# Research on the Niche Evolution Game of Ecological Community Innovation of Corporate Venture Capital Based on Logistic Extended Complexity Model

Authors: Fanglin Meng; Zengrui Tian; Beiquan Chang; Hongxin Yu; Shuai Zhang
Journal: Complexity
 (2020)

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## Abstract

With the gestation and development of new technologies, new products, new formats, and new models, venture capital investment, as one of the most important forms of open innovation in large companies, plays an increasingly important role in the innovation of mature large companies and entrepreneurial enterprises. To deal with the complex and dynamic environment, the niche of Corporate Venture Capital (CVC) ecological community is investigated from the perspective of the innovation ecosystem. By analyzing the innovation of CVC ecological community with the use of the logistic expansion model, this paper analyzes the stability of evolution game through the replicator dynamic equation and discusses ten parameters of niche state. In the end, we conclude that there are four optimization strategies in the coevolution of major corporations and entrepreneurial firms, namely, niche separation, niche expansion, niche K-R, and niche alliance.


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## Body

## 1. Introduction

Innovation has become the endogenous driving force and core competitive advantage of a country's economic growth. In the complex and dynamic digital economy era, it is difficult for enterprises to maintain traditional competition barriers. To keep growing continuously, enterprises must deal with issues such as the increasingly uncertain environment, challenging value creation, and oversupply choices for customers. The traditional value chain creation model is changing to the shared destiny community with a symbiosis creation model. Therefore, large companies are constantly seeking the path of open empowerment. Corporate Venture Capital (CVC) has become an important model and tool for open innovation, access to external technology sources, and value creation. The global venture capital funding in 2018 reached 254 billion US dollars, and the financing amount in 2017 was 174 billion RMB, of which the global company's total venture capital investment was 312 billion US dollars. Investment activities increased by 19% over 2016, and total investment increased by 18% [1]. Companies in countries like Britain, China, and India have hit record highs in their venture capital. The global CVC investment industry has strong interests in areas with high technological innovation and fierce competitions such as Internet, healthcare, and mobile technology.The company's venture capital originated in the United States in the 1960s. It is now one of the main ways for mature large companies to develop outwards. It has a strategic appeal because it provides multiple choice platforms for large companies to innovate. Corporate innovation requires venture capital as a mechanism and driving force. Corporate Venture Capital aims to achieve open innovation, obtain the latest technology in related fields, and overcome the soft constraints of the company's internal R&D budget so that they can improve technology innovation efficiency. It could also reduce the risk of investment in independent R&D and improve organizational capabilities to foster an innovation culture. It benefits the corporate by realizing the value of strategic mergers and acquisitions and initiating entrepreneurial investment in strategic innovation projects. As company's venture capital has a high degree of risk tolerance and a long investment cycle, it can invest in the startups that are struggling to obtain traditional independent venture capital (IVC). It promotes and optimizes mutual regeneration and achieves a better evolutionary cycle for both parties. While mature companies deeply cultivate the Red Sea, they must also actively explore in the Blue Ocean. CVC is a hybrid model that stimulates innovation. It expands industrial boundaries, rebuilds market boundaries, explores cutting-edge technologies, encourages open innovation, and expands organizational structures for large companies. It is regarded as an effective paradigm to promote the evolution of the industry ecosystem. It is also an important way for large companies to acquire innovative technologies and industrial integration [2]. CVC activities are a “dual and two-way” value creation process that includes both strategic and financial values, while creating value for mature large companies and startups. With the advent of the digital economy 2.0 era, ecological collaborative innovation models have gradually taken shape. Typical digital economy companies in China, such as Alibaba, Tencent, Xiaomi, and Baidu, as well as traditional enterprises such as Haier and Fosun, are actively building open innovation enterprise ecosystems. They integrate the company's own technology, capital, and market advantages with external resources to develop new technologies, new products, and new models for new markets.


## 2. Related Work

Hannah and Eisenhardt proposed that, in addition to the relationship between competition and cooperation, enterprises also need to continuously meet customer needs through innovation [3]. Enterprises have evolved from the role of an individual player in the industry into part of the industrial ecosystem. Luo and Ratchford took Apple, IBM, Ford, and Wal-Mart as examples to study focal companies which develop service, technology, and value network platforms to build their own unique business ecosystems and obtain value returns [4]. Yao and Zhou used the theory of natural ecosystem evolution to study the innovation path of high-tech enterprises and found that the dependence of enterprise innovation paths has ecological genetic and variability characteristics [5]. Daniela et al. in “Evolutionary Theory of Economic Change” explain economic changes from a perspective of dynamic evolution. Evolutionary game theory pays attention to the change of population structure and uses evolutionary stable strategy (ESS) to represent a stable state that can resist the invasion of mutation strategy [6]. Levinthal proposed that corporate adaptation and environmental selection are the main paths of population evolution [7]. Zaman et al. believe that internal and external resources of an enterprise are equally important. Enterprises use external resources and external channels to help commercialize their new technological achievements. They also emphasize that enterprises should quickly implement innovation, reduce innovation costs, and work with professional venture capital institutions to jointly improve innovation performance [8].One of the most challenging 125 scientific issues in the 21st century in science is, “how does cooperative behavior evolve?” The innovation ecosystem has the same characteristics of natural evolution, integration, self-organization, periodicity, and openness as natural ecosystems and shares the same characteristics in power, genetics, evolution, and feedback. Important scholars in the CVC field, Jog and Mcconomy, creatively proposed that mature large companies have regarded CVC not only as the window for technology discovery but also as an ecosystem around large companies [9]. This conclusion is based on previous research on CVC enterprise value creation, CVC investment enterprise entrepreneurial performance, investment conditions, and cross-organizational knowledge acquisition.Based on the analysis of nearly 300 CVCs, Jog and Mcconomy proposed that the increasing number of CVCs would contribute in better short-term and long-term performance of the ecosystem, which extends a previous view shared by scholars that the CVC is only an incubator-level participant. Instead, as an ecosystem strategy, CVC intends to “build a constellation” [10]. Therefore, from the perspective of the ecosystem and the niche theory, it is proposed that the CVC ecological community, formed by mature large companies and startups in the form of CVC projects, achieves synchronization through interactions between CVC functions, behavioral processes, and the external environment. In the symbiotic mode, a symbiotic evolution can be developed with the growth of large companies and entrepreneurial enterprises.


