WO2021081685A1

WO2021081685A1 - Three-party evolutionary game analysis method for collaborative innovation among government, industry, and research

Info

Publication number: WO2021081685A1
Application number: PCT/CN2019/103476
Authority: WO
Inventors: 吴洁; 姚潇; 车晓静; 陈璐; 张俊婷; 梁郁
Original assignee: 江苏科技大学; 江苏科技大学海洋装备研究院
Priority date: 2019-10-31
Filing date: 2019-10-31
Publication date: 2021-05-06

Abstract

A three-party evolutionary game analysis method for collaborative innovation among the government, industry, and research, which comprises the following steps: (1) dividing all relevant cooperative innovation parameters of the government, enterprises, and universities into five categories, and providing a basic hypothesis of a cooperative innovation evolutionary game model of government, industry, and research; (2) establishing a payment matrix of a cooperative innovation game among government, industry, and research; (3) establishing a power replication system of the government, enterprises, and universities on the basis of the payment matrix of the cooperative innovation game among government, industry, and research; (4) according to evolutionary game theory, outputting a local equilibrium point of the three-party evolutionary game model; (5) discussing the stability of the equilibrium point in three cases and outputting an evolution stability point of each case; and (6) carrying out example analysis to find key factors that affect the collaborative innovation among government, industry, and research. Thus, evolutionary game behavior containing the three main parts of government, enterprises, and universities is achieved, and the impact of different factors on the evolution of a cooperative innovation relationship is addressed.

Description

A Tripartite Evolutionary Game Analysis Method for Collaborative Innovation of Government, Industry, University and Research

Technical field

The invention relates to the field of industry-university-research collaborative innovation and the computer field, in particular to a tripartite evolutionary game analysis method for government-industry-university-research collaborative innovation.

Background technique

As a brand-new organizational model for enhancing national and regional independent innovation capabilities, industry-university-research collaborative innovation has become a new trend of international scientific and technological innovation activities and a new focus of innovative theoretical research, which can realize the mutual coupling of all links from knowledge production to knowledge commercialization , Is the first choice to solve the problem that education, technology and economic and social development are not closely linked. However, domestic and foreign research on collaborative innovation of industry, university and research focuses on theoretical analysis and mechanism research, and has not built a tripartite game system based on the condition that the government, enterprises, and universities are the main players in the collaborative innovation game. Collaborative innovation cannot be simulated under different factors. Changes in relationships. Therefore, the construction of a tripartite evolutionary game analysis system for government, industry, university and research has important meanings in both theory and reality.

In recent years, domestic and foreign researchers have achieved certain results in collaborative innovation research, mainly based on the process and mechanism of collaborative innovation. On the basis of this research, many documents take universities and enterprises as the basic game main body of collaborative innovation, construct a collaborative innovation benefit game model from the perspective of mathematical models and carry out analysis and research, but only consider enterprises and universities, without taking into account the government. , And in fact the government is also the participant of collaborative innovation. In short, the existing research has a certain reference effect on the development of collaborative innovation, but there are still the following problems:

Most studies use enterprises and universities as the main players in collaborative innovation, but introduce government behaviors as exogenous variables into the game model, and do not use the government as the main actors to conduct game analysis with enterprises and universities; there is no collaborative innovation in government, industry, university, and research institutes. University-led research on the tripartite game model of collaborative innovation has not conducted a detailed analysis of the way the government participates in collaborative innovation. It often only considers financial support and ignores the more important policy support in reality that brings benefits to enterprises and universities. At the same time, the game between collaborative innovation entities does not consider the influence of willingness to participate on the choice of strategy. In this way, the efficiency of industry-university-research cooperation and innovation will be greatly reduced, which is not conducive to the development of industry-university-research cooperation.

Summary of the invention

The technical problem to be solved by the present invention is to provide a tripartite evolutionary game analysis method of government-industry-university-research collaborative innovation. By constructing an industry-university-research collaborative innovation game analysis system with tripartite participation, the initial participation willingness of participating subjects, government preferential policies, and penalties are provided. Simulation analysis is carried out on factors such as strength and benefit distribution coefficient, so as to obtain the influence of different factors on the evolution of collaborative innovation relationship.

