Technology sharing game from ecological perspective

There is no core enterprise in the flat innovation ecosystem and no big strength gap between enterprises. Therefore, we extract two stakeholders: enterprise 1 and enterprise 2. They both play producer roles in the innovation ecosystem, mainly by virtue of technology to obtain product advantages and market competitiveness. The total amount of enterprise technology includes stock and trading. In the innovation ecosystem, technology sharing platforms are the most efficient and convenient way to trade. The enterprise can select from two strategies: sharing technology (we can call ‘sharing’) and not sharing technology, just get technology from the platform (‘non-sharing’). In the case of ‘sharing’, the enterprises will share their technologies to the platform in a certain proportion and search complementary or additional technologies that they need. In the situation of ‘non-sharing’, the enterprises only gain but do not contribute, which is referred to as ‘hitchhiking’.

The innovation ecosystem includes n corporate entities and four kinds of environments. All enterprises have equal status. Any two enterprises trade and share technology through technology innovation platform and will create a technology flow. As enterprise activities cross over on the platform, technology flows evolve from chains to networks. The government provides guarantee and direction for the systematic sustainable development policy environment through the regulation of system and the promulgation of major policies. Universities, scientific research institutions and other enterprises provide the starting point and foundation of technological innovation for the innovation ecosystem. Cultural environment comes from the whole society, mainly including the identity of entrepreneur and consumer, international relations. Technological innovation must be rooted in local culture and actively integrated with the international community. This has a profound impact on the development potential of enterprises. Market environment is the soil of enterprises’ growth. A good market environment will promote the development of whole technology innovation activities and promote the smooth operation of the ecosystem. The relationships of enterprises in the innovation ecosystem are shown in Figure 1.

Fig. 1

The parameters and connotations of the game model are shown in Table 1.

The payoff matrix among two players is established in Table 2. In Table 2, suppose that the willingness that enterprise 1 chooses the sharing strategy is x1, the willingness of choosing non-sharing is 1−x1. Simultaneously, for enterprise 2, the willingness of sharing is x2, non-sharing is 1 − x2, where 0 ≤ x1 ≤ 1, 0 ≤ x2 ≤ 1.