## 3. CVC Niche for Major Corporations and Entrepreneurial Firms

In 1838, the Dutch mathematical biologist Verhulst proposed a logistic equation to study the growth of biological populations. It was found that the population grew fastest at the beginning. When it grew to a certain value, the speed began to slow down until it finally decreased to zero (i.e., stop growing). In 1900, Italian mathematician Volterra proposed the predator and prey populations model. In 1925, Lotka proposed mathematical ecology in chemical reactions. Then in 1926, Volterra used the Lotka–Volterra model to demonstrate the rule of fish population in the port of Fiume. Lotka–Volterra model, which evolved from the logistic extended model, can better explain the relationship between large companies and startups in the CVC ecological community. This model, as an evolutionary game for species or population formation, provides a new perspective to understand community structure optimization and niche evolution [11].The growth of the corporate ecological community involved in CVC also generally conforms to the mechanism of the logistic development; that is, the development of the CVC ecological community is relatively immature: the scale is not large; the growth space is large; and the development speed is fast at S1. However, at this stage, for large enterprises and startups, the initial capital investment, human investment, and technical investment are relatively large. The symbiotic subjects of the CVC ecological community are still in the running-in period with high risks. At node P1, either CVC is offside to enhance the niche, occupying a favorable position in the innovation and entrepreneurship ecosystem, or it may gradually decline. CVCs that operate smoothly, realize technological innovation, and have shared and coordinated development can successfully enter the second stage of the ecological niche beyond P1. In the second stage of S2, the ecological niche of CVC continued to expand; the benefits continued to increase; innovation results and innovative technologies were rapidly transformed; large companies achieved their strategic goals and financial goals; and startup companies also achieved growth. At the second branch point P2, with great innovation potential, the CVC ecological community, formed by large companies with startups, integrates more resources and continues to develop. The symbiotic system will rise to a higher stage, while the ecological shrinkage may also occur. Figure1 is the trend of CVC ecological community evolution.Figure 1
The trend of CVC ecological community evolution.Therefore, the evolution of the niche also reflects the characteristics of repeated games between large companies and startups in the CVC ecological community. CVC activities are also innovative activities. Large companies form CVC ecological communities with startups through venture capital for technological innovation. They aim to realize value cultivation and value innovation and continuously develop new competitive advantages in the industry competition. By improving their own niche, they can achieve their strategic goals and financial goals.From the perspective of biology and evolutionary games, the development of the CVC ecological community is constrained by various factors such as talent, technology, capital, and services, in specific time and space dimensions. The ecological factor domainCi=fz1,z2,z3,⋯,zn is used to represent the various factors z1,z2,z3,⋯,zn that indicate the constraints for the development of the CVC ecological community. There is a range value Ni of the niche width Wi of ecological community i, which represents the competition coefficient αi of the CVC ecological community. β represents the niche overlap value of the CVC ecological community, and χi indicates the impact of CVC investment strategies such as combination strategies, capital injection strategies, exit methods, and space preferences on the innovation of the CVC ecological community.St represents the niche status (i) of the CVC ecological community at time of t, and dSt/dt represents the rate of change in the niche width for large enterprises and entrepreneurial enterprises in the CVC ecology community. Adjusted from the Lotka–Volterra model, the niche evolution equations of the major corporations (MC) and entrepreneurial firms (EF) in the CVC ecosystem are set as follows:(1)dS1tdt=r1S1ρ1+χ1−α1−S1−βS2,dS2tdt=r2S2ρ2+χ2−α2−S2−βS1.Here,S1andS2 represent the niche width limit of MC and EF; ρ1andρ2 represent niche saturation coefficient of MC and EF in the CVC ecological community; α1andα2 represent competition coefficients: α1 is the competitive effect of EF on MC, while α2 is the competitive effect of MC on EF; and β represents niche overlap between MC and EF in the CVC ecological community.Whenβ = 1, there is a complete niche overlap between MC and EF. When β = 0, there is a complete niche separation for MC and EF. If the value of β is between 0 and 1, there is partial overlap between MC and EF. The β is proportional to α1andα2, which means the bigger the overlap between MC and EF, the more the fierce competition.According to the above differences inβ, the evolution of the niche of large companies and startups in the CVC ecological community is discussed as follows [12]:(1)
Whenβ = 1, there is a complete niche overlap between MC and EF.IfdS1t/dt=0dS2t/dt=0, the balanced position includes H1ρ1+χ1−α1,0, H2ρ2+χ2−α2,0,H30,ρ1+χ1−α1, H40,ρ2+χ2−α2, O0,0.The equation for MC in the CVC ecological community isρ1+χ1−α1−S1−S2=0.The equation for EF in the CVC ecological community isρ2+χ2−α2−S2−S1=0.As there is an equal slope, the position of the two parallel straight linesL1,L2 depends on the values of parameters ρ1+χ1−α1 and ρ2+χ2−α2.Whenρ1+χ1−α1>ρ2+χ2−α2, we can obtain Figure 2 in the following.The niche width of the MC in the CVC ecological community is larger than the niche width of the EF. MC completely includes the EF, indicating that the MC occupies the entire niche space.Whenρ2+χ2−α2>ρ1+χ1−α1, we can get Figure 3 in the following.Entrepreneurial firm's niche width (L2) in the CVC ecological community is larger than that of major corporation (L1). EF completely includes MC. This indicates that EF occupies the entire niche space. The result of evolution will also approach EF. Therefore, when the MC and EF in the CVC ecological community completely overlap, the direction of the niche evolution depends on the technologies, capital, human resources, and innovation resources used by the MC and EF. The one occupying the resource advantage will eventually control the evolution.(2)
Whenβ = 0, there is a complete niche separation for MC and EF.IfdS1t/dt=0dS2t/dt=0, the balanced position includes H1ρ1+χ1−α1,ρ2+χ2−α2, H2ρ1+χ1−α1,0,H30,ρ2+χ2−α2, O0,0.The equation for MC in the CVC ecological community isL1:S1=ρ1+χ1−α1.The equation for EF in the CVC ecological community isL2:S2=ρ2+χ2−α2.We can obtain a separation as shown in Figure4.L1andL2 divide four areas in the quadrant. In the areas below L1 (dS1t/dt<0), the evolution direction rises, while in the areas above L1 (dS1t/dt>0), the evolution direction goes downward. In the areas on the left of L2 (dS2t/dt<0), the evolution direction goes right, while in the areas on the right of L2(dS2t/dt>0), the evolution direction goes left.In quadrant 1,dS1t/dt>0 and dS2t/dt<0.In quadrant 2,dS1t/dt>0 and dS2t/dt>0.In quadrant 3,dS1t/dt<0 and dS2t/dt<0.In quadrant 4,dS1t/dt<0 and dS2t/dt>0.Therefore, we can conclude that the result of evolution tends to equilibriumH1ρ1+χ1−α1,ρ2+χ2−α2, where the large companies and startups in the CVC ecological community occupy their respective niche. Its niche size is related to the niche saturation coefficients ρi of both parties, the competition coefficient αi of large enterprises and startups in the CVC ecosystem, and the impact coefficient χi of CVC ecological community innovation CVC investment strategy (CVC portfolio strategy, CVC investment stage strategy, CVC exit method, CVC investment space preference).(3)
When 0 <β < 1, MC and EF niche partially overlap. The evolution path depends on the ecological domain space of their respective resources.Figure 2
Evolution of niche overlap, when MC contains EF.Figure 3
Evolution of niche overlap, when EF contains MC.Figure 4
Niche separation of CVC.IfdS1t/dt=0dS2t/dt=0, the balanced position includes O0,0, H1ρ1+χ1−α1,0, H20,ρ1+χ1−α1/β,H3ρ2+χ2−α2/β,0, and H40,ρ2+χ2−α2:(2)Gρ1+χ1−α1−βρ2+χ2−α21−β2,ρ2+χ2−α2−βρ1+χ1−α11−β2.As the values of the parameters are different, the analytical expressions have different evolution trends. There are four competition situations between the two populations:Situation 1.
Whenρ1+χ1−α1/β>ρ2+χ2−α2 and ρ2+χ2−α2/β<ρ1+χ1−α1.
In the area surrounded by the quads H1, H2, H3, H4 (Figure 5), where dS1t/dt<0¸ dS2t/dt>0, large companies have not reached the maximum capacity for growth; i.e., there is still room for growth and development. While, startups have reached the maximum capacity; i.e., there is little room for continued growth. Large companies have mastered related technological innovations. The corresponding evolution is shown in Figure 5.Figure 5
Large companies occupy part of the startup’s niche.Situation 2.
Whenρ1+χ1−α1/β<ρ2+χ2−α2 and ρ2+χ2−α2/β>ρ1+χ1−α1.
In the area surrounded by the quads H1, H2, H3, H4 (Figure 6), where dS1t/dt>0, dS2t/dt>0, entrepreneurial enterprises in the CVC ecosystem can continue to develop, but large companies have reached their limits. Therefore, entrepreneurial enterprises can invade some ecological domains for large companies, as shown in Figure 6.Figure 6
Startups occupy the ecological domain of large companies.Situation 3.
Whenρ2+χ2−α2/β>ρ1+χ1−α1 and ρ1+χ1−α1/β>ρ2+χ2−α2
L1andL2 come across at point G, as shown in Figure 7.(3)Gρ1+χ1−α1−βρ2+χ2−α21−β2,ρ2+χ2−α2−βρ1+χ1−α11−β2.
In the area of H2GH4, there is still room for growth of startups, while large companies have developed to the maximum capacity, approaching G. In the GH1H3 region, large companies continue to grow, while the growth of startups has reached the upper limit. The movement trends of both parties will gradually approach pointG, where G is the equilibrium point for the coexistence of large enterprises and entrepreneurial enterprises in the CVC ecological community.Figure 7
Ecological stability of large companies and startups.Situation 4.
Whenρ2+χ2−α2/β<ρ1+χ1−α1 and ρ1+χ1−α1/β<ρ2+χ2−α2.
L1andL2 come across at point P, as shown in Figure 8.
In the H2PH4 and H1PH3 areas, both large companies and startups have room for continued innovation and growth. Both sides may have the opportunity to win in the competition process, so they have not reached an equilibrium state. The niche occupation depends on what the two parties have in the initial ecological domain. The larger the initial ecological domain is, the more resources it possesses, and the easier it is to win in the CVC ecological community. This also makes CVC ultimately achieve the strategic goals and financial goals of large companies by IPO, mergers, and acquisitions. While startups get mature, big companies can quit.
In the above analysis, situations (1), (2), and (4) are all unbalanced and stable. In the balanced state (3), large enterprises and startups in the CVC ecosystem can coexist and maximize their own added value.Figure 8
Large companies and startups continue to grow and cannot reach balance.


## 4. Construction of the Evolutionary Game Model for the CVC Ecological Community Innovation

Evolutionary game theory exists in Darwin's idea of natural selection. Based on the dual theory of game theory and biological evolution, this section analyzes the formation mechanism of interaction between populations in ecological communities and studies population growth, evolution, and stability [13].


### 4.1. Evolutionary Game Analysis

The symbiotic evolution between large companies and startups in the CVC ecological community will increase the adaptability of both parties and thus their respective niche. The evolutionary game theory has been used to analyze the operating mechanism of large companies and startups. Here we use evolution stability strategy to analyze the evolution path of CVC ecological community. The strategy adjustment process, trends, and stability of large players and startups in priority game players are considered. ESS evolutionary stability strategy and Taylor and Jonker's replicator dynamic equations are used as well [14]. The niche evolution process of CVC ecological community innovation also requires mutation and selection mechanisms [15]. The formation and development of the CVC eco-community is the game behavior between large companies, startups, and other related entities. Its formation and development are also the result of the dynamic evolution of multiparty games. When there is a two-way causal relationship between a large company and a startup company under a certain feedback mechanism, the adaptive change of the large company will change the adaptability of the startup company, while the change of the startup company will further affect the change of the large company. By assessing their participation in CVC investment activities, the two parties will promote the continuous evolution of the CVC ecological community when the results of multiple rounds of game play with other entities are greater than their nonparticipation.