In order to solve the above technical problems, the technical solution of the present invention is: a tripartite evolutionary game analysis method for collaborative innovation of government, industry, university and research. The innovation is that the analysis method is established in an evolutionary game analysis system and includes the following steps:

(1) According to the role positioning of the government, enterprises, and universities in collaborative innovation, and combining their interest relationships, give the basic assumptions of the tripartite evolutionary game model of government-industry-university-research collaborative innovation. The basic assumptions include participation 5 categories: subject, cooperation strategy, cooperation cost, cooperation benefit and punishment;

(2) Aiming at the interests of the three main bodies of the government, enterprises, and universities, establish a payment matrix of a tripartite evolutionary game model of government-industry-university-research collaborative innovation that satisfies various basic assumptions and constraints, and all variables contained in the payment matrix are determined by all The composition of all the variables involved in the basic hypothesis; according to whether the government participates in industry-university-research collaborative innovation, design two scenarios of game payment matrix for industry-university-research collaborative innovation, the game payment matrix includes the evolutionary game of industry-university-research collaborative innovation under government participation Payment matrix and the government does not participate in the evolutionary game payment matrix of collaborative innovation of industry, university and research;

(3) Based on the payment matrix of the government-industry-university-research collaborative innovation game, establish the replication power system of the government, enterprises and universities. The replication power system includes the government's average income expectation function and replication dynamic equation, and the enterprise's average income expectation function and replication Dynamic equations as well as the expectation function of average income of universities and copy dynamic equations;

(4) According to the evolutionary game theory, output the local equilibrium point of the three-party evolutionary game model;

(5) Discuss the stability of the equilibrium point in three cases, and output the evolutionary stable point of each case; the three cases are as follows:

a. The sum of the penalties paid to universities by enterprises for independent research and development and the funds given to universities by the government is less than the cost of collaborative innovation paid by universities when the government participates in collaborative innovation, and the penalty paid by universities for independent research and development is less than that for enterprises in the government. The cost paid when participating in collaborative innovation;

b. The punishment that enterprises pay to universities for independent research and development is greater than the cost of collaborative innovation that universities pay when the government does not participate in collaborative innovation; or the penalty that universities pay to enterprises for independent research and development is greater than that paid by enterprises when the government does not participate in collaborative innovation cost;

c. The sum of the penalties paid to universities by enterprises for independent research and development and the funds given by the government to universities is greater than the cost of collaborative innovation paid by universities when the government participates in collaborative innovation, and the penalty paid for universities by enterprises for independent research and development is less than that paid by universities in the government The cost of collaborative innovation when not participating in collaborative innovation, or the penalty paid by universities for independent research and development to enterprises is greater than the cost paid by enterprises when the government participates in collaborative innovation, and the penalty paid by universities for independent research and development is less than that for enterprises in government The cost paid when not participating in collaborative innovation;

(6) Introduce a variety of factors into the evolutionary game analysis system, and find out the key factors affecting the collaborative innovation of government, industry, university, and research.

Further, in the step (3), based on the payment matrix of the government-industry-university-research collaborative innovation game, the specific steps for establishing a replication power system for governments, enterprises, and universities are as follows:

Step 3.1, according to the payment matrix, establish the expected income function of the government, enterprises and universities under different participation conditions, so as to establish the average expected function of the three parties;

Step 3.2, derivate the revenue expectation functions of the government, enterprises, and universities to obtain the three-party replication dynamic equation, and then combine the three equations to obtain the replication dynamic system of the government, enterprises, and universities.

Further, the process of outputting the local equilibrium point of the tripartite evolutionary game model in the step (4) is as follows:

Step 4.1: Obtain the Jacobian matrix of the system from the replication power system of the government, enterprises and universities;

Step 4.2: Solve the three equations in the replication power system of the government, enterprise, and university to be equal to 0 to obtain the local equilibrium point of the system.

Further, in the step (5), the stability of the equilibrium point is discussed in three cases, and the process of outputting the evolutionary stable point of each case is as follows:

Step 5.1: Obtain the Jacobian matrix of the system according to the replication power system of the government, enterprise and university, and substitute the local equilibrium points into the Jacobian matrix to obtain the eigenvalues of the Jacobian matrix corresponding to the equilibrium points respectively;

Step 5.2: According to the evolutionary game theory, output the symbols of all the eigenvalues in the Jacobian matrix in the three situations respectively as non-timing equilibrium points.

Further, in the step (6), a variety of factors are introduced into the evolutionary game analysis system, and the specific process of finding the key factors affecting the collaborative innovation of government, industry, university and research is as follows:

Step 6.1, assign values to each variable in the model according to the meaning of the variables, and substitute them into the evolutionary game model of the government, enterprises and universities;

Step 6.2, change the parameter values of the participation willingness of the government, enterprises and universities in the evolutionary game model, and substitute the changed parameter values into the replication dynamic equation to analyze the influence of the participation willingness on the evolution result of the model;

Step 6.3: Change the parameter values of government policy support and financial support in the evolutionary game model, and substitute the changed parameter values into the replication dynamic equation to analyze the influence of government policy support and financial support on the evolution of the model;

Step 6.4, change the parameter value of the penalty intensity in the evolutionary game model, and substitute the changed parameter value into the replication dynamic equation to analyze the influence of the penalty intensity on the evolution result of the model;

Step 6.5, change the parameter value of the income distribution coefficient in the evolutionary game model, and substitute the changed parameter value into the replication dynamic equation to analyze the influence of the income distribution coefficient on the evolution result of the model.

