Research ArticleStudy on Evolutionary Path of University StudentsโEntrepreneurship Training
Daojian Yang and Xicang Zhao
School of Management, Jiangsu University, Zhenjiang, Jiangsu Province 212013, China
Correspondence should be addressed to Daojian Yang; [email protected]
Received 15 February 2014; Accepted 21 April 2014; Published 22 May 2014
Academic Editor: Jianguo Du
Copyright ยฉ 2014 D. Yang and X. Zhao.This is an open access article distributed under the Creative CommonsAttribution License,which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
Aiming at studying the evolution pattern of cultivating the ability of university studentsโ entrepreneurship, this paper establishedthe payoffmatrix between the university and students agent with the evolutionary economics method.The analysis of the evolutionof the communication process model reveals how the choice strategy of individuals influences that of groups. Numerical simulationalso demonstrates the influences of different values of decision-making parameters and the change of initial conditions on the resultof evolution. It is found that the evolution path system of university studentsโ entrepreneurial ability has two kinds of modes: oneis the ideal state; and the other one is the bad โlockโ state. By adjusting parameters, we can jump out of the bad โlockโ state, thusoptimizing cultivation path.
1. Introduction
It has become a necessity for universities to cultivate studentsโentrepreneurial ability to adapt to the economic transfor-mation and upgrading, as well as to the construction anddevelopment of entrepreneurial economy. It is also importantto improve the education system in colleges and universities,strengthening the innovation training of entrepreneurialtalent. With this progress, promoting the overall develop-ment of people and cultivating entrepreneurial qualities ofa new generation can be achieved. Gorman et al. analyzedthe literature about entrepreneurship education in the 10years from 1985 to 1994 and point out that the cultivationof entrepreneurship for college students plays the func-tion of entrepreneurship preparation and can enhance theindividualโs self-efficacy. During this process, universitiesshould focus on the improvement of studentsโ entrepreneurialqualities and skills [1]. Fayolle discussed the concept ofentrepreneurial education and its theoretical framework, thepioneering education paradigm, entrepreneurship educationmode, education assessment, target, function, interdisci-plinary approach, and so forth, putting forward the innova-tive teaching mode to enhance the level of entrepreneurship[2]. OโConnor believes that entrepreneurial talent training isan effective mean of promoting economic development [3].
Research on college studentsโ entrepreneurial abilitytraining was mainly concentrated on the content ofentrepreneurship education and entrepreneurial ability train-ing mode. For entrepreneurial education content, Harrisonand Leitchโs research โEntrepreneurship and Leadership: edu-cation and enlightenmentโ has paved the way for the researchon entrepreneurship education content [4]. Jack and Ander-son find that entrepreneurship education activity involves theareas of science and art, which need to research entrepreneur-ship education theory to connect the gap between scienceand art [5]. Fiet studied the theoretical dimension of teachingentrepreneurship, emphasizing that more attention shouldbe paid to the teaching of entrepreneurship theory [6].Kent and Anderson argue that the spirit of cooperation,social ability, and pioneering consciousness should be putinto the training content of entrepreneurship education [7];some other scholars suggest โbusiness failureโ as one part ofentrepreneurial education [8]. Sudharson et al. tried to wakeup all engineering studentsโ entrepreneurial ideas and inspiretheir entrepreneurial spirit, so in the original curriculumsystem, they design to added a few additional modulesabout entrepreneurship [9]. For entrepreneurial abilitytraining mode, Johannisson et al. make an analysis of kolbโslearning mode. Through the test of entrepreneurial action,they found that different groups (engineering students,
Hindawi Publishing CorporationMathematical Problems in EngineeringVolume 2014, Article ID 535137, 11 pageshttp://dx.doi.org/10.1155/2014/535137
2 Mathematical Problems in Engineering
Table 1: Payoff matrix of universities and studentsโ strategy.
StudentsParticipation ๐
๐No participation ๐
๐
UniversitiesPositive training๐
๐๐ผ(๐พ๐1โ 1)๐ถ
๐โ ๐ถ๐ถ, (๐พ๐1โ 1)๐ถ
๐โ๐ถ๐ถ, (๐พ๐2โ 1)๐ถ
๐
Negative training๐๐
๐ผ (๐พ๐3โ 1)๐ถ
๐, (๐พ๐3โ 1)๐ถ
๐0, (๐พ๐2โ 1)๐ถ
๐
business school students, and the business operators) havedifferent study effects [10]. Fiet explored the teachingdimension of entrepreneurship theory, finding that thereexist some challenges for the research and education ofentrepreneurship. When entrepreneurship teaching becomespredictable, teaching cannot achieve good results. He holdsthat entrepreneurship education should be based on the the-ory of entrepreneurship [6]. Above all, the existing studies aremainly carried out from the perspective of education partโschoolsโto cultivate the ability of entrepreneurship, but theyignore the entrepreneurial ability training process, which isthe mutual process of university and college students.
