Multilingual abstract
Introduction
Methods and data
Rules of the Triple Helix game
Core, Shapley value and nucleolus as indicators
Research data collection
Data treatment
Results
Countries’ total output and Triple Helix spheres’ shares
Country |
U
|
I
|
G
|
UI
|
UG
|
IG
|
UIG
| Total | |
---|---|---|---|---|---|---|---|---|---|
USA | # | 152,449 | 6506 | 24,134 | 7200 | 37,834 | 1782 | 2666 | 232,571 |
% | 65.55 | 2.80 | 10.38 | 3.10 | 16.27 | 0.77 | 1.15 | 100 | |
UK | # | 39,316 | 1167 | 12,020 | 1719 | 13,098 | 394 | 690 | 68,404 |
% | 57.48 | 1.71 | 17.57 | 2.51 | 19.15 | 0.58 | 1.01 | 100 | |
Germany | # | 35,588 | 700 | 8627 | 1028 | 14,003 | 407 | 664 | 61,017 |
% | 58.32 | 1.15 | 14.14 | 1.68 | 22.95 | 0.67 | 1.09 | 100 | |
France | # | 13,571 | 507 | 14,020 | 439 | 11,593 | 452 | 530 | 41,112 |
% | 33.01 | 1.23 | 34.10 | 1.07 | 28.20 | 1.10 | 1.29 | 100 | |
Russia | # | 4978 | 102 | 10,996 | 76 | 6315 | 162 | 138 | 22,767 |
% | 21.86 | 0.45 | 48.30 | 0.33 | 27.74 | 0.71 | 0.61 | 100 | |
India | # | 4134 | 194 | 4563 | 97 | 1813 | 61 | 55 | 10,917 |
% | 37.87 | 1.78 | 41.80 | 0.89 | 16.61 | 0.56 | 0.50 | 100 | |
Brazil | # | 6052 | 46 | 1074 | 137 | 1727 | 32 | 52 | 9120 |
% | 66.36 | 0.50 | 11.78 | 1.50 | 18.94 | 0.35 | 0.57 | 100 | |
China | # | 13,235 | 61 | 3791 | 237 | 4610 | 68 | 114 | 22,116 |
% | 59.84 | 0.28 | 17.14 | 1.07 | 20.84 | 0.31 | 0.52 | 100 |
Characteristic functions
Coalitions |
u
|
i
|
g
|
ui
|
ug
|
ig
|
uig
|
---|---|---|---|---|---|---|---|
USA | 65.55 | 2.80 | 10.38 | 71.44 | 92.19 | 13.94 | 100 |
UK | 57.48 | 1.71 | 17.57 | 61.70 | 94.20 | 19.85 | 100 |
Germany | 58.32 | 1.15 | 14.14 | 61.16 | 95.41 | 15.95 | 100 |
France | 33.01 | 1.23 | 34.10 | 35.31 | 95.31 | 36.43 | 100 |
Russia | 21.86 | 0.45 | 48.30 | 22.65 | 97.90 | 49.46 | 100 |
India | 37.87 | 1.78 | 41.80 | 40.53 | 96.27 | 44.13 | 100 |
Brazil | 66.36 | 0.50 | 11.78 | 68.37 | 97.07 | 12.63 | 100 |
China | 59.84 | 0.28 | 17.14 | 61.19 | 97.83 | 17.72 | 100 |
Cores
Country | USA | UK | Germany | France |
Core |
\( \left\{\begin{array}{c}65.55\le {x}_u\le 86.06\\ {}2.80\le {x}_i\le 7.81\\ {}10.38\le {x}_g\le 28.56\\ {}{x}_u+{x}_i+{x}_g=100\end{array}\right. \)
|
\( \left\{\begin{array}{c}57.48\le {x}_u\le 80.15\\ {}1.71\le {x}_i\le 5.80\\ {}17.57\le {x}_g\le 38.30\\ {}{x}_u+{x}_i+{x}_g=100\end{array}\right. \)
|
\( \left\{\begin{array}{c}58.32\le {x}_u\le 84.05\\ {}1.15\le {x}_i\le 4.59\\ {}14.14\le {x}_g\le 38.84\\ {}{x}_u+{x}_{\mathrm{i}}+{x}_g=100\end{array}\right. \)
|
\( \left\{\begin{array}{c}33.01\le {x}_u\le 63.57\\ {}1.23\le {x}_i\le 4.69\\ {}34.10\le {x}_g\le 64.69\\ {}{x}_u+{x}_i+{x}_g=100\end{array}\right. \)
|