The advantages of the present invention are:

(1) The three-party evolutionary game analysis method for collaborative innovation of government, industry, university and research in the present invention, through ingenious calculation process and example analysis, adds the government to the game of industry, university and research collaborative innovation, taking into account the impact of government funding and policy support on collaborative innovation , To realize the evolutionary game behavior including the three main bodies of government, enterprises and universities, and regard universities as the leader of collaborative innovation and enterprises as participants in collaborative innovation, and solve the influence of different factors on the evolution of collaborative innovation relationships;

(2) The three-party evolutionary game analysis method for collaborative innovation of government, industry, university, and research of the present invention realizes that the government, enterprises, and universities jointly play a game for collaborative innovation, so that the coverage of collaborative innovation actors is more comprehensive and the research on collaborative innovation mechanism is more reasonable; and Compared with the collaborative innovation game behavior that originally only included the two entities of enterprises and universities, the three-party evolutionary game is more reasonable, applicable and in line with the reality;

(3) The tripartite evolutionary game analysis method of the collaborative innovation of government, industry, university and research of the present invention can also find out the key factors affecting the collaborative innovation of government, industry, university and research, and provide more constructive opinions for the sustainable development of subsequent industry, university and research collaborative innovation; in addition, this This idea of implementing a tripartite evolutionary game analysis system for collaborative innovation of government, industry, university, and research can also be used for reference in other similar management issues.

Description of the drawings

The present invention will be further described in detail below in conjunction with the drawings and specific embodiments.

FIG. 1 is a flowchart of a tripartite evolutionary game analysis method for collaborative innovation of government, industry, university and research provided by an embodiment of the present invention.

Figure 2 is the evolutionary result of simultaneous changes in the participation willingness of the government, enterprises, and universities.

Figure 3 shows the evolutionary result of changes in government participation willingness.

Figure 4 shows the evolutionary result of changes in the willingness of enterprises to participate.

Figure 5 is the evolutionary result of changes in the willingness to participate in colleges and universities.

Figure 6 is the evolutionary result of simultaneous changes in the willingness of enterprises and universities to participate.

Figure 7 shows the evolutionary result of unchanged government participation willingness.

Figure 8 is the evolutionary result of changes in government policy support.

Figure 9 shows the evolutionary result of changes in government funding support.

Figure 10 is the evolutionary result of changes in the corporate default penalty.

Figure 11 is the evolutionary result of changes in the penalties for breach of contract in colleges and universities.

Figure 12 and Figure 13 are the evolutionary results of the change in the income distribution coefficient.

Detailed ways

The following embodiments can enable those skilled in the art to understand the present invention more comprehensively, but they do not limit the present invention to the scope of the described embodiments.

Example 1

The tripartite evolutionary game analysis method of government-industry-university-research collaborative innovation in this embodiment is established in the evolutionary game analysis system, as shown in Figure 1, and includes the following steps:

(1) According to the role positioning of the government, enterprises, and universities in collaborative innovation, and combining their interest relationships, give the basic assumptions of the tripartite evolutionary game model of government-industry-university-research collaborative innovation. The basic assumptions include participation There are 5 categories of subject, cooperation strategy, cooperation cost, cooperation benefit and punishment, as follows:

a. Participants. In the process of collaborative innovation of government, industry, university and research, there are three types of participants: government, universities and enterprises. The government mainly provides different incentives and supervision mechanisms for enterprises and universities to promote collaborative innovation cooperation between enterprises and universities; It is mainly responsible for providing collaborative innovation resources and the transformation of collaborative innovation results; universities are mainly responsible for the output of collaborative innovation knowledge, technology and talents, and the three parties are bounded in the game process to find the optimal strategy through multiple games;

b. Cooperative strategy. In the process of the collaborative innovation game of government, industry, university and research, the government's strategy set is (participate, not participate), and the strategy set of universities and enterprises is (cooperation, non-cooperation);

c. The cost of cooperation. The cost of the government is reflected in the formulation of preferential policies for collaborative innovation and the supervision of the collaborative innovation process of enterprises and universities; the cost of enterprises and universities is reflected in the human, material and financial resources invested in the process of collaborative innovation. When the government chooses to participate in collaboration When innovating, the preferential policies provided by the government will reduce the total cost invested by enterprises and universities in the process of collaborative innovation;

d. Cooperation income. The income when the government chooses the "participation" strategy is reflected in the tax income of sales income generated by the research and development of new products. The income of enterprises and universities is reflected in the initial income before collaborative innovation and the additional income generated by collaborative innovation. Additional income It is shared by enterprises and universities, and a part of the income of universities comes from the government's financial support;

e. Punishment. When a company chooses to conduct collaborative innovation and a university chooses not to conduct collaborative innovation, the university needs to pay a certain penalty to the company. Similarly, when a university chooses to conduct collaborative innovation but the company chooses not to conduct collaborative innovation, the company needs to pay a certain penalty to the university ；