Evolutionary game theory combines the game theorywith dynamic evolution process. It is the result of biologicalevolutionary theory. The analysis of the system of socialhabits, specification, or spontaneous formation and influencefactors has made remarkable achievements. In fact, due tothe insufficient understanding of entrepreneurial ability, toomuch attention has been focused on the theory, less oncultivating the ability of entrepreneurship; thus, problemsexist. In this case, this paper is intended to discuss how tomake both universities and students evolve in an expectedway (inspiring and guiding studentsโ entrepreneurial ability)so as to improve the training effectiveness of studentsโentrepreneurial ability.
2. Model Building
In constructing an evolutionary game model, we must makesome basic assumptions of behavior interaction betweenuniversity and college students, up to the present statusof the management of universities. The two sides are theuniversity and students, respectively, with both sides havinglimited rationality. The group-colleges and universities havetwo strategies: one is to actively develop the studentsโ abilityof entrepreneurship through various channels, hereinafterreferred to as โpositive training,โ remembered as ๐
๐and
the other strategy is negative cultivation of college studentsโentrepreneurial ability, which means universities do not evendo anything, which is referred to as โnegative training,โremembered as ๐
๐. Strategy community of university is
set as ๐๐ถ{positive training, ๐
๐; negative training, ๐
๐}.
The group-students also have two strategies: one is activelyparticipating in activities to develop their entrepreneurialskills, hereinafter referred to as โparticipation,โ rememberedas ๐๐, while the second strategy is not involved in their
activities that develop their entrepreneurial skills, hereinafterreferred to as โno participation,โ noted as๐
๐. The strategy of
university student group is set as ๐๐{participation, ๐
๐and
no participation,๐๐}.
If universities actively cultivate their studentsโentrepreneurial ability, they will improve the system ofentrepreneurship education management and entrepreneur-ship education system and create entrepreneurship trainingbase and so on. The cost of these activities is set as ๐ถ
๐ถ.
If students are actively involved in developing theirentrepreneurial ability, they need to spend the costs of timeand energy, set as ๐ถ
๐.
When universities are active in entrepreneurial abilitytraining and students are also active in developing theirbusiness ability, students will increase their human capitalvalue, and their costs will have higher returns ๐พ
๐1, ๐พ๐1
โฅ 1.At this point, the net income for the students is (๐พ
๐1โ 1)๐ถ
๐.
The net income of colleges and universities is ๐ผ(๐พ๐1โ 1)๐ถ
๐โ
๐ถ๐ถ, where ๐ผ is the reputation and alumni support through
cultivating high level students for colleges and universities,and 0 โค ๐ผ โค 1. If students do not participate in developingthe ability of business, they can spare the time and energy inother activities, so at this time, the investment rate of returnis ๐พ๐2, and ๐พ
๐2โค ๐พ๐1. At this point, the net income for the
students is (๐พ๐2
โ 1)๐ถ๐and the net income of universities is
โ๐ถ๐ถ.When universities are negative in cultivating the studentsโ
entrepreneurial ability, students can promote entrepreneur-ship ability through self-study or internship. Without thehelp, support, and guidance of universities, the rate of returnon its investment is lower, set as ๐พ
๐3, ๐พ๐3
โค ๐พ๐2. At this point,
the net income for the students is (๐พ๐3
โ 1)๐ถ๐and the net
income of universities is ๐ผ(๐พ๐3โ 1)๐ถ
๐. If students themselves
do not actively promote entrepreneurship ability but spendthe time and energy in other activities, the net income forthe students would be (๐พ
๐2โ 1)๐ถ
๐, and the net income of
universities is 0.Based on the above assumptions, we constructed the
strategy payoff matrix between the universities and students,as shown in Table 1.
3. The Evolution of the Model andIts Equilibrium Analysis
3.1. The Evolution of the Model. Assume that, in the initialstate, the proportion of universities choosing๐
๐is๐ and that
the proportion of universities choosing strategy๐๐is 1 โ ๐;
the proportion of students choosing strategy๐๐is ๐; then, the
proportion of students choosing๐๐is 1โ๐. Herewe calculate
the corresponding expected revenue and average income.
Mathematical Problems in Engineering 3
Table 2: Local stability analysis results.
