students	$\mathbf{C} \left(\mathbf{y}\right)$	$\mathbf{NC} \left(1 - \mathbf{y}\right)$
Teachers
$\mathrm{S} (\mathrm{x}$)		${\mathrm{m}}_1+{\mathrm{m}}_2 - \mathrm{q}+{\mathsf{\pi }}_1,$ ${\mathrm{n}}_1+{\mathrm{n}}_2 - \mathrm{q}+{\mathsf{\pi }}_2$	${\mathrm{m}}_0- \mathrm{q}+{\mathsf{\pi }}_1,{\mathrm{n}}_0- \mathrm{b}$
$\mathrm{NS} \left(1 - \mathrm{x}\right)$		${\mathrm{m}}_1 - \mathrm{a},{\mathrm{n}}_0 - \mathrm{q}+{\mathsf{\pi }}_2$	${\mathrm{m}}_0- \mathrm{a},{\mathrm{n}}_0- \mathrm{b}$

.

3.5. Construct the Principal–Agent Model

Universities, as principals, expect that the “IPEIEE” teaching model and talent-cultivation can be achieved; teachers aim to satisfy the maximization of the benefits of teaching outcomes as agents. The implementation process of the teaching model of IPEIEE can yield comprehensive value $\mathrm{V}$, and its external value and conventional value have a direct relationship. When analyzing the results of the game model, the conventional value of IPEIEE is mainly considered and different values of IPEIEE are integrated. The comprehensive value of IPEIEE values is positively correlated with the effort level, but these values are also uncertain:

$$\mathrm{V}=\mathrm{ie}+\mathsf{\theta }$$

(9)

where $\mathrm{i}$ is the teachers’ level of effort to implement IPEIEE as an agent, $\mathrm{e}$ is the conversion factor for the comprehensive value, the uncertainty of environments for IPEIEE is denoted by $\mathsf{\theta }$; its mean is 0 and variance is ${\mathsf{\sigma }}^2$. Therefore, the comprehensive value created by the teacher is only related to his level of effort$\mathrm{e}$, but it is independent of the environmental uncertainty $\mathsf{\theta }$.

Following the theory of incentive compatibility constraint, this study assumes a linear relationship between the principals’ incentives for the agents and the comprehensive value of IPEIEE:

$$\mathrm{S}\left(\mathrm{V}\right)=\mathrm{K}+\mathsf{\beta }\mathrm{V}$$

(10)

where $\mathrm{K}$ means fixed incentives of universities for the agents; $\mathsf{\beta }$ presents agents with incentives based on changes in a unit’s comprehensive value. If $\mathsf{\beta }=0$ indicates that the agents do not need to take risks that are created by the implementation of the IPEIEE teaching model, $\mathsf{\beta }=1$ indicates that the agents need to take all the risks.

Suppose the utility function of universities is expressed as

$$\mathrm{P}[\mathrm{V}-\mathrm{S}(\mathrm{V}\left)\right]$$

(11)

Universities want equal profits with desired revenue as risk neutral people, that is

$$\mathrm{E}\left\{\mathrm{P}\left[\mathrm{V}-\mathrm{S}\left(\mathrm{V}\right)\right]\right\}=\mathrm{E}\left[\mathrm{V}-\mathrm{S}\left(\mathrm{V}\right)\right]=-\mathrm{k}+\left(1 - \mathsf{\beta }\right)\mathrm{E}\left(\mathrm{V}\right)=-\mathrm{k}+\left(1 - \mathsf{\beta }\right)\mathrm{ie}$$

(12)

If we assume that the utility function of agents is risk-averse $\mathsf{\upsilon }= -{\mathrm{e}}^{-\mathsf{\rho }\mathsf{\omega }}$, the degree of risk aversion denoted by $\mathsf{\rho }$, and the actual income of agents from IPEIEE represented as $\mathsf{\omega }$.

The implementation cost of agents is $\mathrm{c}\left(\mathrm{e}\right)={\displaystyle \frac{1}{2}}\mathrm{b}{\mathrm{e}}^2$, and the effort costs coefficient of agents denoted by $\mathrm{b}$. When $\mathrm{b}$ > 0, if $\mathrm{b}$is larger, the costs of agents are larger, which causes a larger negative effect in the case of a constant level of effort $\mathrm{e}$. Then the real benefits of agents are

$$\mathrm{W}=\mathrm{S}\left(\mathrm{V}\right) - \mathrm{c}\left(\mathrm{e}\right)=\mathrm{k}+\mathsf{\beta }\mathrm{V}-{\displaystyle \frac{1}{2}}\mathrm{b}{\mathrm{e}}^2=\mathrm{k}+\mathsf{\beta }\left(\mathrm{ie}+\mathsf{\theta }\right)-{\displaystyle \frac{1}{2}}\mathrm{b}{\mathrm{e}}^2$$

(13)

Due to the agents being risk-averse, the equivalent revenue of agents should remove the cost of risks ${\displaystyle \frac{1}{2}}\mathsf{\rho }{\mathsf{\beta }}^2{\mathsf{\sigma }}^2$ on top of the original revenue when $\mathsf{\beta }=0$ and the cost of risks are 0.

$$\mathrm{CE}=\mathrm{E}\left(\mathrm{w}\right) -{\displaystyle \frac{1}{2}}\mathsf{\rho }{\mathsf{\beta }}^2{\mathsf{\sigma }}^2=\mathrm{k}+\mathrm{i}\mathsf{\beta }\mathrm{e}-{\displaystyle \frac{1}{2}}\mathrm{b}{\mathrm{e}}^2-{\displaystyle \frac{1}{2}}\mathsf{\rho }{\mathsf{\beta }}^2{\mathsf{\sigma }}^2$$

(14)