Supposing that E₁₁ represents the expected earnings of enterprise 1 when adopt sharing strategy, E₁₂ represents the expected earnings of enterprise 1 that chooses non-sharing strategy. E1¯ \overline {{E_1}} represents the expected earnings of enterprise 1 that choose the average return of both strategies. Then: E11=x2(P1N1+Pe−μτ1r1αN1βN2−C1)+(1−x2)(P1N1−C1)=x2Pe−μτ1r1αN1βN2+P1N1−C1E12=x2(P1N1+P2βN2e−μτ1−ε1K1)+(1−x2)P1N1=x2P2βN2e−μτ1+P1N1−x2ε1K1E1¯=x1E11+(1−x1)E12=x1(x2Pe−μτ1r1αN1βN2+P1N1−C1)+(1−x1)(x2P2βN2e−μτ1+P1N1−x2ε1K1) \matrix{ {{E_{11}} = {x_2}\left( {{P_1}{N_1} + P{e^{ - \mu {\tau _1}}}{r_1}\alpha {N_1}\beta {N_2} - {C_1}} \right) + \left( {1 - {x_2}} \right)\left( {{P_1}{N_1} - {C_1}} \right) = {x_2}P{e^{ - \mu {\tau _1}}}{r_1}\alpha {N_1}\beta {N_2} + {P_1}{N_1} - {C_1}} \cr {{E_{12}} = {x_2}\left( {{P_1}{N_1} + {P_2}\beta {N_2}{e^{ - \mu {\tau _1}}} - {\varepsilon _1}{K_1}} \right) + \left( {1 - {x_2}} \right){P_1}{N_1} = {x_2}{P_2}\beta {N_2}{e^{ - \mu {\tau _1}}} + {P_1}{N_1} - {x_2}{\varepsilon _1}{K_1}} \cr {\overline {{E_1}} = {x_1}{E_{11}} + \left( {1 - {x_1}} \right){E_{12}} = {x_1}\left( {{x_2}P{e^{ - \mu {\tau _1}}}{r_1}\alpha {N_1}\beta {N_2} + {P_1}{N_1} - {C_1}} \right) + \left( {1 - {x_1}} \right)\left( {{x_2}{P_2}\beta {N_2}{e^{ - \mu {\tau _1}}} + {P_1}{N_1} - {x_2}{\varepsilon _1}{K_1}} \right)} \cr } The replicator dynamics equation of the willingness x₁ for enterprise 1 is dx1dt=x1(E11−E1¯)=x1(1−x1)[x2(Pe−μτ1r1αN1βN2−P2βN2e−μτ1+ε1K1)−C1] {{d{x_1}} \over {dt}} = {x_1}\left( {{E_{11}} - \overline {{E_1}} } \right) = {x_1}\left( {1 - {x_1}} \right)\left[ {{x_2}\left( {P{e^{ - \mu {\tau _1}}}{r_1}\alpha {N_1}\beta {N_2} - {P_2}\beta {N_2}{e^{ - \mu {\tau _1}}} + {\varepsilon _1}{K_1}} \right) - {C_1}} \right] In the same way, supposing that E₂₁ represents the expected earnings of enterprise 2 when adopt sharing strategy, E₂₂ represents the expected earnings of enterprise 2 that choose non-sharing strategy. E2¯ \overline {{E_2}} represents the expected earnings of enterprise 2 that choose the average return of both strategies. The replicator dynamic equation of the willingnessfor enterprise 1 is dx2dt=x2(E21−E2¯)=x2(1−x2)[x1(Pe−μτ2r2αN1βN2−P1αN1e−μτ2+ε2K2)−C2] {{d{x_2}} \over {dt}} = {x_2}\left( {{E_{21}} - \overline {{E_2}} } \right) = {x_2}\left( {1 - {x_2}} \right)\left[ {{x_1}\left( {P{e^{ - \mu {\tau _2}}}{r_2}\alpha {N_1}\beta {N_2} - {P_1}\alpha {N_1}{e^{ - \mu {\tau _2}}} + {\varepsilon _2}{K_2}} \right) - {C_2}} \right] In the replicator dynamic system, make dx1dt=0 {{d{x_1}} \over {dt}} = 0 , dx2dt=0 {{d{x_2}} \over {dt}} = 0 . We can get 5 equilibrium points, which include Q1(0,0),Q2(1,0),Q3(0,1),Q4(1,1)Q5(C2Pe−μτ2r2αN1βN2−P1αN1e−μτ2+ε2K2,C1Pe−μτ1r1αN1βN2−P2βN2e−μτ1+ε1K1). \matrix{ {{Q_1}(0,0),{Q_2}(1,0),{Q_3}(0,1),{Q_4}(1,1)} \cr {{Q_5}({{{C_2}} \over {P{e^{ - \mu {\tau _2}}}{r_2}\alpha {N_1}\beta {N_2} - {P_1}\alpha {N_1}{e^{ - \mu {\tau _2}}} + {\varepsilon _2}{K_2}}},{{{C_1}} \over {P{e^{ - \mu {\tau _1}}}{r_1}\alpha {N_1}\beta {N_2} - {P_2}\beta {N_2}{e^{ - \mu {\tau _1}}} + {\varepsilon _1}{K_1}}}).} \cr }

Since the local equilibrium point is not necessarily the evolution stability strategy (ESS) of system, the local stability analysis method of the Jacobi matrix is selected in this paper [18].

The Jacobi matrix of the evolutionary system is J=(a11a12a21a22). J = \left( {\matrix{ {{a_{11}}} & {{a_{12}}} \cr {{a_{21}}} & {{a_{22}}} \cr} } \right). Among them, a11=(1−2x1)[x2(Peμτ1r1αN1βN2−P2βN2e−μτ1+ɛ1K1)−C1]a12=x1(1−x1)(Pe−μτ1r1αN1βN2−P2βN2e−μτ1+ɛ1K1)a21=x2(1−x2)(Pe−μτ2r2αN1βN2−P1αN1e−μτ2+ɛ2K2)a22=(1−2x2)[x1(Pe−μτ2r2αN1βN2−P1αN1e−μτ2+ɛ2K2)−C2] \matrix{ {{a_{11}} = (1 - 2{x_1})[{x_2}(P{e^{\mu {\tau _1}}}{r_1}\alpha {N_1}\beta {N_2} - {P_2}\beta {N_2}{e^{ - \mu {\tau _1}}} + {\varepsilon_1}{K_1}) - {C_1}]} \cr {{a_{12}} = {x_1}(1 - {x_1})(P{e^{ - \mu {\tau _1}}}{r_1}\alpha {N_1}\beta {N_2} - {P_2}\beta {N_2}{e^{ - \mu {\tau _1}}} + {\varepsilon_1}{K_1})} \cr {{a_{21}} = {x_2}(1 - {x_2})(P{e^{ - \mu {\tau _2}}}{r_2}\alpha {N_1}\beta {N_2} - {P_1}\alpha {N_1}{e^{ - \mu {\tau _2}}} + {\varepsilon_2}{K_2})} \cr {{a_{22}} = (1 - 2{x_2})[{x_1}(P{e^{ - \mu {\tau _2}}}{r_2}\alpha {N_1}\beta {N_2} - {P_1}\alpha {N_1}{e^{ - \mu {\tau _2}}} + {\varepsilon_2}{K_2}) - {C_2}]} \cr }