The composition of all variables involved in the basic hypothesis is as follows:

G——Government

S——University

E——Enterprise

G ₁ -the total cost of government participation in collaborative innovation

C——The total cost of enterprises and universities participating in collaborative innovation;

J-The preferential policies provided by the government reduce the total cost of enterprises and universities in the process of collaborative innovation

t——The cost-sharing ratio coefficient of enterprises and universities

R ₁ ——The government's benefits when it chooses the "participation" strategy

b——The proportion of the government's income from choosing the "non-participation" strategy to the government's income from choosing the "participation" strategy

R ₂ —— indicates the initial income of the enterprise before collaborative innovation

R ₃ —— indicates the initial income of universities before collaborative innovation

R-The additional benefits that companies and universities bring to companies and universities when both companies and universities choose collaborative innovation

a——The apportionment ratio coefficient of the additional income

L ₁ ——The income obtained by the company's independent research and development

L ₂ ——Benefits from independent research and development of universities

G ₂ ——The government's financial support for universities that actively participate in collaborative innovation

W-Punishment paid to enterprises when colleges and universities breach the contract

K-the punishment paid to the enterprise when the enterprise breaches the contract

x-The government's willingness to choose to participate in collaborative innovation

y——The willingness of enterprises to choose to conduct collaborative innovation

z——The willingness of universities to choose collaborative innovation

(2) Aiming at the interests of the three main bodies of government, enterprises and universities, establish a payment matrix of a tripartite evolutionary game model of government-industry-university-research collaborative innovation that satisfies various basic assumptions and constraints. According to whether the government participates in industry-university-research collaborative innovation, Design two scenarios of game payment matrix for industry-university-research collaborative innovation, including:

The evolutionary game payment matrix of the collaborative innovation of industry, university and research institute under government participation, as shown in Table 1;

Table 1 The payment matrix of the cooperative innovation game of industry, university and research institute under government participation

The government does not participate in the evolutionary game payment matrix of the collaborative innovation of industry, university and research institute, as shown in Table 2;

Table 2 The payment matrix of the cooperative innovation game between industry, university and research institute without government participation

(3) Based on the payment matrix of the collaborative innovation game of government, industry, university and research, establish a replication power system for governments, enterprises and universities;

Step 3.1, according to the payment matrix, establish the expected income function of the government, enterprises and universities under different participation conditions, so as to establish the average expected function of the three parties, including:

When the government chooses the "participation" strategy in the game, the expected benefits are:

U _g1 =yz(R ₁ -G ₁ -G ₂ )+y(1-z)(R ₁ -G ₁ )+(1-y)z(R ₁ -G ₁ -G ₂ )+(1-y )(1-z)(R ₁ -G ₁ )

When the government chooses the "not participating" strategy in the game, the expected benefits are:

U _g2 =yzbR ₁ +y(1-z)bR ₁ +(1-y)zbR ₁ +(1-y)(1-z)bR ₁

The average expected return of the government in the game is:

The expected benefits of enterprises choosing the "coordination" strategy in the game are:

U _e1 = zx[R ₂ +aR-t(CJ)]+(1-z)x[R ₂ -t(CJ)+W]+z(1-x)(R ₂ +aR-tC)+( 1-z)(1-x)(R ₂ -tC+W)

The expected benefits of the “non-coordination” strategy that the enterprise chooses in the game are:

U _e2 = zx(R ₂ +L ₁ -K)+(1-z)xR ₂ +z(1-x)(R ₂ -K+L ₁ )+(1-z)(1-x)R ₂

The average expected return of the enterprise in the game is:

The expected benefits of colleges and universities choosing the "coordinated" strategy in the game are:

U _s1 =xy[R ₃ +(1-a)R-(1-t)(CJ)+G ₂ ]+x(1-y)[R ₃ -(1-t)(CJ)+K+G ₂ ]+(1-x)y[R ₃ +(1-a)R-(1-t)C]+(1-x)(1-y)(R ₃ -(1-t)C+K )

The expected benefits of colleges and universities choosing the "non-coordination" strategy in the game are:

U _s2 =xy(R ₃ -W+L ₂ )+x(1-y)R ₃ +(1-x)y(R ₃ -W+L ₂ )+(1-x)(1-y)R ₃

The average expected return of colleges and universities in the game is:

Step 3.2: Derivate the revenue expectation functions of the government, enterprises, and universities to obtain the three-party replication dynamic equation, and then combine the three equations to obtain the replication dynamic system of the government, enterprises, and universities, including:

The government’s dynamic equation for replication is:

The dynamic equation of enterprise replication is:

The dynamic equation for copying in universities is:

The replication power system of governments, enterprises and universities is:

(4) According to the evolutionary game theory, output the local equilibrium points of the three-party evolutionary game model: E ₁ (0,0,0), E ₂ (0,0,1), E ₃ (0,1,0), E ₄ (0,1,1), E ₅ (1,0,0), E ₆ (1,0,1), E ₇ (1,1,0), E ₈ (1,1,1);

Step 5.1, according to the copying power system of the government, enterprises and universities, the Jacobian matrix of the system is obtained as:

Step 5.2: Substituting the 8 equilibrium points into the Jacobian matrix respectively, and the eigenvalues of the Jacobian matrix corresponding to the equilibrium points can be obtained as shown in Table 3;

Table 3 Eigenvalues of Jacobian matrix

Step 5.3, according to the evolutionary game theory, the signs of all eigenvalues in the Jacobian matrix in the three situations are shown in Table 4, and the evolutionary stable points in the three situations are output respectively;

Table 4 Local stability of equilibrium points (cases 1, 2, 3)

According to the equilibrium point that satisfies that all the eigenvalues of the Jacobian matrix are non-timing, the evolutionary stability point (ESS) of the system is obtained, and the evolutionary stability point in each case is obtained, which specifically includes:

In case 1, the system has two stable points (1,0,0) and (1,1,1), and the corresponding evolution strategy is (participation, non-cooperation, non-cooperation) and (participation, cooperation, coordination);

In case 2, the system has a stable point (1, 1, 1), and its corresponding evolution strategy is (participation, collaboration, collaboration);

In case 3, the system has a stable point (1, 1, 1), and its corresponding evolution strategy is (participation, collaboration, collaboration);

Example 2

This example is an example of the influence of initial willingness on the evolution of collaborative innovation relationships. Based on the actual situation of the collaborative innovation center of universities in Jiangsu Province, the tripartite evolutionary game method is used to study the mechanism of collaborative innovation of government, industry, university and research. The collaborative innovation center of Jiangsu Province mainly relies on universities and extensively Collaborate with enterprises to carry out collaborative innovation. The relevant government departments set up special funds for collaborative innovation plans for collaborative innovation centers and other preferential policies to reduce the cost of collaborative innovation, so as to guide enterprises and universities to participate in collaborative innovation centers; in the process of collaborative innovation, collaboration Enterprises and universities in the innovation center also have to bear certain penalties for their breach of contract to constrain the behavior of enterprises and universities. The initial parameters of the entire model are shown in Table 5.

Table 5 Table of initial values of variables included in the model

变量variable	变量初始值Variable initial value
R ₁ R ₁	40百万元40 million yuan

G ₁ G ₁	5百万元5 million yuan
bb	0.50.5
CC	45百万元45 million yuan
tt	0.50.5
RR	100百万元100 million yuan
aa	0.50.5
L ₁ L ₁	25百万元25 million yuan
L ₂ L ₂	30百万元30 million yuan

WW	5百万元5 million yuan

KK	5百万元5 million yuan
xx	0.50.5
yy	0.50.5
zz	0.50.5

Through the above analysis and the setting of the initial value, this paper uses Matlab software to simulate the dynamic evolution process of the government, enterprise and university's strategy selection under different initial states. According to the simulation analysis results, the participants’ initial willingness to participate will be discussed. The specific process as follows:

①With other parameters unchanged, the simulation of the influence of the initial willingness of the government, enterprises and universities to participate in collaborative innovation on the collaborative innovation strategy is analyzed. The results show that the critical value of the initial willingness of the three parties is between 0.4-0.5. When x, y, z are all less than the critical value, x converges to 1, y, z converges to 0, and the final equilibrium point tends to (1,0,0); when the initial willingness x, y, z are all greater than the critical value When, x, y, z all converge to 1, the final equilibrium point tends to (1,1,1), the specific results are shown in Figure 2;

②Under the condition that other parameters remain unchanged, the simulation of the influence of changes in the government's initial participation willingness on the participation of universities and enterprises in collaborative innovation strategies is analyzed. The results show that the initial willingness of enterprises and universities to participate in y, z is in a medium state, and the government's initial willingness to participate x The critical value of is between 0.3-0.4. When x is less than the critical value, y, z converges to 0, and the final equilibrium point converges to (1,0,0). At this time, the increase of x makes the convergence speed of y, z Slow down, and the convergence rate of z is less than y; when x is greater than the critical value, y, z converge to 1, and the final equilibrium point converges to (1,1,1). The specific results are shown in Figure 3;