If we let $\mathsf{\varpi }$ denote the utility obtained by carrying out work outside the teaching model of IPEIEE for agents, then, when $\mathrm{CE}<\mathsf{\varpi }$, the agents will not accept the incentives. Therefore, the agents should satisfy the incentive compatibility constraint, that is

$$\mathrm{s}.\mathrm{t} \left(\mathrm{IR}\right) \mathrm{k}+\mathrm{i}\mathsf{\beta }\mathrm{e}-{\displaystyle \frac{1}{2}}\mathrm{b}{\mathrm{e}}^2-{\displaystyle \frac{1}{2}}\mathsf{\rho }{\mathsf{\beta }}^2{\mathsf{\sigma }}^2\ge \mathsf{\varpi }$$

(15)

3.5.1. The Optimal Incentive Model in the Case of Information Symmetry

If the universities have access to the agents’ level of effort $e$ of carrying out teaching model of IPEIEE, that means the information between the universities and the teachers is symmetric; thus, the incentive compatibility constraints are no longer effective. University policies do not need to be more favorable to the agents, which means the principal–agent model becomes

$$\mathrm{maxE}\left\{\mathrm{P}\right[\mathrm{V}-\mathrm{S}\left(\mathrm{V}\right)\left]\right\}=-\mathrm{k}+(1 - \mathsf{\beta })\mathrm{ie}$$

(16)

$$\mathrm{s}.\mathrm{t} \left(\mathrm{IR}\right) \mathrm{k}+\mathrm{i}\mathsf{\beta }\mathrm{e} -{\displaystyle \frac{1}{2}}\mathrm{b}{\mathrm{e}}^2 -{\displaystyle \frac{1}{2}}\mathsf{\rho }{\mathsf{\beta }}^2{\mathsf{\sigma }}^2\ge \mathsf{\varpi }$$

(17)

where the incentive constraints (IR) can be transformed into

$$-\mathrm{k}\le \mathrm{i}\mathsf{\beta }\mathrm{e} - 1/2 {\mathrm{b}}^2 {\mathsf{\sigma }}^2 - 1/2 \mathsf{\rho }{\mathsf{\beta }}^2 {\mathsf{\sigma }}^2 - \mathsf{\varpi }$$

(18)

The optimal incentive problem is transformed into

$$\underset{\mathsf{\beta }, \mathrm{e}}{\max }\left(\mathrm{ie} -{\displaystyle \frac{1}{2}}\mathrm{b}{\mathrm{e}}^2-{\displaystyle \frac{1}{2}}\mathsf{\rho }{\mathsf{\beta }}^2{\mathsf{\sigma }}^2 - \mathsf{\varpi }\right)$$

(19)

where $\mathsf{\varpi }$ is given, the derivatives of $\mathrm{e}$ and $\mathsf{\beta }$ are obtained, respectively:

$${\mathrm{e}}^{*}={\displaystyle \frac{\mathrm{i}}{\mathrm{b}}}; {\mathsf{\beta }}^{*}=0$$

(20)

Bringing this condition into the constraints yields, we can obtain

$${\mathrm{k}}^{*}=\mathsf{\varpi }+{\displaystyle \frac{{\mathrm{i}}^2}{2\mathrm{b}}}$$

(21)

Based on the above formula, the optimal incentive model can be derived:

$${\mathrm{S}}^{*}\left(\mathrm{V}\right)={\mathrm{k}}^{*}+{\mathsf{\beta }}^{*}\mathrm{V}={\mathrm{k}}^{*}=\mathsf{\varpi }+{\displaystyle \frac{{\mathrm{i}}^2}{2\mathrm{b}}}=\mathsf{\varpi }+{\displaystyle \frac{1}{2}}\mathrm{b}\left({\mathrm{e}}^{*}\right)2$$

(22)

This is the Pareto optimal incentive contract. Due to the information being symmetrical, universities can observe how much effort the agent puts into implementing IPEIEE; $\mathrm{e}$ is the agent’s level of effort. When the universities observe $\mathrm{e}<{\mathrm{e}}^{*}$, then incentives $\mathrm{S}<{\mathrm{S}}^{*}$; when $\mathrm{S}<\mathsf{\varpi }$, the agents must increase effort $\mathrm{e}$ until ${\mathrm{e}}^{*}={\displaystyle \frac{\mathrm{i}}{\mathrm{b}}}$. Therefore, the agent does not take risks in the case of information symmetry, the optimal incentive model for the university as incentive subject is to fix the incentive for the incentive subject, and the university does not carry out indirect incentives that can be changed.

Optimal Incentive Models for the IPEIEE = Fixed Incentives

3.5.2. The Optimal Incentive Model in the Case of Non-Information Symmetry

The teaching model of IPEIEE is facing information asymmetry in China at the moment. Universities cannot correctly evaluate the size of $\mathrm{e}$ in such the environment, thus failing to achieve Pareto optimality. Therefore, the incentive compatibility condition is valid in the case of information asymmetry.