Based on the Jacobi matrix, when an equilibrium point makes Det(J) ≻ 0, tr(J) ≺ 0, the point is a local asymptotic stability point, and the corresponding strategy is the system ESS. Five local equilibrium points were substituted into the matrix for calculation, and the results are shown in Table 3.

Among Table 3, M1=C2(Pe−μτ2r2αN1βN2−P1αN1e−μτ2+ε2K2−C2)(Pe−μτ1r1αN1βN2−P2N2e−μτ1+ɛ1K1)(Pe−μτ2r2αN1βN2−P1αN1e−μτ2+ε2K2)2M2=C2(Pe−μτ1r1αN1βN2−P2βN2e−μτ1+ε1K1−C1)(Pe−μτ2r2αN1βN2−P1αN1e−μτ2+ε2K2)(Pe−μτ1r1αN1βN2−P2βN2e−μτ1+ε1K1)2 \matrix{ {{M_1} = {{{C_2}(P{e^{ - \mu {\tau _2}}}{r_2}\alpha {N_1}\beta {N_2} - {P_1}\alpha {N_1}{e^{ - \mu {\tau _2}}} + {\varepsilon _2}{K_2} - {C_2})(P{e^{ - \mu {\tau _1}}}{r_1}\alpha {N_1}\beta {N_2} - {P_2}{N_2}{e^{ - \mu {\tau _1}}} + {_1}{K_1})} \over {{{(P{e^{ - \mu {\tau _2}}}{r_2}\alpha {N_1}\beta {N_2} - {P_1}\alpha {N_1}{e^{ - \mu {\tau _2}}} + {\varepsilon _2}{K_2})}^2}}}} \cr {{M_2} = {{{C_2}(P{e^{ - \mu {\tau _1}}}{r_1}\alpha {N_1}\beta {N_2} - {P_2}\beta {N_2}{e^{ - \mu {\tau _1}}} + {\varepsilon _1}{K_1} - {C_1})(P{e^{ - \mu {\tau _2}}}{r_2}\alpha {N_1}\beta {N_2} - {P_1}\alpha {N_1}{e^{ - \mu {\tau _2}}} + {\varepsilon _2}{K_2})} \over {{{(P{e^{ - \mu {\tau _1}}}{r_1}\alpha {N_1}\beta {N_2} - {P_2}\beta {N_2}{e^{ - \mu {\tau _1}}} + {\varepsilon _1}{K_1})}^2}}}} \cr }

From Table 3, is the saddle point. It is not the stable strategy point because the trace of the determinant is 0. At the equilibrium points Q₂(1,0) and Q₃(0,1), the stability conditions of the Jacobi matrix are contradictory that cannot satisfy both conditions Det(J) ≻ 0 and tr(J) ≺ 0. So Q₂ and Q₃ are not stable strategy points. For the equilibrium points Q₁(0,0) and Q₄(1,1), according to different situations in the evolution process, namely, different values of various parameters, we will analyse the stability strategy under three conditions. The results of evolutionary stability analysis under different conditions are shown in Table 4.

ESS, evolution stability strategy.

Fig. 2

Fig. 3

Enterprise has more technical advantages than enterprise 2, so suppose the technology transformation time of enterprise 1 is less than that of enterprise 2 and τ₁ = 0.4, τ₂ = 0.5. The proportion of technology sharing α = 0.5 for enterprise (1), β = 0.3 for enterprise 2, and the image factor for enterprises ɛ is both 0.2.