### 4.2. Research Hypothesis and Model Building

#### 4.2.1. Research Hypothesis

The changes in the niche of large companies and startups in the CVC ecosystem are affected by a variety of ecological factors in the symbiotic environment of venture capital. At the same time, the strategy obtained by the opponent based on the irrational selection is an important factor. Entrepreneurial enterprises will play dynamic games. First, assuming that the strategy set of MC is niche maintenance and niche expansion, the strategy set of an entrepreneurial company can be participation in competition and acceptance. In this case, there is a two-stage game in the CVC investment activity process. This can be regarded as an evolutionary game of dual population and dual strategy [16]. Second, assuming that both large companies and startups are bounded in rationality, they choose the best strategy based on their own situation and environment. Third, in the CVC ecological community, large companies, and startups make strategic adjustments based on their strategy and the external environment. A repeated game would happen as the adjustment also depends on the choices and the performance of these companies.


#### 4.2.2. Construction of Fitness Function Matrix

Assuming that the niche separation of large companies and startups does not affect them, the two types of corporate populations in their own ecological space and time have the benefits of independent innovationR1 and R2. When the MC population chooses to expand its niche through CVC activities, it can realize innovation benefits, including the benefits created by knowledge sharing as a result of sharing various resources and technology spillovers. It can be represented by λa+bΔr, where λ is the absorptive capacity coefficient of the large company population; a and b are the knowledge sharing coefficient and the technology spillover coefficient, respectively; and Δr is unit excesses benefit. If the MC expands, the EF also carries out the niche expansion, which can achieve excess returns. Both parties need to pay a certain cost during the niche expansion process. The cost paid by the large company can be expressed as C1, and the cost paid by startup company is represented by C2. There are also large companies that expand their niche, and startups choose to keep the same niche. In this case, they can get a profit e. The probability that a large company will expand its niche is p, and the probability of maintaining it is 1 − p. The probability of participating in competition based on feedback from startups is q, and the probability of maintaining the original ecology is 1 − q. The game fitness payment matrix is established in Table 1.Table 1
Niche game fitness function matrix.
Subject niche in CVCEFExpanding nicheMaintaining nicheMCExpandingR1+λa+bΔr−C1R1−C1R2+1−λa+bΔr−C2R2+eMaintainingR1+eR1R2−C2R2


### 4.3. Evolution Path Analysis

#### 4.3.1. Replicator Dynamic Equation Solving

According to the game fitness function matrix above, it can be concluded that, for the MC, which chooses to expand the niche, that is, to carry out CVC investment activities, the expected return is(4)U11=qR1+λa+bΔr−C1+1−qR1−C1=R1+qλa+bΔr−C1,U12=qR1+e+1−qR1=qe+R1,U1¯=pU11+1−pU12=pqλa+bΔr−qe−C1+qe+R1.In the same way, for the EF, the expected income and expansion of the niche expansion areU21 and U22, while the average expectation of the startup enterprise is U2¯:(5)U21=pR2+1−λa+bΔr−C2+1−p,R2−C2=R2+p1−λa+bΔr−C2,U22=pR2+e+1−pR2=e+R2,U2¯=qU21+1−qU22,=qR2+p1−λa+bΔr−C2+1−qpe+R2=qp1−λa+bΔr−pe−C2+pe+R2.According to the replicator dynamic formula of the evolutionary game, the replicator dynamic equations of large companies and startups in the CVC ecosystem can be obtained as follows:(6)Fp=dpdt=pU11−U1¯=p1−pqλa+bΔr−e−C1,Fq=dqdt=qU22−U2¯=q1−qp1−λa+bΔr−e−C2.


#### 4.3.2. Evolutionary Stability Strategies for MC

According to the dynamic equations for MC, we have(7)Fp=dpdt=pU11−U1¯=p1−pqλa+bΔr−e−C1.Three stable points of the equation can be obtained, namely,p1∗=0, p2∗=1, and p3∗=C1/λa+bΔr−e. If an evolutionary stable strategy is required, the derivative dynamic equation needs to be derived and satisfy d2p/d2t<0. We will obtain(8)d2pd2t=1−2pqλa+bΔr−e−C1.Whenq>C1/λa+bΔr−e, we get p2∗=1, an evolutionary expansion strategy, which means MC will choose niche expansion strategy. When q<C1/λa+bΔr−e, we get p1∗=0, an evolutionary stability strategy, which means MC will choose strategies to maintain their original niche. When q=C1/λa+bΔr−e, dp/dt equals zero, which is always a stable status.


#### 4.3.3. Evolutionary Stability Strategies for EF

According to dynamic equations for EF, we have(9)Fq=dqdt=qU22−U2¯=q1−qp1−λa+bΔr−e−C2.Three stable points of the equation can be obtained, namely,q1∗=0, q2∗=1, and q3∗=C2/1−λa+bΔr−e.Whenp=C2/1−λa+bΔr−e, we get dq/dt=0, with q being in stable status. When p>C2/1−λa+bΔr−e, we get dq/dt<0, which is an evolutionary expansion strategy. EF also chooses to expand its niche to enter MC’s related industries. When p<C2/1−λa+bΔr−e, we get q1∗=0, which is an evolutionary stable strategy. EF maintains its original niche.The above discussion does not consider the relationship and size of the parameters. When the combination of parameters changes, the game strategy of large enterprises and entrepreneurial enterprises in the CVC ecological community changes.


#### 4.3.4. Impact of Parameter Changes on Evolutionary Game Strategies

The first topic is about the effect of parameter changes on the evolutionary stability strategy of MC:(1)
For0<C1/λa+bΔr−e<1, evolutionary stable equilibrium is determined by two situations of q. When q>C1/λa+bΔr−e, we get p2∗=1, an evolutionary expansion strategy (EES), while when q<C1/λa+bΔr−e, we get p1∗=0, an evolutionary stable strategy (ESS).(2)
ForC1/λa+bΔr−e≥1, we always get q<C1/λa+bΔr−e, and p1∗=0, which is ESS. That is, the cost of niche expansion is high, and large companies maintain their original niche.The second topic is about the impact of changes in parameters on the evolutionary stability strategy of EF:(1)
For0<C2/1−λa+bΔr−e<1, there are two possibilities. When p>C2/1−λa+bΔr−e, we get q2∗=1, an EES. When p<C2/1−λa+bΔr−e, we get q1∗=0, an ESS.(2)
ForC2/1−λa+bΔr−e≥1, we always get p<C2/1−λa+bΔr−e, q1∗=0, which is an ESS.By a comprehensive analysis of the stability strategies of the two sides of the game analyzed above, we get five balance points, namely,O0,0,P1,0,Q0,1,R1,1=EC1/λa+bΔr−e,C2/1−λa+bΔr−e.


### 4.4. Game Process with Niche Parameters

#### 4.4.1. Evolution Strategy of MC in the CVC Ecological Community

When considering the status and momentum of large companies and startups in the CVC ecosystem, that is, the growth of large companies' innovation efforts and potential innovation capabilities, the fitness function needs to consider the status value of the large company population (T1) and potential value (S1). The game player's entrepreneurial state value is T2, and the potential value is S2. The higher the values of T1, S1, T2, and S2, the stronger the ability to obtain innovative resources and the stronger the ability to expand the niche. The matrix above can be adjusted to Table2.Table 2
Population fitness function matrix in CVC ecological community.
Subject niche in CVCEFExpanding nicheMaintaining nicheMCExpandingR1+λa+bΔr−C1R1−C1R2+1−λa+bΔr−C2R2+e+T2S2MaintainingR1+e+T1S1R1R2−C2R2The corresponding income formula is as follows:(10)U11=qR1+λa+bΔr−C1+1−qR1−C1,U12=qR1+e+T1S1+1−qR1=qe+T1S1+R1,U1¯=pU11+1−pU12=pqλa+bΔr−qe+T1S1−C1+qe+T1S1+R1.The dynamic equation is as follows:(11)Fp=dpdt=pU11−U1¯=p1−pqλa+bΔr−e+T1S1−C1.ForFp=0, the stable points are q1∗=0, q2∗=1, and q3∗=C2/1−λa+bΔr−e+T1S1:(1)
Whenq=C1/λa+bΔr−e+T1S1, dp/dt equals zero, and the value of p is stable(2)
Whenq>C1/λa+bΔr−e+T1S1, d2p/d2t<0, we obtain p2∗=1, an EES(3)
Whenq<C1/λa+bΔr−e+T1S1, d2p/d2t>0, we obtain p1∗=0, an ESS


#### 4.4.2. Evolutionary Strategies of EF

The corresponding income formula is as follows:(12)U21=pR2+1−λa+bΔr−C2+1−pR2−C2=R2+p1−λa+bΔr−C2,U22=pR2+e+T2S2+1−pR2=pe+T2S2+R2,U2¯=qU21+1−qU22=qR2+p1−λa+bΔr−C2+1−qpe+T2S2+R2=qp1−λa+bΔr−pe+T2S2−C2+pe+T2S2+R2.The dynamic equation is as follows:(13)Fq=dqdt=qU22−U2¯=q1−qp1−λa+bΔr−e+T2S2−C2.ForFq=0, the stable points are q1∗=0, q2∗=1, and q3∗=C2/1−λa+bΔr−e+T2S2:(1)
Whenp=C2/1−λa+bΔr−e+T2S2, any value of q is an ESS(2)
Whenp>C2/1−λa+bΔr−e+T2S2, we get q2∗=1, an ESS(3)
Whenp<C2/1−λa+bΔr−e+T2S2, we get q1∗=0, an ESS