The incentive compatibility constraint of agents is

$$\underset{\mathrm{k},\mathsf{\beta },\mathrm{e}}{\max }\left(\mathrm{k}+\mathrm{i}\mathsf{\beta }\mathrm{e} -{\displaystyle \frac{1}{2}}\mathrm{b}{\mathrm{e}}^2 -{\displaystyle \frac{1}{2}}\mathsf{\rho }{\mathsf{\beta }}^2{\mathsf{\sigma }}^2\right)$$

(23)

Finding the first order derivative of $\mathrm{e}$ with respect to the above equation gives

$${\mathrm{e}}^{*}={\displaystyle \frac{\mathrm{i}\mathsf{\beta }}{\mathrm{b}}}$$

(24)

The optimal incentive model for the principal college becomes

$${}_{\mathrm{k},\mathsf{\beta },\mathrm{e}}{}^{\max }\mathrm{E}\left\{\mathrm{P}\left[\mathrm{V}-\mathrm{S}\left(\mathrm{V}\right)\right]\right\}= -\mathrm{k}+(1 - \mathsf{\beta })\mathrm{ie}$$

(25)

$$\mathrm{s}.\mathrm{t} \left(\mathrm{IR}\right) \mathrm{k}+\mathrm{i}\mathsf{\beta }\mathrm{e}-{\displaystyle \frac{1}{2}}\mathrm{b}{\mathrm{e}}^2-{\displaystyle \frac{1}{2}}\mathsf{\rho }{\mathsf{\beta }}^2{\mathsf{\sigma }}^2\ge \mathsf{\varpi }$$

(26)

$$\left(\mathrm{IC}\right) \mathrm{e}={\displaystyle \frac{\mathrm{i}\mathsf{\beta }}{\mathrm{b}}}$$

(27)

Bringing Equations (26) and (27) into (25), the optimization problem can be expressed as

$$\underset{\mathsf{\beta }}{\max }\left({\displaystyle \frac{{\mathrm{i}}^2\mathsf{\beta }}{\mathrm{b}}}-{\displaystyle \frac{{\mathrm{i}}^2{\mathsf{\beta }}^2}{2\mathrm{b}}}-{\displaystyle \frac{1}{2}}\mathsf{\rho }{\mathsf{\beta }}^2{\mathsf{\sigma }}^2 - \mathsf{\varpi }\right)$$

(28)

Finding the first-order derivative of $\mathsf{\beta }$ to Equation (28) gives

$$\mathsf{\beta }={\mathrm{i}}^2/({\mathrm{i}}^2+\mathrm{b}\mathsf{\rho }{\mathsf{\sigma }}^2)>0$$

(29)

4. Results

4.1. Analysis of the Results of the Game between Educators and Students

The strategic choices and payoff matrices of teachers and students were found to be closely related to each other’s choices, through a game analysis. According to the evolutionary stability strategy, only when ${\mathrm{x}>\mathrm{x}}^{*},{\mathrm{y}>\mathrm{y}}^{*}$ can the teachers choose to support the IPEIEE and the students choose to cooperate with the teachers, forming good interaction and leading to the best Pareto-optimal equilibrium state. Thus, to decrease the values of ${\mathrm{x}}^{*},{\mathrm{y}}^{*}$, we should increase the values of $m_2,n_1,n_2$ and decrease the values of $q’, q$, and increase the values of $n_1+n_2 - n_0$. At the same time, the value of x, y should also increase by increasing the level of returns of the Pareto-optimal equilibrium.

However, it is inefficient and risky when only relying on teachers and students to achieve the Pareto-optimal equilibrium as shown by the parameter modification above, which will also make the teachers and students behave negatively towards the sustainable collaboration in IPEIEE. According to the behavioral science, human behavior is the result of demands and motivation. It is external stimuli that influence human behavior, which in turn affects demands. Therefore, the universities should take measures with their “visible hand” to guide the participants during IPEIEE implementation, to influence their behavior, which should reach the maximum benefit for IPEIEE. Based on the analysis of model parameters, universities can apply talent development, reputation incentives, economic support, publicity, and education in order to reach the optimum equilibrium for system evolution by modifying the parameters’ value in the model.

4.2. Introduction of Behavioral Analysis in Universities

4.2.1. A Study of Teachers’ Stability Strategies Following the Introduction of University Behaviors

In the two-party game that introduces the university’s behavior, based on the payoff matrix, the payoff of the teachers’ choice to support IPEIEE collaboration is

$${\mathrm{U}}_{11}’=\mathrm{y}\left({\mathrm{m}}_1+{\mathrm{m}}_2- \mathrm{q}’+{\mathsf{\pi }}_1\right)+\left(1 - \mathrm{y}\right)\left({\mathrm{m}}_0 - \mathrm{q}’+{\mathsf{\pi }}_1\right)$$

(30)

The payoff of teachers choosing not to support IPEIEE collaboration is

$${\mathrm{U}}_{12}’=\mathrm{y}\left({\mathrm{m}}_1 - \mathrm{a}\right)+\left(1-\mathrm{y}\right)\left({\mathrm{m}}_0 - \mathrm{a}\right)$$

(31)

The average expected payoff for the teacher population is

$${\mathrm{U}}_1’={\mathrm{xU}}_{11}’+\left(1- \mathrm{x}\right){\mathrm{U}}_{12}’$$

(32)

The replicator dynamics equations arising from analyzing ‘Support for IPEIEE collaboration’ selection for the teacher population can be expressed as follows:

$$\mathrm{F}\left(\mathrm{x}\right)={\displaystyle \frac{\mathrm{dx}}{\mathrm{dt}}}=\mathrm{x}\left({\mathrm{U}}_{11}’- {\mathrm{U}}_1’\right)=\mathrm{x}\left(1- \mathrm{x}\right)\left({\mathrm{m}}_2\mathrm{y}-\mathrm{q}’+{\mathsf{\pi }}_1+\mathrm{a}\right)$$

(33)

For differential equations to reach equilibrium, the stability theorem states

$$\mathrm{F}\left(\mathrm{x}\right)=0,{\mathrm{x}}_1^{*}=0,{\mathrm{x}}_2^{*}=1,{\mathrm{y}}^{**}={\displaystyle \frac{\mathrm{q}’-{\mathsf{\pi }}_1-\mathrm{a}}{{\mathrm{m}}_2}}$$

(34)

When $\mathrm{y}={\mathrm{y}}^{**}$, ∀$\mathrm{x}$, F($\mathrm{x}$)$\equiv 0$, F’$\left(\mathrm{x}\right)\equiv 0$, The proportion of those who choose to cooperate with IPEIEE collaboration in student population is ${\mathrm{y}}^{**}={\displaystyle \frac{\mathrm{q}’-{\mathsf{\pi }}_1-\mathrm{a}}{{\mathrm{m}}_2}}$, and the proportions of those who choose to support IPEIEE collaboration and those who choose not to support IPEIEE collaboration, in the teacher population, reach equilibrium.