③Under the condition that other parameters remain unchanged, the simulation of the influence of the change of the initial participation willingness of the enterprise on the government and enterprises participating in the collaborative innovation strategy is analyzed, and the result shows that the initial willingness x and z of the government and universities to participate are in a medium state, and the initial participation willingness of the enterprise y The critical value of is between 0.4-0.5. When y is less than the critical value, x converges to 1, y, z converges to 0, and the final equilibrium point tends to (1,0,0). At this time, the increase in y makes z When y is greater than the critical value, x converges to 1, y, z converges to 1, and the final equilibrium point tends to (1,1,1). The specific results are shown in Figure 4;

④Under the condition that other parameters remain unchanged, analyze the simulation of the influence of the change of the initial participation willingness of universities on the government and enterprises to participate in the collaborative innovation strategy. The initial willingness x and y of the government and enterprises to participate are in a medium state, and the initial willingness to participate z of the universities is critical. The value is between 0.4-0.5. When z is less than the critical value, x converges to 1, y, z converges to 0, and the final equilibrium point converges to (1,0,0). At this time, the increase in z makes y converge The speed slows down, and the convergence speed of enterprises is significantly higher than that of universities; when z is greater than the critical value, x converges to 1, y, z converges to 1, and the final equilibrium point tends to (1,1,1). The specific results are shown in the figure 5;

⑤Under the condition that other parameters remain unchanged, analyze the simulation of the impact on the collaborative innovation strategy when the initial willingness of enterprises and universities to participate is very high and the initial willingness of the government to participate is very low. The results show that when the initial willingness of government x is very low, y , Z will converge to 1, that is, enterprises and universities will eventually choose to participate in collaborative innovation; when the initial willingness of enterprises and universities to participate in y and z are both low, even when the government's initial willingness to participate x is high, y and z will both converge to 0, that is, enterprises and universities will eventually choose not to participate in collaborative innovation. Moreover, it can be seen from the figure that when companies and universities choose not to participate in collaborative innovation, the speed of y converging to 0 is significantly higher than that of z, and x will quickly converge to 1. The specific results are shown in Figure 6.

⑥Under the circumstance that other parameters remain unchanged, analyze the simulation of the impact on the collaborative innovation strategy when the initial willingness to participate in the government is high and the initial willingness to participate in the enterprise is low when the initial willingness to participate in the government remains unchanged. The results show that the government, The initial willingness to participate x, y, and z of enterprises and universities will converge to 1. At this time, the willingness to participate in universities will first decrease slightly, but the increase in willingness of enterprises to participate is significantly higher than the rate of decrease in universities. When the willingness rises to a certain value, the willingness of universities to participate will also increase, making universities and enterprises ultimately choose to participate in collaborative innovation; and when the initial willingness to participate y of the enterprise is high, and the initial willingness to participate in the university z is very low, y, z Both converge to 0. At this time, the willingness of universities to participate will increase, and the willingness of enterprises to participate will decrease, and the rate of decrease of enterprises’ willingness to participate is significantly higher than the rate of increase of universities, making universities and enterprises ultimately choose not to innovate in collaboration. Figure 7.

Example 3

This embodiment is an embodiment of the influence of government policy support and financial support on the evolution of the collaborative innovation relationship.

By setting the initial values in Table 5, this paper uses Matlab software to simulate the dynamic evolution process of the government, enterprises, and universities under different initial states of their strategy selection. According to the simulation analysis results, the government’s preferential policies are discussed. The specific process is as follows:

① Under the condition that other parameters remain unchanged, the simulation of the impact of changes in the cost reduction of collaborative innovation brought about by the government's policy support for collaborative innovation on the participation of universities and enterprises in collaborative innovation strategies is analyzed, and the results show that the criticality of the cost reduction J The value is between 6-7. When J is less than the critical value, y, z converges to 0, and the final equilibrium point tends to (1,0,0); when J is greater than the critical value, y, z converges to 1. , The final equilibrium point tends to (1,1,1), the specific results are shown in Figure 8;

②Under the condition that other parameters remain unchanged, the simulation of the impact of changes in government funding subsidies to universities on the participation of universities and enterprises in collaborative innovation strategies is analyzed. The results show that _{the critical value of funding subsidies G 2} is between 6-8, when G _{2 is} less than At this critical value, y, z converges to 0, and the final equilibrium point tends to (1,0,0); when G _{2 is} greater than the critical value, y, z converges to 1, and the final equilibrium point tends to (1,1 ,1), the specific results are shown in Figure 9.

Example 4

This embodiment is an embodiment of the influence of punishment intensity on the evolution of the collaborative innovation relationship.