#### 4.4.3. Coevolution Strategy of MC and EF in the CVC Ecological Community

By unifying the above various game results into a coordinate quadrant, we get comprehensive game process of large companies and startups in CVC ecological community in Figure 9.Figure 9
Comprehensive game process of large companies and startups in CVC ecological community after comprehensive situational factors.It can be seen from the figure that, in the regional QOPE, the evolutionary stability strategy of large companies and startups is (0,0); that is, neither party adopts the strategy of niche expansion in CVC activities. The evolutionary and stable strategies of both enterprises and startups are (1,1), which means that both large companies and startups are actively expanding their niche. However, the strategic actions of large enterprises and startups depend on the position of E. Through discussing the position ofE, the factors that affect the strategic actions of large and startups can be identified.(14)SQOPE=12×1×Ex+12×1×Ey=12Ex+Ey=12C1λa+bΔr−e+T1S1+C21−λa+bΔr−e+T2S2.As long as the probability of more actions taken by large companies and startups on both sides of the game is within SQOPE, both parties choose not to expand the niche. At this time, the evolution direction depends on SQOPE and SQRPE. When SQOPE > SQRPE, the evolution converges to point O. When SQOPE < SQRPE, the evolution converges to point B. When SQOPE = SQRPE, the probability of the two sides converging toward O or R is equal.


### 4.5. Evolution Strategy of CVC Ecological Community

Through the above analysis, 10 parameters that influence the direction of evolution are obtained. The common evolution path is discussed separately for each parameter by seeking partial derivatives:(1)
Impact ofC1andC2 on SQOPE:(15)∂S∂C1=12×1λa+bΔr−e+T1S1>0,∂S∂C2=12×11−λa+bΔre+T2S2>0.This shows that SQOPE is a monotonically increasing function for C1,C2. For MC and EF, the higher the cost of forming a CVC ecological community is, the more it tends to maintain the original niche.(2)
Impact of (a + b) on SQOPE:(16)∂S∂a=12C21−λa+bΔr−e+T2S22−C1λa+bΔr−e+T1S12.Sincea is not monotonic for SQOPE, a second-order derivative is performed:(17)∂2S∂2a=C2Δr21−λa+bΔr−e+T2S23−C1Δr3λa+bΔr−e+T1S13>0.Therefore, there is a minimum value for SQOPE.When(18)∂2S∂2a=C2Δr21−λa+bΔr−e+T2S23−C1Δr3λa+bΔr−e+T1S13=0,we obtain(19)C21−λa+bΔr−e+T2S22=C1λa+bΔr−e+T1S12.At this time, the stable strategy of MC and EF is (1,1). Both of them implement niche expansion strategies. The parameterb is derived from the above a.(3)
Impact ofT1, S1,T2, and S2 on SQOPE:(20)∂S∂T1=12C1λa+bΔr−e+T1S12>0,∂S∂S1=12C1λa+bΔr−e+T1S12>0,∂S∂T2=12C11−λa+bΔr−e+T2S22>0,∂S∂S2=12C11−λa+bΔr−e+T2S22>0.SQOPE is a monotonically increasing function of T1, S1,T2, and S2, indicating that the larger the state and potential of the niche of large companies and startups in the CVC ecosystem (that is, the technology, talents, capital, and social resources of large companies and startups), the better the foundation, and the greater the real dominance and influence that large companies and startups have on the innovation environment. It is more likely that two sides tend to maintain their original niche.(4)
The impact ofe on SQOPE:(21)∂S∂e=12C21−λa+bΔr−e+T2S22+C1λa+bΔr−e+T1S12>0.It shows that SAECO is a monotonically increasing function of e, which means that the greater the innovation income from maintaining the original niche is, the more likely the large enterprises and startups tend to maintain the original niche.(5)
The impact ofΔr on SQOPE:(22)∂S∂Δr=−121−λa+bC21−λa+bΔr−e+T2S22+λa+bC1λa+bΔr−e+T1S12<0.SQOPE is a monotonic reduction function for Δr; that is, the larger the excess returns, the larger the result of the game between the large enterprise and the entrepreneurial enterprise. Both parties choose to expand the niche strategy.(6)
The impact ofλ on SQOPE:(23)∂S∂λ=−121−λa+bC21−λa+bΔr−e+T2S22+λa+bC1λa+bΔr−e+T1S12.SQOPE is a monotonic reduction function for Δr; that is, the larger the excess returns, the larger the result of the game between the MC and the EF. Both parties choose to expand niche strategy.


## 4.1. Evolutionary Game Analysis

The symbiotic evolution between large companies and startups in the CVC ecological community will increase the adaptability of both parties and thus their respective niche. The evolutionary game theory has been used to analyze the operating mechanism of large companies and startups. Here we use evolution stability strategy to analyze the evolution path of CVC ecological community. The strategy adjustment process, trends, and stability of large players and startups in priority game players are considered. ESS evolutionary stability strategy and Taylor and Jonker's replicator dynamic equations are used as well [14]. The niche evolution process of CVC ecological community innovation also requires mutation and selection mechanisms [15]. The formation and development of the CVC eco-community is the game behavior between large companies, startups, and other related entities. Its formation and development are also the result of the dynamic evolution of multiparty games. When there is a two-way causal relationship between a large company and a startup company under a certain feedback mechanism, the adaptive change of the large company will change the adaptability of the startup company, while the change of the startup company will further affect the change of the large company. By assessing their participation in CVC investment activities, the two parties will promote the continuous evolution of the CVC ecological community when the results of multiple rounds of game play with other entities are greater than their nonparticipation.


## 4.2. Research Hypothesis and Model Building

### 4.2.1. Research Hypothesis

The changes in the niche of large companies and startups in the CVC ecosystem are affected by a variety of ecological factors in the symbiotic environment of venture capital. At the same time, the strategy obtained by the opponent based on the irrational selection is an important factor. Entrepreneurial enterprises will play dynamic games. First, assuming that the strategy set of MC is niche maintenance and niche expansion, the strategy set of an entrepreneurial company can be participation in competition and acceptance. In this case, there is a two-stage game in the CVC investment activity process. This can be regarded as an evolutionary game of dual population and dual strategy [16]. Second, assuming that both large companies and startups are bounded in rationality, they choose the best strategy based on their own situation and environment. Third, in the CVC ecological community, large companies, and startups make strategic adjustments based on their strategy and the external environment. A repeated game would happen as the adjustment also depends on the choices and the performance of these companies.


### 4.2.2. Construction of Fitness Function Matrix

Assuming that the niche separation of large companies and startups does not affect them, the two types of corporate populations in their own ecological space and time have the benefits of independent innovationR1 and R2. When the MC population chooses to expand its niche through CVC activities, it can realize innovation benefits, including the benefits created by knowledge sharing as a result of sharing various resources and technology spillovers. It can be represented by λa+bΔr, where λ is the absorptive capacity coefficient of the large company population; a and b are the knowledge sharing coefficient and the technology spillover coefficient, respectively; and Δr is unit excesses benefit. If the MC expands, the EF also carries out the niche expansion, which can achieve excess returns. Both parties need to pay a certain cost during the niche expansion process. The cost paid by the large company can be expressed as C1, and the cost paid by startup company is represented by C2. There are also large companies that expand their niche, and startups choose to keep the same niche. In this case, they can get a profit e. The probability that a large company will expand its niche is p, and the probability of maintaining it is 1 − p. The probability of participating in competition based on feedback from startups is q, and the probability of maintaining the original ecology is 1 − q. The game fitness payment matrix is established in Table 1.Table 1
Niche game fitness function matrix.
Subject niche in CVCEFExpanding nicheMaintaining nicheMCExpandingR1+λa+bΔr−C1R1−C1R2+1−λa+bΔr−C2R2+eMaintainingR1+eR1R2−C2R2


## 4.2.1. Research Hypothesis

The changes in the niche of large companies and startups in the CVC ecosystem are affected by a variety of ecological factors in the symbiotic environment of venture capital. At the same time, the strategy obtained by the opponent based on the irrational selection is an important factor. Entrepreneurial enterprises will play dynamic games. First, assuming that the strategy set of MC is niche maintenance and niche expansion, the strategy set of an entrepreneurial company can be participation in competition and acceptance. In this case, there is a two-stage game in the CVC investment activity process. This can be regarded as an evolutionary game of dual population and dual strategy [16]. Second, assuming that both large companies and startups are bounded in rationality, they choose the best strategy based on their own situation and environment. Third, in the CVC ecological community, large companies, and startups make strategic adjustments based on their strategy and the external environment. A repeated game would happen as the adjustment also depends on the choices and the performance of these companies.