For the teacher population, an evolutionary stabilization strategy is F’$\left(0\right)>0, \mathrm{F}’\left(1\right)<0, {\mathrm{x}}_2^{*}=1, \mathrm{when}\mathrm{y}>{\mathrm{y}}^{**}.$ The teachers can choose to support the IPEIEE, and the students choose to cooperate with the teachers, forming a good interaction and evolving the Pareto-optimal equilibrium state.

For the teacher population, an evolutionary stabilization strategy is F’$\left(0\right)<0, \mathrm{F}’\left(1\right)>0, {\mathrm{x}}_1^{*}=0$, when $\mathrm{y}<{\mathrm{y}}^{**}$. The proportion of those who choose to cooperate with IPEIEE collaboration in the student population fails to reach the initiation site, and teachers who were supportive of IPEIEE collaboration ultimately tend to be unsupportive.

At this time, as is evident from ${\mathrm{y}}^{**}={\displaystyle \frac{\mathrm{q}’-{\mathsf{\pi }}_1-\mathrm{a}}{{\mathrm{m}}_2}}<{\mathrm{y}}^{*}={\displaystyle \frac{\mathrm{q}’}{{\mathrm{m}}_2}}$, the conditions for students to choose to cooperate with the strategy of IPEIEE collaboration are more easily fulfilled with economic incentives from universities; the choice proportion of teachers who ultimately support the strategy of IPEIEE collaboration is also greater.

4.2.2. Analysis of Students’ Stabilizing Habits Strategies after Introducing University Behaviors

For students, the payoff of their choice to cooperate with IPEIEE collaboration is

$${\mathrm{U}}_{21}^{’}=\mathrm{x}\left({\mathrm{n}}_1+{\mathrm{n}}_2- \mathrm{q}+{\mathsf{\pi }}_2\right)+\left(1 - \mathrm{x}\right)\left({\mathrm{n}}_0 - \mathrm{q}+{\mathsf{\pi }}_2\right)$$

(35)

The payoff of students choosing not to cooperate with IPEIEE collaboration is

$${\mathrm{U}}_{22}^{’}=\mathrm{x}\left({\mathrm{n}}_0 - \mathrm{b}\right)+\left(1 - \mathrm{x}\right)\left({\mathrm{n}}_0 - \mathrm{b}\right)$$

(36)

The average expected payoff for the student population is

$${\mathrm{U}}_2^{’}={\mathrm{yU}}_{21}^{’}+\left(1 - \mathrm{y}\right){\mathrm{U}}_{22}^{’}$$

(37)

The replicator dynamics equations arising from analyzing ‘Collaboration with IPEIEE collaboration’ selection for the student population can be expressed as follows:

$$\mathrm{F}\left(\mathrm{y}\right)={\displaystyle \frac{\mathrm{dy}}{\mathrm{dt}}}=\mathrm{y}\left({\mathrm{U}}_{21}^{’}-{\mathrm{U}}_2^{’}\right)=\mathrm{y}\left(1 - \mathrm{y}\right)\left[\mathrm{x}\left({\mathrm{n}}_1+{\mathrm{n}}_2 - {\mathrm{n}}_0\right) - \mathrm{q}+{\mathsf{\pi }}_2+\mathrm{b}\right]$$

(38)

For differential equations to reach equilibrium, the stability theorem states

$$\mathrm{F}\left(\mathrm{y}\right)={\displaystyle \frac{\mathrm{dy}}{\mathrm{dt}}}=0,{\mathrm{y}}_1^{*}=0, {\mathrm{y}}_2^{*}=1, {\mathrm{x}}^{**}={\displaystyle \frac{\mathrm{q}-{\mathsf{\pi }}_2-\mathrm{b}}{{\mathrm{n}}_1+{\mathrm{n}}_2-{\mathrm{n}}_0}}$$

(39)

When ${\mathrm{x}=\mathrm{x}}^{**}$,∀$\mathrm{y}$, F($\mathrm{y}$)$\equiv 0$, F’$\left(\mathrm{y}\right)\equiv 0$, the proportion of those who choose to support IPEIEE collaboration in the teacher population is ${\mathrm{x}}^{**}={\displaystyle \frac{\mathrm{q}-{\mathsf{\pi }}_2-\mathrm{b}}{{\mathrm{n}}_1+{\mathrm{n}}_2-{\mathrm{n}}_0}}$, and the proportions of those who choose to cooperate with IPEIEE collaboration and those who choose not to cooperate with IPEIEE collaboration in the student population reach equilibrium.

For the student population, an evolutionary stabilization strategy is F’$\left(0\right)>0, \mathrm{F}’\left(1\right)<0, {\mathrm{y}}_2^{*}=1,\mathrm{when} {\mathrm{x}>\mathrm{x}}^{**}.$ The students can choose to cooperate with IPEIEE collaboration, and the teachers choose to support IPEIEE collaboration, forming a good interaction and evolving the Pareto-optimal equilibrium state.

For the student population, an evolutionary stabilization strategy is F’$\left(0\right)<0, \mathrm{F}’\left(1\right)>0{, \mathrm{y}}_1^{*}=0, \mathrm{when}{\mathrm{x}<\mathrm{x}}^{**}.$ The proportion of those who support IPEIEE collaboration in the teacher population fails to reach the initiation site, and students who were consciously cooperated with IPEIEE collaboration ultimately tend to be uncooperative.