By setting the initial values in Table 5, this paper uses Matlab software to simulate the dynamic evolution process of the government, enterprises, and universities in their strategic choices under different initial states. According to the simulation analysis results, the punishment intensity is discussed. The specific process is as follows:

①With other parameters unchanged, analyze the simulation of the impact of changes in default penalties paid by companies to universities on the participation of universities and companies in collaborative innovation strategies. The results show that the critical value of default penalty K is between 5-6, when K is less than the critical value Value, y, z converges to 0, and the final equilibrium point tends to (1,0,0); when K is greater than the critical value, y, z converges to 1, and the final equilibrium point tends to (1,1,1) , The specific results are shown in Figure 10;

②Under the condition that other parameters remain unchanged, analyze the simulation of the impact of changes in default penalty paid by universities to companies on the participation of universities and companies in collaborative innovation strategies. The results show that the critical value of default penalty W is between 5-6, when W is less than this value. At the critical value, y, z converges to 0, and the final equilibrium point tends to (1,0,0); when W is greater than the critical value, y, z converges to 1, and the final equilibrium point tends to (1,1,1 ), the specific results are shown in Figure 11.

Example 5

This embodiment is an embodiment of the influence of the income distribution coefficient on the evolution of the collaborative innovation relationship.

By setting the initial values in Table 5, this paper uses Matlab software to simulate the dynamic evolution process of the government, enterprises, and universities in their strategic choices under different initial states. According to the simulation analysis results, the income distribution coefficient is discussed. The specific process is as follows:

① Under the condition that other parameters remain unchanged, analyze the simulation of the impact on joint development of new product strategies when the collaborative innovation income distribution coefficient of enterprises and universities is less than 0.5. The results show that when the cost remains unchanged and the cost allocation coefficient is 0.5, then The critical value of the income distribution coefficient a is 0.46-0.47. When the income distribution coefficient a is less than 0.46-0.47, y and z converge to 0. In the end, both enterprises and universities choose not to innovate collaboratively. The specific results are shown in Figure 12.

②Under the condition that other parameters remain unchanged, analyze the simulation of the impact on the joint development of new product strategy when the collaborative innovation income distribution coefficient of enterprises and universities is greater than 0.5. The results show that when the cost remains unchanged and the cost allocation coefficient is 0.5, then The critical value of the income distribution coefficient a is 0.55-0.56. When the income distribution coefficient a is greater than 0.55-0.56, y and z converge to 0. In the end, both enterprises and universities choose not to innovate collaboratively. The specific results are shown in Figure 13.

In summary, the present invention provides a tripartite evolutionary game analysis system for collaborative innovation of government, industry, university, and research. By constructing a game analysis system for industry-university-research collaborative innovation with tripartite participation, the initial participation willingness of participating entities, government preferential policies, The penalty intensity and benefit distribution coefficient are simulated and analyzed, so as to obtain the influence of different factors on the evolution of the collaborative innovation relationship.

A person of ordinary skill in the art can also understand that all or part of the steps in the method of the foregoing embodiments can be implemented by a program instructing relevant hardware. The program can be stored in a computer readable storage medium. Storage media, including ROM/RAM, magnetic disks, optical disks, etc.

The basic principles and main features of the present invention and the advantages of the present invention have been shown and described above. Those skilled in the industry should understand that the present invention is not limited by the above-mentioned embodiments. The above-mentioned embodiments and descriptions only illustrate the principles of the present invention. Without departing from the spirit and scope of the present invention, the present invention may have Various changes and improvements fall within the scope of the claimed invention. The scope of protection claimed by the present invention is defined by the appended claims and their equivalents.

Claims

A tripartite evolutionary game analysis method for government-industry-university-research collaborative innovation is characterized in that: the analysis method is established in an evolutionary game analysis system, and includes the following steps:

(1) According to the role positioning of the government, enterprises, and universities in collaborative innovation, and combining their interest relationships, give the basic assumptions of the tripartite evolutionary game model of government-industry-university-research collaborative innovation. The basic assumptions include participation 5 categories: subject, cooperation strategy, cooperation cost, cooperation benefit and punishment;

(2) Aiming at the interests of the three main bodies of the government, enterprises, and universities, establish a payment matrix of a tripartite evolutionary game model of government-industry-university-research collaborative innovation that satisfies various basic assumptions and constraints, and all variables contained in the payment matrix are determined by all The composition of all variables involved in the basic hypothesis; according to whether the government participates in industry-university-research collaborative innovation, design two scenarios of industry-university-research collaborative innovation game payment matrix, the game payment matrix includes the government participation in industry-university-research collaborative innovation evolutionary game Payment matrix and the government does not participate in the evolutionary game payment matrix of collaborative innovation of industry, university and research;