## 4.2.2. Construction of Fitness Function Matrix

Assuming that the niche separation of large companies and startups does not affect them, the two types of corporate populations in their own ecological space and time have the benefits of independent innovationR1 and R2. When the MC population chooses to expand its niche through CVC activities, it can realize innovation benefits, including the benefits created by knowledge sharing as a result of sharing various resources and technology spillovers. It can be represented by λa+bΔr, where λ is the absorptive capacity coefficient of the large company population; a and b are the knowledge sharing coefficient and the technology spillover coefficient, respectively; and Δr is unit excesses benefit. If the MC expands, the EF also carries out the niche expansion, which can achieve excess returns. Both parties need to pay a certain cost during the niche expansion process. The cost paid by the large company can be expressed as C1, and the cost paid by startup company is represented by C2. There are also large companies that expand their niche, and startups choose to keep the same niche. In this case, they can get a profit e. The probability that a large company will expand its niche is p, and the probability of maintaining it is 1 − p. The probability of participating in competition based on feedback from startups is q, and the probability of maintaining the original ecology is 1 − q. The game fitness payment matrix is established in Table 1.Table 1
Niche game fitness function matrix.
Subject niche in CVCEFExpanding nicheMaintaining nicheMCExpandingR1+λa+bΔr−C1R1−C1R2+1−λa+bΔr−C2R2+eMaintainingR1+eR1R2−C2R2


## 4.3. Evolution Path Analysis

### 4.3.1. Replicator Dynamic Equation Solving

According to the game fitness function matrix above, it can be concluded that, for the MC, which chooses to expand the niche, that is, to carry out CVC investment activities, the expected return is(4)U11=qR1+λa+bΔr−C1+1−qR1−C1=R1+qλa+bΔr−C1,U12=qR1+e+1−qR1=qe+R1,U1¯=pU11+1−pU12=pqλa+bΔr−qe−C1+qe+R1.In the same way, for the EF, the expected income and expansion of the niche expansion areU21 and U22, while the average expectation of the startup enterprise is U2¯:(5)U21=pR2+1−λa+bΔr−C2+1−p,R2−C2=R2+p1−λa+bΔr−C2,U22=pR2+e+1−pR2=e+R2,U2¯=qU21+1−qU22,=qR2+p1−λa+bΔr−C2+1−qpe+R2=qp1−λa+bΔr−pe−C2+pe+R2.According to the replicator dynamic formula of the evolutionary game, the replicator dynamic equations of large companies and startups in the CVC ecosystem can be obtained as follows:(6)Fp=dpdt=pU11−U1¯=p1−pqλa+bΔr−e−C1,Fq=dqdt=qU22−U2¯=q1−qp1−λa+bΔr−e−C2.


### 4.3.2. Evolutionary Stability Strategies for MC

According to the dynamic equations for MC, we have(7)Fp=dpdt=pU11−U1¯=p1−pqλa+bΔr−e−C1.Three stable points of the equation can be obtained, namely,p1∗=0, p2∗=1, and p3∗=C1/λa+bΔr−e. If an evolutionary stable strategy is required, the derivative dynamic equation needs to be derived and satisfy d2p/d2t<0. We will obtain(8)d2pd2t=1−2pqλa+bΔr−e−C1.Whenq>C1/λa+bΔr−e, we get p2∗=1, an evolutionary expansion strategy, which means MC will choose niche expansion strategy. When q<C1/λa+bΔr−e, we get p1∗=0, an evolutionary stability strategy, which means MC will choose strategies to maintain their original niche. When q=C1/λa+bΔr−e, dp/dt equals zero, which is always a stable status.


### 4.3.3. Evolutionary Stability Strategies for EF

According to dynamic equations for EF, we have(9)Fq=dqdt=qU22−U2¯=q1−qp1−λa+bΔr−e−C2.Three stable points of the equation can be obtained, namely,q1∗=0, q2∗=1, and q3∗=C2/1−λa+bΔr−e.Whenp=C2/1−λa+bΔr−e, we get dq/dt=0, with q being in stable status. When p>C2/1−λa+bΔr−e, we get dq/dt<0, which is an evolutionary expansion strategy. EF also chooses to expand its niche to enter MC’s related industries. When p<C2/1−λa+bΔr−e, we get q1∗=0, which is an evolutionary stable strategy. EF maintains its original niche.The above discussion does not consider the relationship and size of the parameters. When the combination of parameters changes, the game strategy of large enterprises and entrepreneurial enterprises in the CVC ecological community changes.


### 4.3.4. Impact of Parameter Changes on Evolutionary Game Strategies

The first topic is about the effect of parameter changes on the evolutionary stability strategy of MC:(1)
For0<C1/λa+bΔr−e<1, evolutionary stable equilibrium is determined by two situations of q. When q>C1/λa+bΔr−e, we get p2∗=1, an evolutionary expansion strategy (EES), while when q<C1/λa+bΔr−e, we get p1∗=0, an evolutionary stable strategy (ESS).(2)
ForC1/λa+bΔr−e≥1, we always get q<C1/λa+bΔr−e, and p1∗=0, which is ESS. That is, the cost of niche expansion is high, and large companies maintain their original niche.The second topic is about the impact of changes in parameters on the evolutionary stability strategy of EF:(1)
For0<C2/1−λa+bΔr−e<1, there are two possibilities. When p>C2/1−λa+bΔr−e, we get q2∗=1, an EES. When p<C2/1−λa+bΔr−e, we get q1∗=0, an ESS.(2)
ForC2/1−λa+bΔr−e≥1, we always get p<C2/1−λa+bΔr−e, q1∗=0, which is an ESS.By a comprehensive analysis of the stability strategies of the two sides of the game analyzed above, we get five balance points, namely,O0,0,P1,0,Q0,1,R1,1=EC1/λa+bΔr−e,C2/1−λa+bΔr−e.


## 4.3.1. Replicator Dynamic Equation Solving

According to the game fitness function matrix above, it can be concluded that, for the MC, which chooses to expand the niche, that is, to carry out CVC investment activities, the expected return is(4)U11=qR1+λa+bΔr−C1+1−qR1−C1=R1+qλa+bΔr−C1,U12=qR1+e+1−qR1=qe+R1,U1¯=pU11+1−pU12=pqλa+bΔr−qe−C1+qe+R1.In the same way, for the EF, the expected income and expansion of the niche expansion areU21 and U22, while the average expectation of the startup enterprise is U2¯:(5)U21=pR2+1−λa+bΔr−C2+1−p,R2−C2=R2+p1−λa+bΔr−C2,U22=pR2+e+1−pR2=e+R2,U2¯=qU21+1−qU22,=qR2+p1−λa+bΔr−C2+1−qpe+R2=qp1−λa+bΔr−pe−C2+pe+R2.According to the replicator dynamic formula of the evolutionary game, the replicator dynamic equations of large companies and startups in the CVC ecosystem can be obtained as follows:(6)Fp=dpdt=pU11−U1¯=p1−pqλa+bΔr−e−C1,Fq=dqdt=qU22−U2¯=q1−qp1−λa+bΔr−e−C2.


## 4.3.2. Evolutionary Stability Strategies for MC

According to the dynamic equations for MC, we have(7)Fp=dpdt=pU11−U1¯=p1−pqλa+bΔr−e−C1.Three stable points of the equation can be obtained, namely,p1∗=0, p2∗=1, and p3∗=C1/λa+bΔr−e. If an evolutionary stable strategy is required, the derivative dynamic equation needs to be derived and satisfy d2p/d2t<0. We will obtain(8)d2pd2t=1−2pqλa+bΔr−e−C1.Whenq>C1/λa+bΔr−e, we get p2∗=1, an evolutionary expansion strategy, which means MC will choose niche expansion strategy. When q<C1/λa+bΔr−e, we get p1∗=0, an evolutionary stability strategy, which means MC will choose strategies to maintain their original niche. When q=C1/λa+bΔr−e, dp/dt equals zero, which is always a stable status.


## 4.3.3. Evolutionary Stability Strategies for EF

According to dynamic equations for EF, we have(9)Fq=dqdt=qU22−U2¯=q1−qp1−λa+bΔr−e−C2.Three stable points of the equation can be obtained, namely,q1∗=0, q2∗=1, and q3∗=C2/1−λa+bΔr−e.Whenp=C2/1−λa+bΔr−e, we get dq/dt=0, with q being in stable status. When p>C2/1−λa+bΔr−e, we get dq/dt<0, which is an evolutionary expansion strategy. EF also chooses to expand its niche to enter MC’s related industries. When p<C2/1−λa+bΔr−e, we get q1∗=0, which is an evolutionary stable strategy. EF maintains its original niche.The above discussion does not consider the relationship and size of the parameters. When the combination of parameters changes, the game strategy of large enterprises and entrepreneurial enterprises in the CVC ecological community changes.