At this time, as is evident from ${\mathrm{x}}^{**}={\displaystyle \frac{\mathrm{q}-{\mathsf{\pi }}_2-\mathrm{b}}{{\mathrm{n}}_1+{\mathrm{n}}_2-{\mathrm{n}}_0}}<{\mathrm{x}}^{*}={\displaystyle \frac{\mathrm{q}}{{\mathrm{n}}_1+{\mathrm{n}}_2-{\mathrm{n}}_0}}$, the conditions for teachers to choose to support the strategy of IPEIEE collaboration are more easily fulfilled with economic incentives from universities; the choice proportion of students who ultimately cooperate with the strategy of IPEIEE collaboration is also greater.

4.3. Analysis of the Results of the Incentive Model

The effect of the optimal incentive model of the university on the agents in the market with asymmetric information is that the agents take some of the project risks according to their oven risk reference. For universities, providing their agents with both fixed and variable incentive is essential. Therefore, the optimal incentive model looks like this:

Optimal incentives for the development of the IPEIEE teaching model = Fixed Incentive + Risk Sharing Coefficient x Client Benefits.

When ${\displaystyle \frac{\partial \mathsf{\beta }}{\partial \mathrm{b}}}= -{\displaystyle \frac{\mathrm{p}{\mathrm{i}}^2{\mathsf{\sigma }}^2}{{\left({\mathrm{i}}^2+\mathrm{bp}{\mathsf{\sigma }}^2\right)}^2}}$ < 0, the ratio β of variable subsidy for the agent by university is negatively correlated with the coefficient of effort cost b. Thus, the higher economic subsidy is achieved only after the agent lowers the unit cost of effort while keeping the other conditions unchanged.

When ${\displaystyle \frac{\partial \mathsf{\beta }}{\partial \mathrm{p}}}=-{\displaystyle \frac{\mathrm{b}{\mathrm{i}}^2{\mathsf{\sigma }}^2}{{\left({\mathrm{i}}^2+\mathrm{bp}{\mathsf{\sigma }}^2\right)}^2}}$ < 0, the ratio β of variable subsidy for the agent by university is negatively correlated with the coefficient of risk avoidance ρ—universities receive smaller economic incentives when the agent has a higher risk-aversion coefficient.

When ${\displaystyle \frac{\partial \mathsf{\beta }}{\partial {\mathsf{\sigma }}^2}}= -{\displaystyle \frac{\mathrm{b}{\mathrm{i}}^2\mathrm{p}}{{\left({\mathrm{i}}^2+\mathrm{bp}{\mathsf{\sigma }}^2\right)}^2}}$ < 0, there is a negative correlation between the ratio β of variable subsidy for the agent by university and the variance of external uncertainty${ \mathsf{\sigma }}^2$—economic incentives are smaller when external uncertainty is greater. For university teachers and students, they can benefit from reducing returns by external uncertainty.

When ${\displaystyle \frac{\partial \mathsf{\beta }}{\partial \mathsf{\iota }}}= -{\displaystyle \frac{2\mathrm{b}\mathsf{\iota }{\left(\mathrm{p}{\mathsf{\sigma }}^2\right)}^2}{{\left({\mathsf{\iota }}^2+\mathrm{bp}{\mathsf{\sigma }}^2\right)}^2}}>$ 0, there is a positive correlation between the ratio β of variable subsidy for the agent by university and the integrated value transformation coefficient i —the more value the agent creates, the greater the economic incentives are. Since university teachers hardly pay cost in the IPEIEE collaboration project, the economic incentives for the teachers should be provided mainly according to the external value they create, while the economic incentives for the students should consider both the external value they create and the program’s general value.

In our universities, an effective incentive mechanism can, therefore, greatly promote IPEIEE collaboration education by increasing agents’ effort levels. The design of the incentive mechanism should consider the agent’s risk aversion degree ρ, external uncertainty ${\mathsf{\sigma }}^2$, integrated value transformation coefficient i, and cost-effort coefficient b by analyzing the optimal incentive model. Only in this way can we achieve the optimal incentive objective.

5. Incentive Mechanism Design and Policy Recommendation

5.1. Incentive Mechanism

In order to formulate a unified but differentiated incentive mechanism and to form a new approach to “IPEIEE” talent cultivation that is tailored to the demands of the current time, when designing the incentive mechanism of the IPEIEE, we should make full use of the value-driven effect, relying on the agents’ value needs and on the factors affecting optimal incentives to put forward different incentive means, respectively.

• Incentives for teachers in undergraduate education

During implementation of the collaborative and sustainable work in IPEIEE in undergraduate education in universities, the cost for the implementation by the university teachers is 0, the cost of effort coefficient b is almost 0, and the coefficient of risk avoidance ρ is low. The main reason why teachers are not keen on participating in the promotion of the IPEIEE’s collaborative and sustained work is the absence of systematic professional learning and training, and the lack of practical experience in specialized technological innovations.

Hence, for undergraduate education in universities, the teachers’ incentive model should be based on a cooperative mechanism for teachers’ training with joint participation of schools and enterprises, followed by a small financial subsidy, which internalizes the external value.

2.

Incentives for students

Students primarily pursue the regular value of the program and are the implementers of the IPEIEE collaborative work in undergraduate education across the universities. The primary causes of students’ lack of enthusiasm for carrying out the IPEIEE collaborative work are the high external uncertainty coefficient ${\sigma }^2$, the low interest of students in IPEIEE education, and the insignificant integrated value conversion coefficient i, according to the principal–agent model.