Country | Russia | India | Brazil | China |
Core |
\( \left\{\begin{array}{c}21.86\le {x}_u\le 50.54\\ {}0.45\le {x}_i\le 2.10\\ {}48.30\le {x}_g\le 77.35\\ {}{x}_u+{x}_i+{x}_g=100\end{array}\right. \)
|
\( \left\{\begin{array}{c}37.87\le {x}_u\le 55.87\\ {}1.78\le {x}_i\le 3.73\\ {}41.80\le {x}_g\le 59.47\\ {}{x}_u+{x}_i+{x}_g=100\end{array}\right. \)
|
\( \left\{\begin{array}{c}66.36\le {x}_u\le 87.37\\ {}0.50\le {x}_i\le 2.93\\ {}11.78\le {x}_g\le 31.63\\ {}{x}_u+{x}_i+{x}_g=100\end{array}\right. \)
|
\( \left\{\begin{array}{c}59.84\le {x}_u\le 82.28\\ {}0.28\le {x}_i\le 2.17\\ {}17.14\le {x}_g\le 38.81\\ {}{x}_u+{x}_i+{x}_g=100\end{array}\right. \)
|
USA | UK | Germany | France | Russia | India | Brazil | China | |
---|---|---|---|---|---|---|---|---|
University | 20.51 | 22.67 | 25.72 | 30.56 | 28.68 | 18.00 | 21.01 | 22.43 |
Industry | 5.01 | 4.10 | 3.44 | 3.46 | 1.65 | 1.95 | 2.42 | 1.89 |
Government | 18.18 | 20.73 | 24.70 | 30.59 | 29.06 | 17.67 | 19.86 | 21.67 |
Shapley values and nucleoli
Player | University | Industry | Government | |
---|---|---|---|---|
USA | Shapley value | 75.61 | 5.11 | 19.28 |
Nucleolus | 78.70 | 7.11 | 14.20 | |
UK | Shapley value | 68.64 | 3.59 | 27.77 |
Nucleolus | 74.16 | 5.44 | 20.41 | |
Germany | Shapley value | 71.00 | 2.69 | 26.31 |
Nucleolus | 78.33 | 4.74 | 16.94 | |
France | Shapley value | 48.07 | 2.75 | 49.18 |
Nucleolus | 59.20 | 5.15 | 35.66 | |
Russia | Shapley value | 36.10 | 1.17 | 62.72 |
Nucleolus | 49.03 | 2.40 | 48.57 | |
India | Shapley value | 46.78 | 2.67 | 50.55 |
Nucleolus | 53.85 | 3.65 | 42.50 | |
Brazil | Shapley value | 76.77 | 1.62 | 21.61 |
Nucleolus | 83.58 | 2.76 | 13.66 | |
China | Shapley value | 70.07 | 1.14 | 27.89 |
Nucleolus | 79.26 | 2.19 | 18.55 |
Discussion
Biggest Triple Helix producer leads to and creates synergy
Government shows solidarity to maintain synergy
Russia | France | Germany | China | Brazil | UK | India | USA | |
---|---|---|---|---|---|---|---|---|
University | 13.02 | 12.19 | 9.63 | 9.41 | 8.25 | 7.53 | 7.46 | 5.8 |
Industry | 0.1 | 0.2 | 0.18 | 0.09 | 0.1 | 0.16 | 0.08 | 0.18 |
Government | − 13.13 | − 12.39 | − 9.8 | − 9.5 | − 8.34 | − 7.68 | − 7.54 | − 5.98 |
Extent of synergy varies over countries
State intervention policy determines the position of the core
Comparison with mutual information and transmission power
Rank | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 |
---|---|---|---|---|---|---|---|---|
Shapley value u | Brazil | USA | China | Germany | UK | France | India | Russia |
Shapley value i | USA | UK | France | Germany | India | Brazil | Russia | China |
Shapley value g | Russia | India | France | UK | China | Germany | Brazil | USA |