## 4.3.4. Impact of Parameter Changes on Evolutionary Game Strategies

The first topic is about the effect of parameter changes on the evolutionary stability strategy of MC:(1)
For0<C1/λa+bΔr−e<1, evolutionary stable equilibrium is determined by two situations of q. When q>C1/λa+bΔr−e, we get p2∗=1, an evolutionary expansion strategy (EES), while when q<C1/λa+bΔr−e, we get p1∗=0, an evolutionary stable strategy (ESS).(2)
ForC1/λa+bΔr−e≥1, we always get q<C1/λa+bΔr−e, and p1∗=0, which is ESS. That is, the cost of niche expansion is high, and large companies maintain their original niche.The second topic is about the impact of changes in parameters on the evolutionary stability strategy of EF:(1)
For0<C2/1−λa+bΔr−e<1, there are two possibilities. When p>C2/1−λa+bΔr−e, we get q2∗=1, an EES. When p<C2/1−λa+bΔr−e, we get q1∗=0, an ESS.(2)
ForC2/1−λa+bΔr−e≥1, we always get p<C2/1−λa+bΔr−e, q1∗=0, which is an ESS.By a comprehensive analysis of the stability strategies of the two sides of the game analyzed above, we get five balance points, namely,O0,0,P1,0,Q0,1,R1,1=EC1/λa+bΔr−e,C2/1−λa+bΔr−e.


## 4.4. Game Process with Niche Parameters

### 4.4.1. Evolution Strategy of MC in the CVC Ecological Community

When considering the status and momentum of large companies and startups in the CVC ecosystem, that is, the growth of large companies' innovation efforts and potential innovation capabilities, the fitness function needs to consider the status value of the large company population (T1) and potential value (S1). The game player's entrepreneurial state value is T2, and the potential value is S2. The higher the values of T1, S1, T2, and S2, the stronger the ability to obtain innovative resources and the stronger the ability to expand the niche. The matrix above can be adjusted to Table2.Table 2
Population fitness function matrix in CVC ecological community.
Subject niche in CVCEFExpanding nicheMaintaining nicheMCExpandingR1+λa+bΔr−C1R1−C1R2+1−λa+bΔr−C2R2+e+T2S2MaintainingR1+e+T1S1R1R2−C2R2The corresponding income formula is as follows:(10)U11=qR1+λa+bΔr−C1+1−qR1−C1,U12=qR1+e+T1S1+1−qR1=qe+T1S1+R1,U1¯=pU11+1−pU12=pqλa+bΔr−qe+T1S1−C1+qe+T1S1+R1.The dynamic equation is as follows:(11)Fp=dpdt=pU11−U1¯=p1−pqλa+bΔr−e+T1S1−C1.ForFp=0, the stable points are q1∗=0, q2∗=1, and q3∗=C2/1−λa+bΔr−e+T1S1:(1)
Whenq=C1/λa+bΔr−e+T1S1, dp/dt equals zero, and the value of p is stable(2)
Whenq>C1/λa+bΔr−e+T1S1, d2p/d2t<0, we obtain p2∗=1, an EES(3)
Whenq<C1/λa+bΔr−e+T1S1, d2p/d2t>0, we obtain p1∗=0, an ESS


### 4.4.2. Evolutionary Strategies of EF

The corresponding income formula is as follows:(12)U21=pR2+1−λa+bΔr−C2+1−pR2−C2=R2+p1−λa+bΔr−C2,U22=pR2+e+T2S2+1−pR2=pe+T2S2+R2,U2¯=qU21+1−qU22=qR2+p1−λa+bΔr−C2+1−qpe+T2S2+R2=qp1−λa+bΔr−pe+T2S2−C2+pe+T2S2+R2.The dynamic equation is as follows:(13)Fq=dqdt=qU22−U2¯=q1−qp1−λa+bΔr−e+T2S2−C2.ForFq=0, the stable points are q1∗=0, q2∗=1, and q3∗=C2/1−λa+bΔr−e+T2S2:(1)
Whenp=C2/1−λa+bΔr−e+T2S2, any value of q is an ESS(2)
Whenp>C2/1−λa+bΔr−e+T2S2, we get q2∗=1, an ESS(3)
Whenp<C2/1−λa+bΔr−e+T2S2, we get q1∗=0, an ESS


### 4.4.3. Coevolution Strategy of MC and EF in the CVC Ecological Community

By unifying the above various game results into a coordinate quadrant, we get comprehensive game process of large companies and startups in CVC ecological community in Figure 9.Figure 9
Comprehensive game process of large companies and startups in CVC ecological community after comprehensive situational factors.It can be seen from the figure that, in the regional QOPE, the evolutionary stability strategy of large companies and startups is (0,0); that is, neither party adopts the strategy of niche expansion in CVC activities. The evolutionary and stable strategies of both enterprises and startups are (1,1), which means that both large companies and startups are actively expanding their niche. However, the strategic actions of large enterprises and startups depend on the position of E. Through discussing the position ofE, the factors that affect the strategic actions of large and startups can be identified.(14)SQOPE=12×1×Ex+12×1×Ey=12Ex+Ey=12C1λa+bΔr−e+T1S1+C21−λa+bΔr−e+T2S2.As long as the probability of more actions taken by large companies and startups on both sides of the game is within SQOPE, both parties choose not to expand the niche. At this time, the evolution direction depends on SQOPE and SQRPE. When SQOPE > SQRPE, the evolution converges to point O. When SQOPE < SQRPE, the evolution converges to point B. When SQOPE = SQRPE, the probability of the two sides converging toward O or R is equal.


## 4.4.1. Evolution Strategy of MC in the CVC Ecological Community

When considering the status and momentum of large companies and startups in the CVC ecosystem, that is, the growth of large companies' innovation efforts and potential innovation capabilities, the fitness function needs to consider the status value of the large company population (T1) and potential value (S1). The game player's entrepreneurial state value is T2, and the potential value is S2. The higher the values of T1, S1, T2, and S2, the stronger the ability to obtain innovative resources and the stronger the ability to expand the niche. The matrix above can be adjusted to Table2.Table 2
Population fitness function matrix in CVC ecological community.
Subject niche in CVCEFExpanding nicheMaintaining nicheMCExpandingR1+λa+bΔr−C1R1−C1R2+1−λa+bΔr−C2R2+e+T2S2MaintainingR1+e+T1S1R1R2−C2R2The corresponding income formula is as follows:(10)U11=qR1+λa+bΔr−C1+1−qR1−C1,U12=qR1+e+T1S1+1−qR1=qe+T1S1+R1,U1¯=pU11+1−pU12=pqλa+bΔr−qe+T1S1−C1+qe+T1S1+R1.The dynamic equation is as follows:(11)Fp=dpdt=pU11−U1¯=p1−pqλa+bΔr−e+T1S1−C1.ForFp=0, the stable points are q1∗=0, q2∗=1, and q3∗=C2/1−λa+bΔr−e+T1S1:(1)
Whenq=C1/λa+bΔr−e+T1S1, dp/dt equals zero, and the value of p is stable(2)
Whenq>C1/λa+bΔr−e+T1S1, d2p/d2t<0, we obtain p2∗=1, an EES(3)
Whenq<C1/λa+bΔr−e+T1S1, d2p/d2t>0, we obtain p1∗=0, an ESS


## 4.4.2. Evolutionary Strategies of EF

The corresponding income formula is as follows:(12)U21=pR2+1−λa+bΔr−C2+1−pR2−C2=R2+p1−λa+bΔr−C2,U22=pR2+e+T2S2+1−pR2=pe+T2S2+R2,U2¯=qU21+1−qU22=qR2+p1−λa+bΔr−C2+1−qpe+T2S2+R2=qp1−λa+bΔr−pe+T2S2−C2+pe+T2S2+R2.The dynamic equation is as follows:(13)Fq=dqdt=qU22−U2¯=q1−qp1−λa+bΔr−e+T2S2−C2.ForFq=0, the stable points are q1∗=0, q2∗=1, and q3∗=C2/1−λa+bΔr−e+T2S2:(1)
Whenp=C2/1−λa+bΔr−e+T2S2, any value of q is an ESS(2)
Whenp>C2/1−λa+bΔr−e+T2S2, we get q2∗=1, an ESS(3)
Whenp<C2/1−λa+bΔr−e+T2S2, we get q1∗=0, an ESS


## 4.4.3. Coevolution Strategy of MC and EF in the CVC Ecological Community

By unifying the above various game results into a coordinate quadrant, we get comprehensive game process of large companies and startups in CVC ecological community in Figure 9.Figure 9
Comprehensive game process of large companies and startups in CVC ecological community after comprehensive situational factors.It can be seen from the figure that, in the regional QOPE, the evolutionary stability strategy of large companies and startups is (0,0); that is, neither party adopts the strategy of niche expansion in CVC activities. The evolutionary and stable strategies of both enterprises and startups are (1,1), which means that both large companies and startups are actively expanding their niche. However, the strategic actions of large enterprises and startups depend on the position of E. Through discussing the position ofE, the factors that affect the strategic actions of large and startups can be identified.(14)SQOPE=12×1×Ex+12×1×Ey=12Ex+Ey=12C1λa+bΔr−e+T1S1+C21−λa+bΔr−e+T2S2.As long as the probability of more actions taken by large companies and startups on both sides of the game is within SQOPE, both parties choose not to expand the niche. At this time, the evolution direction depends on SQOPE and SQRPE. When SQOPE > SQRPE, the evolution converges to point O. When SQOPE < SQRPE, the evolution converges to point B. When SQOPE = SQRPE, the probability of the two sides converging toward O or R is equal.