In this situation, to motivate students, we generally may have two choices. One is to increase the credits of IPEIEE education in the talent cultivation program. Students are forced to complete the credits of IPEIEE before graduation, and thus, achieve the internalization of external value and NPV > 0. The other is that appropriate awards can be given to the design in IPEIEE competition and attract the students to participate in the innovation program so as to improve students’ comprehensive value conversion coefficient i.

5.2. Design for Incentives Mechanism

According to the incentive objectives, principles, optimal incentive model and incentive intensity, a three-phase design process is followed to develop this incentive mechanism.

The first phase is dominated by students. A variety of teaching methods of IPEIEE can be expanded out-of-class and outside the school, and students are actively organized to take part in all kinds of IPEIEE projects and competitions, which, in turn, promotes their innovation and entrepreneurship abilities. The primary participants in IPEIEE teaching practice are university students. And all kinds of IPEIEE practice should be in accordance with the cognition of university students and be able to mobilize the subjective initiative of university students. Research results obtained in the innovative courses declare various disciplinary competitions. Thus, the cost coefficient b is reduced to increase its benefits. Furthermore, a series of positive incentives implemented by the government reduces the cost b and the exogenous variable uncertainty factor ${\mathsf{\sigma }}^2$. So, a series of negative incentives need to be formulated by the governmental departments as well. Additionally, students can participate in the research activities in their own profession or faculty research projects, becoming the research assistants of the full-time faculty. Taking part in actual scientific research projects gives students an opportunity to test their abilities to find and solve problems as well as improve their ability in applying theories, innovation, and entrepreneurship.

The second phase is dominated by teachers whose innovative training mechanisms should be proposed. Teachers’ risk aversion ρ and the uncertainty of external variables ${\sigma }^2$ are relatively small, and the coefficient of cost of effort b is almost 0. They are the guides and implementers of innovative education in schools, which makes them dominant in the IPEIEE education. The successful implementation of the IPEIEE requires a faculty that has both solid professional knowledge and educational skills of the IPEIEE. However, the faculty in some universities who specialize in the education of the IPEIEE have failed to fulfill the developmental demands of the IPEIEE education. Therefore, in the faculty construction of the IPEIEE, universities should increase the financial investment to train a group of specialized faculty and provide environmental protection for the benign development of the faculty. For example, a diversified faculty team of ‘professional mentors + mentors of the IPEIEE + business mentors’ can be formed through regular training, specialized deep training, introduction of industry mentors, establishment of joint venture bases with outstanding alumni, etc., to form the talent pool of the faculty team in the universities.

The third stage is dominated by universities, which should intensify themselves. There is a need for universities to fully recognize the importance of IPEIEE education, to further improve the systems of the IPEIEE education, and to help cultivate innovative talents, through the teaching platform with modern technology, to enhance students’ class experience and cultivate their digital application skills. The platform also provides more immersive scenarios for teachers and students, which reduces the cost coefficient b of teachers and students and, thus, increases their benefits.

When the capabilities of participants of the IPEIEE are greatly improved and broken through, their combined value conversion factor i will be greatly increased. Students are provided with more learning and practice opportunities in the field of the IPEIEE by building and improving the digital teaching platform and with pedagogically rich and fruitful innovative activities.

5.3. Recommendations of Incentive Policy

Based on the combination of the problems existing in the IPEIEE, as well as the game analysis and the design results of the incentive mechanism in Section 4, this section will analyze and explore the incentives for data acquisition in the operational phase of IPEIEE system from three aspects: policy initiatives, managerial strategies, and technological approaches. This research presents the basic framework of incentive policy proposal on IPEIEE as shown in Figure 3.

5.3.1. Legal Policy Instruments and Methods

• Intensify the construction of the policy evaluation index system

Developing a scientific, rational, and multi-level assessment system is crucial for ensuring the effective implementation of IPEIEE. The government should focus on monitoring and establishing evaluation criteria, potentially including third-party assessments, to evaluate the implementation of entrepreneurship education curriculum, faculty, practice platforms, competition awards, and the transfer of scientific research results to industry. Universities should evaluate the entrepreneurship education work of teachers and the learning effectiveness of students. For teachers, universities should not only pay attention to their professional level ability, practical experience, number of lectures, training grade, etc., but also focus on protecting the rights and interests of teachers; for students, universities should focus on assessing their entrepreneurial awareness, entrepreneurial ability, and practical ability.

2.

Perfect the laws and regulations of IPEIEE and form a policy-based guarantee system.

Under the innovation-driven strategy, the government should consider the regional aspect of economic development and employ the policy or platforms, and other means of regulation, to build a new pattern of coordinated promotion among universities, governments, and enterprises, in the context of clarifying the rights and obligations of the three main bodies, namely, universities, governments, and enterprises. The government should actively formulate policies related to innovation and entrepreneurship education in universities to promote the flow of all kinds of social resources to the system of IPEIEE. Enterprises are encouraged by the government to participate in running schools and to work with universities to develop talent training programs. Then, IPEIEE and the adjustment of industrial structure are jointly promoted, making the employment demand of enterprises and talent cultivation of universities realize zero distance docking.

3.

Develop policy-supporting system for IPEIEE

Local governments should increase the emphasis on IPEIEE, conducting in-depth research on the practical problems faced by universities in the process of policy implementation, and introduce corresponding policies to help universities solve their problems. To better implement the policy on IPEIEE, universities can integrate internal and external resources effectively, breaking the traditional three-level organizational form with discipline as the core, formulating a reasonable policy-supporting system.

5.3.2. Administrative Tools and Methods

• Professional Teachers Motivated to Take the Initiative to Implement Innovation and Entrepreneurship Education

To ensure the smooth implementation of IPEIEE mechanism and to accelerate the speed and efficiency of the IPEIEE, universities need to modify the system and promote multi-departmental cooperation. For example, the personnel department should develop the system for teachers going to enterprises to receive practical training and the policy for enterprise technicians coming to schools as part-time teachers under the innovation orientation. In addition, this part of practical training for university teachers should be included in their workload.