Equilibrium point Det๐ฝ Tr Result๐ = 0, ๐ = 0 โ๐ถ
๐ถ(๐พ๐3โ ๐พ๐2)๐ถ๐
+ โ๐ถ๐ถ+ (๐พ๐3โ ๐พ๐2)๐ถ๐
โ ESS๐ = 0, ๐ = 1 โ [๐ผ(๐พ
๐1โ ๐พ๐3)๐ถ๐โ ๐ถ๐ถ] (๐พ๐3โ ๐พ๐2)๐ถ๐
+ ๐ผ(๐พ๐1โ ๐พ๐3)๐ถ๐โ ๐ถ๐ถโ (๐พ๐3โ ๐พ๐2)๐ถ๐
+ Not stable๐ = 1, ๐ = 0 ๐ถ
๐ถ(๐พ๐1โ ๐พ๐2)๐ถ๐
+ ๐ถ๐ถ+ (๐พ๐1โ ๐พ๐2)๐ถ๐
+ Not stable๐ = 1, ๐ = 1 [๐ผ(๐พ
๐1โ ๐พ๐3)๐ถ๐โ ๐ถ๐ถ] (๐พ๐1โ ๐พ๐2)๐ถ๐
+ โ [๐ผ(๐พ๐1โ ๐พ๐3)๐ถ๐โ ๐ถ๐ถ] โ (๐พ
๐1โ ๐พ๐2)๐ถ๐
โ ESS๐ = ๐
โ, ๐ = ๐โ
โ๐โ๐โ(1 โ ๐
โ)(1 โ ๐
โ)๐ผ(๐พ๐1โ ๐พ๐3)2๐ถ๐
2โ 0 saddle point
๐1is the expected return of the selection of universities to
๐๐strategy; ๐
2is the expected return of universities choos-
ing ๐๐
strategy; ๐ is the average income of universities.Consider the following:
๐1= ๐ [๐ผ (๐พ
๐1โ 1)๐ถ
๐โ ๐ถ๐ถ] + (1 โ ๐) (โ๐ถ
๐ถ)
= ๐๐ผ (๐พ๐1โ 1)๐ถ
๐โ ๐ถ๐ถ,
๐2= ๐๐ผ (๐พ
๐3โ 1)๐ถ
๐,
๐ = ๐๐1+ (1 โ ๐)๐
2.
(1)
Similarly, ๐1is the expected return of students choosing
๐๐strategy; ๐
2is the expected return for students choosing
๐๐strategy; ๐ is the average income for students. Consider
the following:
๐1= ๐ (๐พ
๐1โ 1)๐ถ
๐+ (1 โ ๐) (๐พ
๐3โ 1)๐ถ
๐
= ๐ (๐พ๐1โ ๐พ๐3) ๐ถ๐+ (๐พ๐3โ 1)๐ถ
๐,
๐2= (๐พ๐2โ 1)๐ถ
๐,
๐ = ๐๐1+ (1 โ ๐)๐
2.
(2)
According to the Malthusian dynamic equation, thegrowth rate of the strategy is equal to its correspondingfitness [11, 12]; hence, we can draw dynamics equations ofthe interaction strategy that evolved over time betweenuniversities and students:
๐น (๐) =๐๐
๐๐ก= ๐ (๐
1โ ๐)
= ๐ (1 โ ๐) [๐๐ผ (๐พ๐1โ ๐พ๐3) ๐ถ๐โ ๐ถ๐ถ] ,
๐น (๐) =๐๐
๐๐ก= ๐ (๐ โ ๐)
= ๐ (1 โ ๐) [๐ (๐พ๐1โ ๐พ๐3) ๐ถ๐+ (๐พ๐3โ ๐พ๐2) ๐ถ๐] .
(3)
Through (3), we can study the evolution of the interactionbehavior between universities and students. Mark the Jaco-bian matrix of (3) as ๐ฝ which is expressed by
๐ฝ =[[[
[
๐๐น (๐)
๐๐
๐๐น (๐)
๐๐
๐๐น (๐)
๐๐
๐๐น (๐)
๐๐
]]]
]
= [(1 โ 2๐) [๐๐ผ (๐พ
๐1โ ๐พ๐3) ๐ถ๐โ ๐ถ๐ถ] ๐ (1 โ ๐) ๐ผ (๐พ
๐1โ ๐พ๐3) ๐ถ๐
๐ (1 โ ๐) (๐พ๐1โ ๐พ๐3) ๐ถ๐
(1 โ 2๐) [๐ (๐พ๐1โ ๐พ๐3) ๐ถ๐+ (๐พ๐3โ ๐พ๐2) ๐ถ๐]] .