## 4.5. Evolution Strategy of CVC Ecological Community

Through the above analysis, 10 parameters that influence the direction of evolution are obtained. The common evolution path is discussed separately for each parameter by seeking partial derivatives:(1)
Impact ofC1andC2 on SQOPE:(15)∂S∂C1=12×1λa+bΔr−e+T1S1>0,∂S∂C2=12×11−λa+bΔre+T2S2>0.This shows that SQOPE is a monotonically increasing function for C1,C2. For MC and EF, the higher the cost of forming a CVC ecological community is, the more it tends to maintain the original niche.(2)
Impact of (a + b) on SQOPE:(16)∂S∂a=12C21−λa+bΔr−e+T2S22−C1λa+bΔr−e+T1S12.Sincea is not monotonic for SQOPE, a second-order derivative is performed:(17)∂2S∂2a=C2Δr21−λa+bΔr−e+T2S23−C1Δr3λa+bΔr−e+T1S13>0.Therefore, there is a minimum value for SQOPE.When(18)∂2S∂2a=C2Δr21−λa+bΔr−e+T2S23−C1Δr3λa+bΔr−e+T1S13=0,we obtain(19)C21−λa+bΔr−e+T2S22=C1λa+bΔr−e+T1S12.At this time, the stable strategy of MC and EF is (1,1). Both of them implement niche expansion strategies. The parameterb is derived from the above a.(3)
Impact ofT1, S1,T2, and S2 on SQOPE:(20)∂S∂T1=12C1λa+bΔr−e+T1S12>0,∂S∂S1=12C1λa+bΔr−e+T1S12>0,∂S∂T2=12C11−λa+bΔr−e+T2S22>0,∂S∂S2=12C11−λa+bΔr−e+T2S22>0.SQOPE is a monotonically increasing function of T1, S1,T2, and S2, indicating that the larger the state and potential of the niche of large companies and startups in the CVC ecosystem (that is, the technology, talents, capital, and social resources of large companies and startups), the better the foundation, and the greater the real dominance and influence that large companies and startups have on the innovation environment. It is more likely that two sides tend to maintain their original niche.(4)
The impact ofe on SQOPE:(21)∂S∂e=12C21−λa+bΔr−e+T2S22+C1λa+bΔr−e+T1S12>0.It shows that SAECO is a monotonically increasing function of e, which means that the greater the innovation income from maintaining the original niche is, the more likely the large enterprises and startups tend to maintain the original niche.(5)
The impact ofΔr on SQOPE:(22)∂S∂Δr=−121−λa+bC21−λa+bΔr−e+T2S22+λa+bC1λa+bΔr−e+T1S12<0.SQOPE is a monotonic reduction function for Δr; that is, the larger the excess returns, the larger the result of the game between the large enterprise and the entrepreneurial enterprise. Both parties choose to expand the niche strategy.(6)
The impact ofλ on SQOPE:(23)∂S∂λ=−121−λa+bC21−λa+bΔr−e+T2S22+λa+bC1λa+bΔr−e+T1S12.SQOPE is a monotonic reduction function for Δr; that is, the larger the excess returns, the larger the result of the game between the MC and the EF. Both parties choose to expand niche strategy.


## 5. Optimization Strategy for CVC Niche Evolution in Ecological Community

The evolution of the ecological niche of the CVC ecological community is subject to the combined effects of multiple mechanisms, and competition and symbiosis are affected by interest-driven and ecological balance. The benefit-driven mechanism is the inherent growth mechanism of the CVC ecological community under a certain environment of innovation and entrepreneurship. The source of motivation is the maximum pursuit of individual interests by large enterprises and entrepreneurial enterprises. Large enterprise populations and entrepreneurial enterprise populations integrate related resources through horizontal symbiosis, vertical symbiosis, or dynamic alliances to eliminate or reduce resource bottlenecks and promote the smooth development of large enterprises and individual entrepreneurial enterprises. Therefore, the CVC ecological community, as a core part of the innovation and entrepreneurship ecosystem, presents a nonlinear and exponential growth trend. As a self-protection mechanism of the ecological niche of the CVC ecological community, the ecological balance mechanism can ensure the self-sustainment and steady evolution of the CVC niche. In addition to the innovation, entrepreneurship, and ecological resources, the growth of the population is affected by material, energy, and information accumulation but is also balanced and stabilized by self-organization and self-regulation because of environmental factors.The CVC ecological niche represents the status of the CVC ecological community with large companies and startups as the core to own and control human resources, technical resources, capital, and other social resources, as well as the adaptability to the innovative ecological environment and the comprehensive use of various resources. The healthy growth of CVC ecological communities requires specific analysis of internal and external environmental ecological factors, including limiting factors and interest factors. The limiting factor is the bottleneck that restricts the development of the CVC ecological community. Both the large enterprise population and the entrepreneurial enterprise population focus on easing the constraint of the limiting factor to enhance the evolution capacity of the entire CVC ecological community. At the same time, the CVC ecological community also has benefit factors as its driving force for development. The enhanced interest factors of core populations can enable their respective niche evolution to achieve sustainable competitiveness and become an irreproducible and far-reaching advantage through the formation of core competitiveness. The large enterprise population and entrepreneurial enterprise population in the CVC ecological community are usually in different positions in the value chain. Therefore, the CVC ecological community should make full use of the symbiotic resources on the value chain, unblock the symbiotic channels, or form strategic alliances or virtual industries to achieve coevolution for the niche. The large enterprise population and the entrepreneurial enterprise population within the CVC ecological community implement corresponding niche separation strategies, niche expansion strategies, niche K-R strategies, and niche alliance strategies.


### 5.1. CVC Niche Separation Strategy

If the niche overlap between large enterprises and startups in the CVC ecological community indicates that there is a certain industry correlation between large companies and startups, the competition is fierce when the niche overlaps between the two. In order to obtain more living space, the two sides can implement niche separation strategy. Large enterprises and startups can find the most suitable position for their own development through CVC activities. The core of niche separation is to (a) use and integrate innovation and entrepreneurial resources, (b) choose a combination of ecological factors that are different from those of competitors, (c) have a stronger advantage at a certain position of talent, technology, capital, and social resource gradients, and (d) achieve heterogeneity and symmetry. Whether it is a mature large enterprise or a startup enterprise, it can choose two different niche separation strategies: specialization strategy and generalization strategy. The specialization strategy is for narrow-niche enterprises, which can provide a small range of products and services with characteristics to form an agglomeration strategy to concentrate the various resources of species in a limited ecological space, that is, to focus on a certain step in the value chain, so that the niche overlap with other species is reduced. The generalized strategy is similar to the no-difference strategy for relatively wide niche companies, and the risks are relatively small.In the CVC ecological community, whether large companies and startups choose specialization or generalization strategies is related to the richness of resources they can use. Generalization strategies can provide more survival for large companies with strong competitiveness. However, early stage startups, which have limted resources while still implementing generalisation strategies, would easily fail or be acquired by large companies. . Therefore, for startup companies, specialization strategies are more conducive to maintaining their own niche and reducing the ecology overlap with large enterprises, to reduce competition. Startups in the CVC eco-community can also consider adopting a niche separation strategy from the time, space, and target market dimensions.


### 5.2. CVC Niche Expansion Strategy

The investment of mature large enterprises in startup enterprises through CVC activities is a niche expansion strategy. It uses open-ended innovation through venture capital to open up new resource spaces, acquire innovative technologies, and thus achieve the purpose of expanding the niche. They aim to alleviate the competitive pressure brought by overlapping niche. For large enterprises, the introduction of new and efficient ecological elements is their original intention when choosing CVC. It is also an effective means of exploring and developing suitable options for their own development so that they can acquire financial benefits. The introduction of new ecological elements can improve the utilization of various resources in the innovation and entrepreneurship ecosystem. Due to the obvious industry attributes of CVC and the high degree of innovation in the high-tech industry, the technology has a high rate of change; i.e., products and technologies will be updated faster. The uncertainty of independent research and development is high, so large enterprises need to expand their niche through CVC. For large enterprises and startups with weak innovation ability, weak interorganizational learning ability, and low absorptive capacity and involvement, especially for large companies, it is worthwhile to raise the basic niche or explore potential niche through CVC activities [17].