The Academic Affairs Office also needs to revise the incentive system for the creation and the evaluation of teaching materials under the innovation orientation. Those who participant in guiding innovation education or in editing the teaching material for IPEIEE will be granted certain amount for workload.

2.

Encourage students to actively participate in innovation and entrepreneurship education

Universities add innovation and entrepreneurship education credits to the talent cultivation program and specify how many innovation and entrepreneurship credits students must complete before they can graduate. The Academic Affairs Office gives appropriate credit awards to students involved in innovation and entrepreneurship within their majors; the Youth League Committee gives appropriate awards for the audit of innovation and entrepreneurship clubs, the design of innovation and entrepreneurship competitions, etc., and innovation awards to students who win prizes for participating in professional skills competitions or innovation competitions. Universities encourage all second-level colleges to open their laboratories and to attract students participate in scientific research projects; also, universities can organize a series of interesting science and technology activities, such as science and technology festivals for different majors and levels, science and technology lectures, academic salons, and so on. In short, every student can be trained and inculcated on various platforms of innovation and entrepreneurship education.

3.

Strengthen resource input and public opinion guidance to enhance the influence of innovation and entrepreneurship education

The practice of IPEIEE is inseparable from the market demand, which determines that the development of IPEIEE cannot rely on the investment of universities alone. Government financial support and public opinion guidance are also key factors affecting the effectiveness of IPEIEE in universities. In terms of introducing mentors of IPEIEE, constructing incentive mechanism of IPEIEE, and financing student entrepreneurship, the government should make efforts to create an excellent external environment for the development of IPEIEE. At the same time, guided by the new situation of the current national innovation and development strategy, universities should encourage students to participate in innovation and entrepreneurship with the concept of tolerating failure, and organize students to participate in “Internet +”, “Challenge Cup” and other innovation and entrepreneurship activities, to cultivate students’ innovative spirit and entrepreneurial ability. In addition, universities can also publicize the enterprises and individuals who have won prizes in the competitions and make use of modern network media to vigorously promote the culture of innovation and entrepreneurship.

4.

Adjust teaching strategies and optimizing traditional educational resources

The three dimensions—universities, enterprises, and governments—work together, and constitute an important support force for the current depth of IPEIEE in universities.

First, in the process of integration, the relevant departments should practically adjust the teaching strategy and optimize the traditional educational resources with clear division of labor, which promotes the smooth development of employment and entrepreneurship guidance work in universities. In the process of innovation and creativity, the status of entrepreneurship and employment education is gradually raised by optimizing traditional educational resources, creating special course materials, and constructing our own curriculum, through which the link between professional education and innovation and entrepreneurship education is comprehensively strengthened.

Second, IPEIEE will be developed with the renewal of ideology and expansion of educational resources. Universities, as well as teachers, should make full use of the Internet information technology, combining it with the policy content and adding electronic teaching materials on the basis of traditional teaching materials, so as to ensure that the forms of applied undergraduate education are rich and diverse and, thus, that innovation and entrepreneurship education is effective.

5.3.3. Information Technology Means and Methods

• Build an all-media information service mechanism for students’ innovation and entrepreneurship

Through WeChat, microblogs, websites, and other media, information on innovation and entrepreneurship programs is released in a timely manner, media and colleges build a feedback system of information on innovation and entrepreneurship education, the tracking and investigation mechanism for innovation and entrepreneurship talent cultivation is constructed, and files of innovation and entrepreneurship education for current students and graduates are set up. The government, together with universities, should not only improve the continuous information service system and the information service platform for innovation and entrepreneurship of college students, but also provide services including real-time provision of information on national policies and market trends, docking of innovation and entrepreneurship projects, and intellectual property transactions. Government departments should promote local and industry associations to issue guidelines on entrepreneurship programs, combining regional needs and industry development, and guide university students to identify and to capture innovation and entrepreneurship opportunities and business opportunities.

2.

Create two environments for school–enterprise cooperation and innovation

First, the simulation of innovation and entrepreneurship scenarios is created for students. The effective implementation of the integration mechanism of innovation and entrepreneurship education and professional education requires the participation of enterprises and the support from the industry. The building of the on-campus and off-campus professional internship bases through school–enterprise cooperation will provide students with the simulated scenarios for enterprise innovation and entrepreneurship. The enterprise technical personnel can be hired to the school as part-time teachers who mentor the students in professional practice and innovation competitions.

Second, innovative environments are made available to the specialized teachers in universities. For example, the university formulates incentive policies to create conditions for teachers to go to the front line of production in enterprises for practical training of professional skills, the university selects a group of professional teachers with innovation and entrepreneurship awareness to carry out special training to create an innovation and entrepreneurship faculty with professional teachers as the main body, the university encourages professional teachers to participate in the practice of production skills development in enterprises to improve the innovation awareness and research skills of professional teachers, or the university provides scientific research incentives for professional teachers who participate in production technology transformation and technology development in enterprises.

3.

Strengthen the construction of full-time teachers with innovation and entrepreneurship capability in universities

Based on the principle of full-time focus and the combination of full-time and part-time, universities cultivate and select teachers for basic courses of innovation and entrepreneurship education and provide continuous on-job training and learning opportunities for teachers who are willing to join innovation and entrepreneurship education and have practical experience in it. Teachers with the necessary disciplinary background, academic background, and practical experience in innovation and entrepreneurship serve as teachers of professional courses, and undertake tasks such as the development of course clusters, development of learning modules, and assessment of learning outcomes for innovation and entrepreneurship. They concentrate on enhancing the autonomy and specialization of innovation and entrepreneurship education within universities at a professional level.