(3) Based on the payment matrix of the government-industry-university-research collaborative innovation game, establish the replication power system of the government, enterprises and universities. The replication power system includes the government's average income expectation function and replication dynamic equation, and the enterprise's average income expectation function and replication Dynamic equations as well as the expectation function of average income of universities and copy dynamic equations;

(4) According to the evolutionary game theory, output the local equilibrium point of the three-party evolutionary game model;

(5) Discuss the stability of the equilibrium point in three cases, and output the evolutionary stable point of each case; the three cases are as follows:

a. The sum of the penalties paid to universities by enterprises for independent research and development and the funds given to universities by the government is less than the cost of collaborative innovation paid by universities when the government participates in collaborative innovation, and the penalty paid by universities for independent research and development is less than that for enterprises in the government. The cost paid when participating in collaborative innovation;

b. The punishment that enterprises pay to universities for independent research and development is greater than the cost of collaborative innovation that universities pay when the government does not participate in collaborative innovation; or the penalty that universities pay to enterprises for independent research and development is greater than that paid by enterprises when the government does not participate in collaborative innovation cost;

c. The sum of the penalties paid to universities by enterprises for independent research and development and the funds given by the government to universities is greater than the cost of collaborative innovation paid by universities when the government participates in collaborative innovation, and the penalty paid for universities by enterprises for independent research and development is less than that paid by universities in the government The cost of collaborative innovation when not participating in collaborative innovation, or the penalty paid by universities for independent research and development to enterprises is greater than the cost paid by enterprises when the government participates in collaborative innovation, and the penalty paid by universities for independent research and development is less than that for enterprises in government The cost paid when not participating in collaborative innovation;

(6) Introduce a variety of factors into the evolutionary game analysis system, and find out the key factors affecting the collaborative innovation of government, industry, university, and research.
The tripartite evolutionary game analysis method of government-industry-university-research collaborative innovation according to claim 1, characterized in that: the step (3) is based on the payment matrix of the government-industry-university-research collaborative innovation game to establish a replication power system for governments, enterprises, and universities Specific steps are as follows:

Step 3.1, according to the payment matrix, establish the expected income function of the government, enterprises and universities under different participation conditions, so as to establish the average expected function of the three parties;

Step 3.2: Derivate the revenue expectation functions of the government, enterprises, and universities to obtain the three-party replication dynamic equation, and then combine the three equations to obtain the replication dynamic system of the government, enterprises, and universities.
The tripartite evolutionary game analysis method of government-industry-university-research collaborative innovation according to claim 1, wherein the process of outputting the local equilibrium point of the tripartite evolutionary game model in the step (4) is as follows:

Step 4.1: Obtain the Jacobian matrix of the system from the replication power system of the government, enterprises and universities;

Step 4.2: Solve the three equations in the replication power system of the government, enterprise, and university to be equal to 0 to obtain the local equilibrium point of the system.
The tripartite evolutionary game analysis method of government-industry-university-research collaborative innovation according to claim 3, characterized in that: in the step (5), the stability of the equilibrium point is discussed in three situations, and the process of outputting the evolutionary stable point of each situation as follows:

Step 5.1: Obtain the Jacobian matrix of the system according to the replication power system of the government, enterprise and university, and substitute the local equilibrium points into the Jacobian matrix to obtain the eigenvalues of the Jacobian matrix corresponding to the equilibrium points respectively;

Step 5.2: According to the evolutionary game theory, output the symbols of all the eigenvalues in the Jacobian matrix in the three situations respectively as non-timing equilibrium points.
The tripartite evolutionary game analysis method for collaborative innovation of government, industry, university and research according to claim 1, characterized in that: in the step (6), multiple factors are introduced into the evolutionary game analysis system to find out the key to the collaborative innovation of government, industry, university, and research The specific process of the factors is as follows:

Step 6.1, assign values to each variable in the model according to the meaning of the variables, and substitute them into the evolutionary game model of the government, enterprises and universities;

Step 6.2, change the parameter values of the participation willingness of the government, enterprises and universities in the evolutionary game model, and substitute the changed parameter values into the replication dynamic equation to analyze the influence of the participation willingness on the evolution result of the model;

Step 6.3: Change the parameter values of government policy support and financial support in the evolutionary game model, and substitute the changed parameter values into the replication dynamic equation to analyze the influence of government policy support and financial support on the evolution of the model;

Step 6.4, change the parameter value of the penalty intensity in the evolutionary game model, and substitute the changed parameter value into the replication dynamic equation to analyze the influence of the penalty intensity on the evolution result of the model;

Step 6.5, change the parameter value of the income distribution coefficient in the evolutionary game model, and substitute the changed parameter value into the replication dynamic equation to analyze the influence of the income distribution coefficient on the evolution result of the model.