(4)
The determinant of the Jacobian matrix is marked as Det ๐ฝ,and the trace of the Jacobianmatrix ismarked as Tr. Consider
Det ๐ฝ = (1 โ 2๐) (1 โ 2๐) [๐๐ผ (๐พ๐1โ ๐พ๐3) ๐ถ๐โ ๐ถ๐ถ]
ร [๐ (๐พ๐1โ ๐พ๐3) ๐ถ๐+ (๐พ๐3โ ๐พ๐2) ๐ถ๐]
โ ๐๐ (1 โ ๐) (1 โ ๐) ๐ผ(๐พ๐1โ ๐พ๐3)2๐ถ๐
2,
(5)
Tr = (1 โ 2๐) [๐๐ผ (๐พ๐1โ ๐พ๐3) ๐ถ๐โ ๐ถ๐ถ]
+ (1 โ 2๐) [๐ (๐พ๐1โ ๐พ๐3) ๐ถ๐+ (๐พ๐3โ ๐พ๐2) ๐ถ๐] .
(6)
3.2. Equilibrium and Its Stability Analysis. Since ๐ and ๐,respectively, represent the proportion of universitiesโ andstudentsโ choices of the strategies above, it is drawn that 0 โค
๐ โค 1, 0 โค ๐ โค 1. On a plane ๐โ= {(๐, ๐) | 0 โค ๐, ๐ โค 1}, the
system has 5 equilibrium points: (0, 0), (0, 1), (1, 0), (1, 1),and (๐
โ, ๐โ). Among them, ๐โ = (๐พ
๐2โ ๐พ๐3)/(๐พ๐1โ ๐พ๐3) and
๐โ= ๐ถ๐ถ/๐ผ(๐พ๐1โ๐พ๐3)๐ถ๐. According to the Jacobianmatrix, we
can have the local buckling analysis results in Table 2.According to Table 2, (๐โ, ๐โ) is the saddle point, and
(0, 1) and (1, 0) are the instability points. (0, 0) and (1, 1)
are the evolutionary stable strategy, corresponding to themodes (๐
๐, ๐๐) and (๐
๐, ๐๐). Here, (๐
๐, ๐๐)means the
university and students both choose negative action, which
4 Mathematical Problems in Engineering
q
o p
N(0, 1)
M(pโ, qโ)
L(1, 1)
H(1, 0)
Figure 1: Systematic dynamic evolution.
is badly locked; (๐๐, ๐๐)means the university and students
choose positive action, which is an ideal condition. Figure 1shows the strategy communication process of university andstudents groups.
4. The Influence of Parameter Change onthe Convergence System
(1) The impact of ๐ถ๐ถ, ๐ผ and ๐ถ
๐on the system convergence
In the saddle point, ๐๐/๐๐ถ๐ถ
= 0, ๐๐/๐๐ถ๐ถ
= 1/๐ผ(๐พ๐1
โ
๐พ๐3)๐ถ๐
> 0. When other parameters remain constant, ๐ถ๐ถ
increases, ๐ผ or ๐ถ๐decreases, and saddle point goes upward
vertically. The probability of converging to mode (๐๐, ๐๐)
increases, and the probability of convergence to (๐๐, ๐๐)
decreases; on the contrary, the probability of converging tomode (๐
๐, ๐๐) is reduced, and the probability of conver-
gence to (๐๐, ๐๐) increases, which is shown in Figure 2.
(2) The impact of ๐พ๐1on the system convergence
In the saddle point, ๐๐/๐๐พ๐1
= โ(๐พ๐2โ ๐พ๐3)/(๐พ๐1โ ๐พ๐2)2<
0, ๐๐/๐๐พ๐1
= โ๐ถ๐ถ/๐ผ(๐พ๐1โ ๐พ๐3)2๐ถ๐
< 0. When the otherparameters remain constant, ๐พ
๐1increases, and saddle point
moves to the lower left corner, so the probability of con-verging to mode (๐
๐, ๐๐) is reduced, and the probability
of convergence in (๐๐, ๐๐) increases; on the contrary, the
probability of converging to mode (๐๐, ๐๐) increases, and
the probability of convergence in (๐๐, ๐๐) is reduced, which
is shown in Figure 3.(3) The impact of ๐พ
๐2on the system convergence
In the saddle point, ๐๐/๐๐พ๐2
= 1/(๐พ๐1โ๐พ๐2) > 0, ๐๐/๐๐พ
๐2=
0. When the other parameters remain constant, ๐พ๐2increases,
and saddle point moves to the right corner, so the probabilityof converging to mode (๐
๐, ๐๐) increases, and the proba-
bility of convergence in (๐๐, ๐๐) decreases; on the contrary,
the probability of converging to mode (๐๐, ๐๐) reduces,
and the probability of convergence in (๐๐, ๐๐) increases,
which is shown in Figure 4.