### 5.3. CVC Niche K-R Strategy

Ray proposed a niche selection strategy. The K strategy indicates that, by increasing competitiveness, improving resource utilization efficiency, and increasing the environmental capacity of species in a stable environment, a higher saturation density can be achieved. TheR strategy means that, by breeding in large numbers, new offspring can be adapted to the unstable environment, thereby identifying its own niche [18].The choice of K strategy will be limited by the environment. When the niche develops to a certain degree, it will reach the limit of affordability. In the CVC ecological community, the development of large enterprise populations also follows the KR strategy. The large enterprise population of the K strategy is characterized by a low reproduction rate and slow growth, but it can achieve strategic goals through CVC and continuously adapt to new environmental changes. It has unique core competitiveness in related industries. Its products and services are not easily copied and imitated. When large enterprises become the leading companies in an industry, environmental resources will be the biggest obstacle to their development [19]. The startups of R strategy are usually small in size, are not constrained by the environment, and have a fast reproduction capacity. When they grow to a certain degree, the growth rate also starts to decline.The CVC ecological community uses theR strategy and the K strategy, respectively. The abscissa indicates the size of niche space occupied by the large enterprises and startups in the ecological community at time t, while the ordinate represents the size of the niche space occupied by species at time t + 1. The dotted line indicates that the size of the niche space has not changed (Nt+1/Nt=1). The part above the dotted line indicates that the ecology of large enterprises or startups has become larger; that is, Nt+1>Nt. The curve below the dotted line indicates that the niche space has become smaller; that is Nt+1<Nt (Figure 10).Figure 10
Coevolution of niche-cooperation relationships in CVC ecological communities.There are two intersections between the growth curve and the dotted line for K strategy.X is an unstable equilibrium point [20]. There may be two situations for large enterprises or startups at point X. First, when the CVC ecological community survives, there are large niche spaces that have not been occupied yet. Companies using K strategy to grow rapidly. Second, the overall space of the CVC ecological community has continued to shrink during the recession period, until the K strategy companies die out. When it is at a stable point, it indicates the maximum capacity of the ecosystem space and the maximum market capacity of technology, talent, capital, social resources, etc. When the K strategy prevents the individual from falling below stability, the scale is expanded to achieve stability. When the K strategy enterprise is above the stability point, its downsizing resumes [21]. The sustainable development of the CVC eco-community can be achieved if the large enterprise population and the entrepreneurial enterprise population in the CVC eco-community can adjust the niche countermeasures in a timely and accurate manner at different stages in the development process.


### 5.4. CVC Niche Alliance Strategy

In the CVC ecological community, large companies and startups can expand their niche by establishing a mutually beneficial symbiotic relationship. This strategy is called the niche alliance strategy. When the weaker startups and the stronger large companies can improve their respective competitiveness through symbiotic relationships, symbiotic parties in the CVC ecosystem can either choose their own appropriate niche or expand the boundaries of the entire ecological community from the perspective of enhancing the symbiotic system, promoting the metabolism of the entire CVC ecological community based on innovation. If the implementation of the niche alliance strategy requires the evaluation of their respective niche, the niche overlap and market crossover of both sides should be minimized to avoid parasitic or favorable symbiosis and form conflicts of interest [22]. Large enterprises and startups can seek intersections, that is, new requirements between the two sides. They can use the positive feedback effect of the innovation and entrepreneurship environment to create higher-level niche that is beneficial to both sides and can realize the coevolution of the niche. The main motivation of CVC activities is that large enterprises need to seek technological progress. Entrepreneurs in small and medium habitats in the industry can obtain more cooperation resources through the form of CVC, so that they can expand their survival through cooperative technological innovation, management innovation, and differentiated service innovation. In this case, they can expand the width of the niche and then penetrate or embed other industries. The formation and evolution of large enterprises and entrepreneurial enterprises in the CVC ecological community will also generate greater benefits in their own or other fields.


## 5.1. CVC Niche Separation Strategy

If the niche overlap between large enterprises and startups in the CVC ecological community indicates that there is a certain industry correlation between large companies and startups, the competition is fierce when the niche overlaps between the two. In order to obtain more living space, the two sides can implement niche separation strategy. Large enterprises and startups can find the most suitable position for their own development through CVC activities. The core of niche separation is to (a) use and integrate innovation and entrepreneurial resources, (b) choose a combination of ecological factors that are different from those of competitors, (c) have a stronger advantage at a certain position of talent, technology, capital, and social resource gradients, and (d) achieve heterogeneity and symmetry. Whether it is a mature large enterprise or a startup enterprise, it can choose two different niche separation strategies: specialization strategy and generalization strategy. The specialization strategy is for narrow-niche enterprises, which can provide a small range of products and services with characteristics to form an agglomeration strategy to concentrate the various resources of species in a limited ecological space, that is, to focus on a certain step in the value chain, so that the niche overlap with other species is reduced. The generalized strategy is similar to the no-difference strategy for relatively wide niche companies, and the risks are relatively small.In the CVC ecological community, whether large companies and startups choose specialization or generalization strategies is related to the richness of resources they can use. Generalization strategies can provide more survival for large companies with strong competitiveness. However, early stage startups, which have limted resources while still implementing generalisation strategies, would easily fail or be acquired by large companies. . Therefore, for startup companies, specialization strategies are more conducive to maintaining their own niche and reducing the ecology overlap with large enterprises, to reduce competition. Startups in the CVC eco-community can also consider adopting a niche separation strategy from the time, space, and target market dimensions.


## 5.2. CVC Niche Expansion Strategy

The investment of mature large enterprises in startup enterprises through CVC activities is a niche expansion strategy. It uses open-ended innovation through venture capital to open up new resource spaces, acquire innovative technologies, and thus achieve the purpose of expanding the niche. They aim to alleviate the competitive pressure brought by overlapping niche. For large enterprises, the introduction of new and efficient ecological elements is their original intention when choosing CVC. It is also an effective means of exploring and developing suitable options for their own development so that they can acquire financial benefits. The introduction of new ecological elements can improve the utilization of various resources in the innovation and entrepreneurship ecosystem. Due to the obvious industry attributes of CVC and the high degree of innovation in the high-tech industry, the technology has a high rate of change; i.e., products and technologies will be updated faster. The uncertainty of independent research and development is high, so large enterprises need to expand their niche through CVC. For large enterprises and startups with weak innovation ability, weak interorganizational learning ability, and low absorptive capacity and involvement, especially for large companies, it is worthwhile to raise the basic niche or explore potential niche through CVC activities [17].


## 5.3. CVC Niche K-R Strategy

Ray proposed a niche selection strategy. The K strategy indicates that, by increasing competitiveness, improving resource utilization efficiency, and increasing the environmental capacity of species in a stable environment, a higher saturation density can be achieved. TheR strategy means that, by breeding in large numbers, new offspring can be adapted to the unstable environment, thereby identifying its own niche [18].The choice of K strategy will be limited by the environment. When the niche develops to a certain degree, it will reach the limit of affordability. In the CVC ecological community, the development of large enterprise populations also follows the KR strategy. The large enterprise population of the K strategy is characterized by a low reproduction rate and slow growth, but it can achieve strategic goals through CVC and continuously adapt to new environmental changes. It has unique core competitiveness in related industries. Its products and services are not easily copied and imitated. When large enterprises become the leading companies in an industry, environmental resources will be the biggest obstacle to their development [19]. The startups of R strategy are usually small in size, are not constrained by the environment, and have a fast reproduction capacity. When they grow to a certain degree, the growth rate also starts to decline.The CVC ecological community uses theR strategy and the K strategy, respectively. The abscissa indicates the size of niche space occupied by the large enterprises and startups in the ecological community at time t, while the ordinate represents the size of the niche space occupied by species at time t + 1. The dotted line indicates that the size of the niche space has not changed (Nt+1/Nt=1). The part above the dotted line indicates that the ecology of large enterprises or startups has become larger; that is, Nt+1>Nt. The curve below the dotted line indicates that the niche space has become smaller; that is Nt+1<Nt (Figure 10).Figure 10
Coevolution of niche-cooperation relationships in CVC ecological communities.There are two intersections between the growth curve and the dotted line for K strategy.X is an unstable equilibrium point [20]. There may be two situations for large enterprises or startups at point X. First, when the CVC ecological community survives, there are large niche spaces that have not been occupied yet. Companies using K strategy to grow rapidly. Second, the overall space of the CVC ecological community has continued to shrink during the recession period, until the K strategy companies die out. When it is at a stable point, it indicates the maximum capacity of the ecosystem space and the maximum market capacity of technology, talent, capital, social resources, etc. When the K strategy prevents the individual from falling below stability, the scale is expanded to achieve stability. When the K strategy enterprise is above the stability point, its downsizing resumes [21]. The sustainable development of the CVC eco-community can be achieved if the large enterprise population and the entrepreneurial enterprise population in the CVC eco-community can adjust the niche countermeasures in a timely and accurate manner at different stages in the development process.


## 5.4. CVC Niche Alliance Strategy

In the CVC ecological community, large companies and startups can expand their niche by establishing a mutually beneficial symbiotic relationship. This strategy is called the niche alliance strategy. When the weaker startups and the stronger large companies can improve their respective competitiveness through symbiotic relationships, symbiotic parties in the CVC ecosystem can either choose their own appropriate niche or expand the boundaries of the entire ecological community from the perspective of enhancing the symbiotic system, promoting the metabolism of the entire CVC ecological community based on innovation. If the implementation of the niche alliance strategy requires the evaluation of their respective niche, the niche overlap and market crossover of both sides should be minimized to avoid parasitic or favorable symbiosis and form conflicts of interest [22]. Large enterprises and startups can seek intersections, that is, new requirements between the two sides. They can use the positive feedback effect of the innovation and entrepreneurship environment to create higher-level niche that is beneficial to both sides and can realize the coevolution of the niche. The main motivation of CVC activities is that large enterprises need to seek technological progress. Entrepreneurs in small and medium habitats in the industry can obtain more cooperation resources through the form of CVC, so that they can expand their survival through cooperative technological innovation, management innovation, and differentiated service innovation. In this case, they can expand the width of the niche and then penetrate or embed other industries. The formation and evolution of large enterprises and entrepreneurial enterprises in the CVC ecological community will also generate greater benefits in their own or other fields.



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*Source: 6327218-2020-08-28.xml*