When the time-delay coefficient of enterprise 2 is 0.5, and τ₁ takes different values, the sharing willingness of enterprise 1 changes over time, which is shown in the first picture of Figure 4. As the time-delay coefficient increases, enterprise 1 will be more inclined to non-sharing. The threshold is in the interval [0.25,0.3], when τ₁ ≺ 0.25, enterprise 1 will decisively choose to share technology. When τ₁ = 0.3, enterprise 1 is in a state of hesitation. At first, there was a clear preference for sharing technology, but as time went on, enterprise 1 finally chooses not to share. When τ₁ ≻ 0.3, enterprise 1's hesitation time becomes shorter and shorter, and the willingness to share technology is becoming less obvious. In the end, it will choose not to share technology with other businesses in the innovation ecosystem. The second picture shows the change of technology sharing intention of enterprise 2 with time under different time-delay coefficients. The overall evolution law of enterprise 2 is similar to that of enterprise 1, and its threshold interval is [0.35, 0.4].

Fig. 4

When the time-delay coefficient of each enterprise is lower than its corresponding threshold, the enterprise will finally choose the sharing strategy. In the situation, the technology innovation platform will play its biggest role, and the innovation ecosystem will present a good situation of cooperation and symbiosis, promoting the further development of technology and economy; therefore, the ability of enterprise technology transformation plays an important role in technology transfer in the whole innovation ecosystem. All relevant parties should attach importance to improving the transformation level of technological achievements of enterprises, encourage enterprises to make good use of intelligent means, acquire complementary technologies and talents in various ways and strive to improve their ability to adapt to and absorb new technologies. At the same time, it is necessary to reduce the hesitation of enterprise decision-makers to avoid missing the opportunity of obtaining the best technology and marketing investment.

The image factor represents the impression an enterprise leaves on the outside world. The smaller the image factor, the better the image of the enterprise in the whole ecosystem. This factor is related to the previous behaviour of the enterprise, for example, enterprises often break promises, default or ‘hitchhiking’ and so on, then the system is bound to be very difficult to tolerate their bad behaviour again. Enterprises have also been punished more severely. In the principle of encouraging in the system, if an enterprise with a clean bill of health accidentally ‘hitchhiking’, the system will treat it lightly. The enterprise will be less penalised. The image factor increases with the increase in the number of bad behaviours.

Supposing that α = 0.5, β = 0.3, τ₁ = 0.45, τ₂ = 0.5, when ɛ₂ = 0.5, the willingness of enterprise 1 to choose technology sharing strategy increases with the increase in the image factor of enterprise 2 because the increase in the number of ‘hitchhiking’ means that the penalties for the enterprises are increased. Then enterprises will do their best to avoid excessive losses. Similarly, the trend of enterprises 2 is also direct proportionality curve. The threshold interval of both enterprise 1 and enterprise 2 is [0.5,0.55], which is shown in Figure 5. The influence of image factor on enterprises’ choice of technology sharing strategy has nothing to do with the nature of enterprises, it is only about behaviour. When the image factor is higher than the threshold value, if the enterprise wants to continue to develop well in the ecosystem, its optimal strategy is sharing.

Fig. 5

When β = 0.3, α = 0.4, as the proportion of one enterprise to choose technology sharing increases, the willingness of another to choose technology sharing becomes stronger. The technology sharing threshold interval of enterprise 1 is [0.35,0.4]. It indicates that when enterprise 1 determines that 40% of the technology stock will be shared, the premise for its choice of sharing technology is that the technology sharing proportion of enterprise 2 is higher than the threshold [0.35,0.4]. If the technology sharing ratio of enterprise 2 is lower than 0.35, enterprise 1 will finally choose non-sharing without too much hesitation. If the technology sharing ratio of enterprise 2 is higher than 0.4, enterprise 1 will not hesitate to choose technology sharing, and the sharing time will be shortened as the sharing ratio of the other party increases. When enterprise 2 decided to share 30% of its technology, then the threshold interval of enterprise 1 is [0.55, 0.6]. That is, when the threshold value is higher, enterprise 2 will choose the technology sharing strategy. Enterprise 2 has a period of hesitation when α = 0.55, and as α decreases, the hesitation time decreases. When the technology sharing ratio of enterprise 1 is higher than 0.6, enterprise 2 will resolutely choose technology sharing to build a good technology sharing platform of innovation ecosystem together with enterprise 1. The change curve is shown in Figure 6.

Fig. 6

By contrast, we find that when choosing strategy, superior enterprises have lower requirements on the technology sharing proportion of the other party. Due to its high technology stock and value, it is better able to take risks. Once the other enterprise gets ‘hitchhiking’, the enterprise can also bear the losses caused by the situation. On the contrary, weak enterprises will pay more attention to the technology sharing proportion of the superior enterprises. Only when the proportion is high enough, will be at ease to put technology on the shared platform, to share with the superior enterprises.