(4) The impact of ๐พ๐3on the system convergence
In the saddle point, ๐๐/๐๐พ๐3
= โ1/(๐พ๐1
โ ๐พ๐2) <
0, ๐๐/๐๐พ๐3
= ๐ถ๐ถ/๐ผ(๐พ๐3
โ ๐พ๐1)2๐ถ๐
> 0. When the otherparameters remain constant, ๐พ
๐3increases, and the saddle
point moves to the top left; on the contrary, the saddle pointmoves to the lower right, as is shown in Figure 5. The impactof ๐พ๐3
on the results of the convergence system is not clear,which needs further numerical analysis.
5. The Result Analysis ofNumerical Experiments
In behavior strategy communication system between uni-versity and students, some parameters are involved: theproportion of initial population ๐ and ๐, the respective costof college and students ๐ถ
๐ถand ๐ถ
๐, the rate of reward ๐พ
๐1, ๐พ๐2,
and ๐พ๐3
of students under different situations, and rewardcoefficient ๐ผ of universities. These parameters will influencethe earnings of university and students, which will furtherinfluence the evolution of the system.
(1)The impact of the changes of ๐0and ๐0on the result of
system evolutionAccording to the numerical experiment shown in
Figure 6, ๐0and ๐
0, respectively, represent the proportion
of the initial population that university chooses ๐๐and
students who choose๐๐. Parameter values are ๐ถ
๐ถ= 1, ๐ถ
๐=
10, ๐ผ = 0.2, ๐พ๐1
= 2, ๐พ๐2
= 1.5, and ๐พ๐3
= 1.2. It can be seenfrom Figure 6 the dependence of the path when universityand students are in the process of behavior strategy interac-tion. With different initial ratio the convergence curves donot overlap before reaching their equilibrium. Convergencespeed is influenced not only by the initial proportion studentschoosing to have entrepreneurial ability training, but also bythe initial proportion that students have related actions toimprove their entrepreneurial abilities at the same time. Thecloser the proportion gets to the equilibrium, the faster theconvergence speed is. As long as the proportion of initial๐๐strategy use is very low (e.g., ๐
0= 0.1), the system will
eventually be locked in a โbadโ state; if this proportion isvery high (e.g., ๐
0= 0.9), the system can eventually evolve
to the ideal mode (๐๐, ๐๐). In general circumstances, as
the proportion of students choosing to have positive actionincreases, it will also help the system evolve toward theideal mode; therefore, universities must first enhance theentrepreneurship education actively, arousing the studentsโenthusiasm.
(2)The impact of the change of๐ถ๐ถon the result of system
evolutionNumerical test results of the impact are shown inFigure 7.
The reason that we set the proportion of students taking partin the entrepreneurship activities as 0.4 is that as the impactof the change of the initial population on the evolution is ana-lyzed above, it is clear that when the initial choice ratio of uni-versitiesโ cultivating studentsโ entrepreneurship is high, thesystem will converge to (๐
๐, ๐๐) mode; if the initial choice
ratio of universitiesโ cultivating studentsโ entrepreneurshipis lower, the system will converge to mode (๐
๐, ๐๐). So
๐ = 0.4 is a typical situation. At the same time, combining
Mathematical Problems in Engineering 5
q
o p
N(0, 1)
M(pโ, qโ)
L(1, 1)
H(1, 0)
(a) The situation of ๐ถ๐ถ increases, ๐ผ or ๐ถ๐ decreases
q
o p
N(0, 1)
M(pโ, qโ)
L(1, 1)
H(1, 0)
(b) The situation of ๐ถ๐ถ decreases, ๐ผ or ๐ถ๐ increases
Figure 2: The impact of ๐ถ๐ถ, ๐ผ, ๐ถ
๐on the system convergence.
q
o p
N(0, 1)
M(pโ, qโ)
L(1, 1)
H(1, 0)
(a) The situation when ๐พ๐1 increases
q
o p
N(0, 1)
M(pโ, qโ)
L(1, 1)
H(1, 0)
(b) The situation when ๐พ๐1 decreases
Figure 3: The impact of ๐พ๐1on the system convergence.
the fact that the overall university students are in highenthusiasm but with lower ability in entrepreneurial activities(national college students entrepreneurship research reportshows that 14% of students participated in a training programor entrepreneurship competition and that 48.8% of collegestudents hope to be provided with business related profes-sional training) and choosing ๐ = 0.4, which is more inline with the actual situation, other parameter values are asfollows: ๐ถ
๐= 10, ๐ผ = 0.2, ๐พ
๐1= 2, ๐พ
๐2= 1.5, and ๐พ
๐3= 1.2.