With the main line of integrating innovation and entrepreneurship education and professional education deeply, professional teachers in colleges and departments are attracted to engage actively in the teaching and practice of innovation and entrepreneurship education. Teachers, particularly those who have excelled in science and technology innovation and entrepreneurship, are incentivized through diverse avenues to infuse innovative and entrepreneurial perspectives, knowledge, and skills into specialized courses, so as to foster students’ capacity for in-depth learning and problem solving using a combination of “professional knowledge + innovative and entrepreneurial thinking”.

Universities should establish teacher training initiatives dedicated to innovation and entrepreneurship education, emphasizing the enhancement of educators’ awareness and proficiency in this domain as a pivotal component of their professional growth and development. It is also significant to broaden the vision of innovation and entrepreneurship teachers and cultivate their practical ability by establishing a system for full-time teachers to work on a temporary basis in enterprises.

6. Discussion

The utilization of game theory in educational management holds significant potential for advancing education system reform [73], optimizing resource allocation [74], and fostering the high-quality development of innovation and entrepreneurship education in universities [75]. It has been extensively employed to investigate stability strategies among multiple stakeholders [44,45,46]. Drawing on game theory, the IPEIEE constructs a dynamic evolutionary game model involving multiple stakeholders to unveil interactive relationships and behaviors among educational entities. This study demonstrates the application of an evolutionary game based on the principal–agent model to assess different regulatory modes of stakeholders, yielding favorable outcomes.

Existing research primarily addresses IPEIEE’s behavioral aspects and methods for promoting it; however, there remains a dearth in studies focusing on incentivizing policies to facilitate collaborative and sustainable advancement within Innovation and Entrepreneurship Education. This research framework offers a distinct advantage through its equilibrium-based regulatory strategies grounded in game theory. It encompasses not only simulative analyses pertaining to university-introduced incentive behaviors but also evaluates diverse strategy impacts on evolutionary game strategic stability. Our study places significant emphasis on ensuring comprehensive consideration for stability within control measures while establishing dynamic mechanisms. The ultimately chosen control method guarantees both effective incentivization as well as seamless implementation of a regulatory scheme—representing an optimal approach towards achieving sustainability in IPEIEE.

The findings of this study align with those of other researchers. In the current era driven by innovation, there has been a significant focus on the necessity and implementation of comprehensive education that integrates professional courses in universities with innovation and entrepreneurship training. These studies have established a robust theoretical basis for sustainable development in IPEIEE research and have exerted substantial influence on subsequent investigations [76]. Furthermore, they suggest the need for further exploration to advance institutional innovation within IPEI-EE, establish relevant incentive mechanisms, and enhance the significance of IPEIEE in universities to effectively contribute to its sustainable development. Additionally, this paper places greater emphasis on the Socio-Ecosystem Framework for sustainable development in IPEIEE, which constitutes the core focus of this study. This is primarily because integrating the framework facilitates illustrating interactions among core subsystems. Accordingly, stakeholders are categorized into universities, teachers, and students based on system interactions and outcomes influenced by direct causality as well as feedback from core subsystems. Aligned with their respective objectives, strategies and behaviors for the “IPEIEE” teaching model are formulated among them, thereby impacting the social-ecological system’s effectiveness and efficiency.

7. Conclusions

This paper establishes a dynamic game model involving universities, teachers, and students. It analyzes the problems of the imperfect mechanism of IPEIEE in universities, the insufficient motivation of teachers, and the lack of enthusiasm of students. Through theoretical analysis, it is determined that the economic incentives and management incentives should be in parallel in the development stage of IPEIEE. In order to realize the collaborative and sustainable development of IPEIEE, teachers and students must be motivated at the same time so that the system can reach the Pareto-optimal equilibrium as soon as possible. In addition, this paper also studied the problem about how to incentivize by constructing the ideal incentive model and applying the principal–agent theory. It is found that, under information symmetry, the optimal incentive is a “fixed incentive”, while in scenarios characterized by information asymmetry, the optimal incentive comprises a combination of “fixed incentive + variable incentive”. The key determinants influencing the optimal incentive model include the cost–effort coefficient (denoted as “b”), the degree of risk aversion (represented by “ρ”), the level of external uncertainty (captured by “σ²”), and the coefficient for integrated value transformation (referred to as “i”). The paper also points out that the determination of incentive intensity should cover multiple factors comprehensively, deriving both intrinsic and extrinsic values created by the integration of professional education and innovation and entrepreneurship education. Finally, the incentive approaches for different stakeholders are proposed according to the incentive influencing factors. The design for the comprehensive incentive mechanism is completed according to the incentive target, leading to the generation of the corresponding incentive policy.

This research helps teachers, students, and universities to obtain a better understanding of the problems and challenges in the integration of professional education and innovation and entrepreneurship education work. It provides references and suggestions for promoting the integration of professional education and innovation and entrepreneurship education so as to support the education department and universities to formulate relevant incentive measures and to promote the integration of the integration of professional education and innovation and entrepreneurship education in a better way.

This paper acknowledges certain limitations. To streamline the analysis of the multi-party game model, it focuses solely on the strategic choices of the three primary players involved. Consequently, the model may not offer a comprehensive representation of the entire multi-party game process. In fact, in the process of promoting development of the integration of professional education and innovation and entrepreneurship education, it is necessary to pay attention to the power of business organizations and the government. Future research should aim to incorporate a larger number of participants into the IPEIEE framework within the gaming model in order to explore the intricate interrelationships and influence mechanisms among them. The current qualitative analysis of incentive levels necessitates further study to quantify these incentives. These considerations will facilitate the provision of more realistic recommendations for stakeholders.