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Technology sharing game from ecological perspective

Hua Zou
Hua Zou
 and 
Deyu He
Deyu He
   | Mar 30, 2021
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Published Online: Mar 30, 2021
Page range: 81 - 92
Received: Nov 26, 2020
Accepted: Jan 31, 2021
DOI: https://doi.org/10.2478/amns.2021.1.00018
Keywords
© 2021 Hua Zou et al., published by Sciendo
This work is licensed under the Creative Commons Attribution 4.0 International License.

Fig. 1

Innovation ecosystem relationships based on technology sharing.
Innovation ecosystem relationships based on technology sharing.

Fig. 2

Phase evolution diagram in scenario (i).
Phase evolution diagram in scenario (i).

Fig. 3

Phase evolution diagram in scenario (ii)
Phase evolution diagram in scenario (ii)

Fig. 4

The influence of τ on the shared strategy of enterprise.
The influence of τ on the shared strategy of enterprise.

Fig. 5

The influence of ɛ on the shared strategy of enterprise.
The influence of ɛ on the shared strategy of enterprise.

Fig. 6

The influence of α and β on the shared strategy of enterprise.
The influence of α and β on the shared strategy of enterprise.

Game model parameters and connotations.

Parameters Connotations
x1 Probability that enterprise 1 chooses to share technology
x2 Probability that enterprise 2 chooses to share technology
P New technical value after sharing
P1 Original technical value of enterprise 1
P2 Original technological value of enterprise 2
r1 Technical value distribution coefficient after sharing 1
r2 Technical value distribution coefficient after sharing 2
N1 The technical stock of enterprise 1
N2 The technical stock of enterprise 2
α Proportion of technology shared by enterprise 1
β Proportion of technology shared by enterprise 2
τ1 The time-delay coefficient of enterprise 1
τ2 The time-delay coefficient of enterprise 2
K1 Punishment for enterprise 1
K2 Punishment for enterprise 2
μ Constant
ɛ1 The image factor of enterprise 1
ɛ2 The image factor of enterprise 2
C1 Technology sharing costs in enterprise 1, C1=c1αN1
C2 Technology sharing costs in enterprise 2, C2=c2βN2

Payoff matrix.

Enterprise 2
Sharing (x2) Non-sharing (1 − x2)
Enterprise 1 Sharing (x1) P1N1 + Pe−μτ1r1 αN1β N2 −C1 P1N1 − C1
P2N2 + Pe−μτ2r2αN1βN2− C2 P2N2 + P1αN1e−μτ2− ɛ2K2
Non-sharing (1 − x1) P1N1 + P2β N2e−μτ1−ɛ1K1 P1N1
P2N2 −C2 P2N2

Value of the Jacobi matrix at the local equilibrium

Stability point a11 a12 a21 a22
Q1 −C1 0 0 −C2
Q2 C1 0 0 Pe−μτ2r2αN1βN2 − P1αN1e−μτ2+ɛ2K2 − C2
Q3 Pe−μτ1r1αN1βN2 − P2βN2e−μτ1+ɛ1K1 − C1 0 0 C2
Q4 −Pe−μτ1r1αN1βN2 + P2βN2e−μτ1−ɛ1K1 + C1 0 0 −Pe−μτ2r2αN1βN2 + P1αN1e−μτ2−ɛ2K2 + C2
Q5 0 M1 M2 0

The evolutionary stability analysis under different conditions.

Equilibrium point Condition 1 Condition 2 Condition 3
e−μτ1βN2(P2 − Pr1αN1); ≺ C1 − ɛ1K1C2 ≺ ɛ2K2 C1 ≺ ɛ1K1; e−μτ2αN1(P1 − Pr2βN2) ≺ C2 − ɛ2K2 C1 ≺ ɛ1K1; C2 ≺ ɛ2K2
Q1 ESS ESS ESS
Q2 Instability Instability Instability
Q3 Instability Instability Instability
Q4 Instability Instability ESS
Q5 Saddle point Saddle point Saddle point
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