As Figure 7 shows, with the increase of universityโstraining cost ๐ถ
๐ถ, the convergence speed of the system slows
down and the time of convergence to equilibrium mode
increases, and the systemโs evolutionary direction convertsfrommode (๐
๐, ๐๐) to a bad lockmode (๐
๐, ๐๐). Univer-
sitiesโ training cost represents the burden of entrepreneurshiptraining of universities. Under the certain level of total costof entrepreneurship training, universitiesโ burden should beeased by broadening the financing channels. This can notonly guarantee the training level, but also arouse universitiesโtraining enthusiasm.
(3)The impact of the change of ๐ถ๐on the result of system
evolutionThe impact is shown in Figure 8. The parameter values
are as follows: ๐ = 0.4, ๐ถ๐ถ
= 1, ๐ผ = 0.2, ๐พ๐1
=
6 Mathematical Problems in Engineering
q
o p
N(0, 1)
M(pโ, qโ)
L(1, 1)
H(1, 0)
(a) The situation when ๐พ๐2 increases
q
o p
N(0, 1)
M(pโ, qโ)
L(1, 1)
H(1, 0)
(b) The situation when ๐พ๐2 decreases
Figure 4: The impact of ๐พ๐2on the system convergence.
q
op
N(0, 1)
M(pโ, qโ)
L(1, 1)
H(1, 0)
(a) The situation when ๐พ๐3 increases
q
o p
N(0, 1)
M(pโ, qโ)
L(1, 1)
H(1, 0)
(b) The situation when ๐พ๐3 decreases
Figure 5: The impact of ๐พ๐3on system convergence.
2, ๐พ๐2
= 1.5, and ๐พ๐3
= 1.2. It can be seen fromFigure 8 that with the increase of studentsโ entrepreneurialactivity costs๐ถ
๐, system convergence speeds up, and the time
of converging to equilibrium mode reduces. The evolutiondirection of the system will also change from bad lock mode(๐๐, ๐๐) to the ideal mode (๐
๐, ๐๐). The cost ๐ถ
๐reflects
the difficulty level of promoting entrepreneurship skills. Wecan see that more college students tend to participate inthe schoolโs entrepreneurial ability training program, ratherthan to choose self-study to gain their entrepreneurial skills.Therefore, in the process of entrepreneurship education, uni-versities should paymore attention to the core and important
business knowledge, while the simple and easy knowledgecan be learned by students themselves. Universities need todistinguish between the focus of entrepreneurship educationand the investment of education resources.
(4)The impact of the change of ๐พ๐1on the result of system
evolutionThe impact is shown in Figure 9, and the parameter value
selections are as follows: ๐ = 0.4, ๐ถ๐ถ
= 1, ๐ถ๐= 10, ๐ผ =
0.2, ๐พ๐2
= 1.5, ๐พ๐3
= 1.2.As can be seen from Figure 9, with the increase of the
investment return ratio ๐พ๐1of studentsโ entrepreneurial ability
improvement, the system convergence speeds up, and the
Mathematical Problems in Engineering 7
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
p
0 10 20
t
p0 = 0.1
p0 = 0.4
p0 = 0.6
p0 = 0.9
p0 = 0.1
p0 = 0.4
p0 = 0.6
p0 = 0.9
p0 = 0.1
p0 = 0.4
p0 = 0.6
p0 = 0.9
p0 = 0.1
p0 = 0.4
p0 = 0.6
p0 = 0.9
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
p
0 10 20
t
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
p
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
p
0 10 20
t
0 10 20
t
q0 = 0.1 q0 = 0.4 q0 = 0.6 q0 = 0.9
Figure 6: Impact of the change of ๐0and ๐
0on the result of the system evolution.
0 20 40
t
0 20 40
t
0 20 40
t
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
p
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
p
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
p
p0 = 0.1
p0 = 0.4
p0 = 0.6
p0 = 0.9
p0 = 0.1
p0 = 0.4
p0 = 0.6
p0 = 0.9
p0 = 0.1
p0 = 0.4
p0 = 0.6
p0 = 0.9
CC = 0.5 CC = 1.0 CC = 1.5
Figure 7: Impact of the changes of ๐ถ๐ถon the result of the system evolution.
8 Mathematical Problems in Engineering
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
p
p0 = 0.1
p0 = 0.4
p0 = 0.6
p0 = 0.9
p0 = 0.1
p0 = 0.4
p0 = 0.6
p0 = 0.9
p0 = 0.1
p0 = 0.4
p0 = 0.6
p0 = 0.9
0 20 40
t
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
p
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
p
0 20 40
t
0 20 40
t
CS = 7 CS = 10 CS = 15
Figure 8: Impact of the changes of ๐ถ๐on the result of the system evolution.
0 20 40
t
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
p
0 20 40
t
0 20 40
t
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
p
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
p
p0 = 0.1
p0 = 0.4
p0 = 0.6
p0 = 0.9
p0 = 0.1
p0 = 0.4
p0 = 0.6
p0 = 0.9
p0 = 0.1
p0 = 0.4
p0 = 0.6
p0 = 0.9
๐พS1 = 1.8 ๐พS1 = 2.0 ๐พS1 = 2.5
Figure 9: Impact of the change of ๐พ๐1on the result of the system evolution.
Mathematical Problems in Engineering 9
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
p
0 10 20
t
0 10 20
t
0 10 20
t
p0 = 0.1
p0 = 0.4
p0 = 0.6
p0 = 0.9
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
p
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
p
p0 = 0.1
p0 = 0.4
p0 = 0.6
p0 = 0.9
p0 = 0.1
p0 = 0.4
p0 = 0.6
p0 = 0.9
๐พS2 = 1.3 ๐พS2 = 1.5 ๐พS2 = 1.8
Figure 10: Impact of the change of ๐พ๐2on the result of the system evolution.
evolution direction of the system will be changed from(๐๐, ๐๐) into the ideal mode (๐
๐, ๐๐). Increasing ๐พ
๐1
means that more entrepreneurial investment can lead toability improvement and significant increase of their ownhuman capital value. At the same time universities can alsoget high school reputation. In the condition of a higher ๐พ
๐1,
both universities and students tend to take positive action.Only when the investment return ratio is high enough, theenthusiasm of university studentsโ participation will be high.Therefore, universities need to improve training effectivenessfurther to increase the investment return ratio of universitystudentsโ entrepreneurial ability improvement.
(5)The impact of the change of ๐พ๐2on the result of system
evolutionThe impact is shown in Figure 10, and the parameter value
selections are as follows: ๐ = 0.4, ๐ถ๐ถ
= 1, ๐ถ๐= 10, ๐ผ =
0.2, ๐พ๐1
= 2, and ๐พ๐3
= 1.2.Figure 10 indicates that the rate of system convergence
increases with the growth of ๐พ๐2, with systematic evolution
transforming from mode (๐๐, ๐๐) to mode (๐
๐, ๐๐). So,
when making decision on participating in entrepreneurshiptraining or not, university students consider not only theinvestment return ratio, but also the opportunity costs of par-ticipation. It again showed that improvement training effec-tiveness further to increase the gains of university studentsโparticipation is the key to improve the studentsโ enthusiasmto participate in the entrepreneurial ability training.
(6)The impact of the change of ๐พ๐3on the result of system
evolutionFigure 11 shows the influence of return rate ๐พ
๐3of
enhancement of college studentsโ entrepreneurial ability on
system convergence.The parameters are listed as follows: ๐ =
0.4, ๐ถ๐ถ= 1, ๐ถ
๐= 10, ๐ผ = 0.2, ๐พ
๐1= 2, and ๐พ
๐2= 1.5.
We may find that, in Figure 11, the impact of ๐พ๐3
onsystematic evolvement direction is similar to that of ๐พ
๐1on
the system; the impact of ๐พ๐3
on system convergence rate,however, is more obvious. It becomes slow with the increaseof ๐พ๐3. ๐0= 0.4 and ๐
0= 0.6 evolve in the direction towards
(๐๐, ๐๐) in the early periods and then in a short time they
change towards (๐๐, ๐๐) and converge at (๐
๐, ๐๐).
Further analysis finds that ๐พ๐1, ๐พ๐2, and ๐พ
๐3are decided
by the values of ๐พ๐1
โ ๐พ๐3
and ๐พ๐2
โ ๐พ๐3, which are further
decided by the balance of return rate and return rate of timeand energy used in other field, with or without assistanceby universities. A larger balance between ๐พ
๐1and ๐พ๐2
bringsthe evolvement to (๐
๐, ๐๐) in the ideal stage. But a larger
balance between ๐พ๐2and ๐พ๐3brings (๐
๐, ๐๐) more to a bad
lock mode. Anyway, higher investment of entrepreneurshiptraining leads to easier involvement to ideal mode. Hence,higher education institutions should take more efforts toenhance the efficiency in talent education so as to increasethe reward rate of studentsโ participation in the education.
(7) The impact of ๐ผ on the result of system evolutionFigure 12 shows the influence of return coefficient ๐ผ of
university entrepreneurship training on system convergence.Parameters are listed as follows: ๐ = 0.4, ๐ถ
๐ถ= 1, ๐ถ
๐=
10, ๐พ๐1
= 2, ๐พ๐2
= 1.5, and ๐พ๐3
= 1.2.Figure 12 shows that, with the increase of return coeffi-
cient ๐ผ, system converges faster to the ideal mode (๐๐, ๐๐)
and the systemwill change toward the ideal mode. In collegesand universities, the purpose of entrepreneurship educationand entrepreneurial ability is mainly to relieve employment
10 Mathematical Problems in Engineering
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
p
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
p
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
p
p0 = 0.1
p0 = 0.4
p0 = 0.6
p0 = 0.9
p0 = 0.1
p0 = 0.4
p0 = 0.6
p0 = 0.9
p0 = 0.1
p0 = 0.4
p0 = 0.6
p0 = 0.9
0 20 40
t
0 20 40
t
0 20 40
t
๐พS3 = 0.7 ๐พS3 = 1.2 ๐พS3 = 1.4
Figure 11: The influence of the change of ๐พ๐3on the result of the system evolution.
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
p
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
p
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
p
p0 = 0.1
p0 = 0.4
p0 = 0.6
p0 = 0.9
p0 = 0.1
p0 = 0.4
p0 = 0.6
p0 = 0.9
p0 = 0.1
p0 = 0.4
p0 = 0.6
p0 = 0.9
0 20 40
t
0 20 40
t
0 20 40
t
a = 0.15 a = 0.2 a = 0.3
Figure 12: The influence of return coefficient ๐ผ of university entrepreneurship training on system convergence.
Mathematical Problems in Engineering 11
pressure, and by conducting entrepreneurial education andtraining, to inspire studentsโ entrepreneurial enthusiasmand encourage studentsโ entrepreneurship. The purpose ofcultivating the ability of entrepreneurship is not only toencourage students to take part in the entrepreneurial activi-ties during their stay in school or after graduation, but also tofocus on the implementation of the studentsโ entrepreneurialpotential and help students accumulate human capitals andentrepreneurial energy stored for appropriate time for future.
6. Conclusion
Entrepreneurial talent training needs studentsโ positive par-ticipation. The purpose of this research is to investigatethe interaction between universities and students in theprocess of studentsโ entrepreneurial ability training and thesystem evolution law, in order to find effective strategiesfor promoting the enthusiasm and initiative of universitystudentsโ entrepreneurial ability.
Through the construction of payoff matrix of studentsโbehavior, the evolution of behavior interaction system, itsequilibrium, and the influence of different parameters on thesystem convergence are analyzed. The MatLab software isused for the results of numerical experiments under differentparameters of the evolution system. We found that modes(๐๐, ๐๐) and (๐
๐, ๐๐) are two evolutionary stable strate-
gies by the interaction between universities and students, andthe mode (๐
๐, ๐๐) is badly locked.
At present, studentsโ understanding of entrepreneurialability is insufficient. There exist some negative attitudestoward entrepreneurship education activity, which is notconducive to the improvement of studentsโ entrepreneurialability. Model analysis and numerical experiment show thatthe system can evolve towards ideal pattern through improv-ing the initial proportion of the positive involvement of groupselection of entrepreneurial talent training in universities,reducing investment cost of universitiesโ entrepreneurship,increasing the rate of return of universitiesโ entrepreneurshipeducation, stressing the investment on higher knowledge andability, or increasing the efficiency of the entrepreneurialability training to promote the reward rate of both universitiesand students.
Conflict of Interests
The authors declare that there is no conflict of interestsregarding the publication of this paper.
Acknowledgments
This work was supported in part by the National Natu-ral Science Foundation of China under Grants 71373104and 71171099, the Jiangsu Philosophy and Societal Sci-ence Research Project under Grants 2012SJB630010 and2012SJB880021, the Soft Science Research Project of Zhen-jiang City under Grant YJ2012005, and the College StudentsโIdeological and Political Education Project of JiangsuUniver-sity under Grant JDXGCB201305.
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