# Nestedness-Based Measurement of Evolutionarily Stable Equilibrium of Global Production System

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## Abstract

**:**

## 1. Introduction

## 2. Literature Review

## 3. Data and Model

#### 3.1. Data Sources and Structure

#### 3.2. Network Modeling

#### 3.3. Network Pruning

## 4. Measurement

## 5. Results

#### 5.1. Divergence Analysis

#### 5.2. Trend Analysis

#### 5.3. Stability Analysis

#### 5.4. Evolutionary Mechanism

## 6. Econometric Analysis

#### 6.1. Correlation between Variables

#### 6.2. Regression Model

## 7. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Data Availability Statement

## Conflicts of Interest

## Appendix A. Basic Information about Eora26

No. | Abbr. | Country | No. | Abbr. | Country |
---|---|---|---|---|---|

1 | AFG | Afghanistan | 96 | LSO | Lesotho |

2 | ALB | Albania | 97 | LBR | Liberia |

3 | DZA | Algeria | 98 | LBY | Libya |

4 | AND | Andorra | 99 | LIE | Liechtenstein |

5 | AGO | Angola | 100 | LTU | Lithuania |

6 | ATG | Antigua | 101 | LUX | Luxembourg |

7 | ARG | Argentina | 102 | MAC | Macao SAR |

8 | ARM | Armenia | 103 | MDG | Madagascar |

9 | ABW | Aruba | 104 | MWI | Malawi |

10 | AUS | Australia | 105 | MYS | Malaysia |

11 | AUT | Austria | 106 | MDV | Maldives |

12 | AZE | Azerbaijan | 107 | MLI | Mali |

13 | BHS | Bahamas | 108 | MLT | Malta |

14 | BHR | Bahrain | 109 | MRT | Mauritania |

15 | BGD | Bangladesh | 110 | MUS | Mauritius |

16 | BRB | Barbados | 111 | MEX | Mexico |

17 | BLR | Belarus | 112 | MCO | Monaco |

18 | BEL | Belgium | 113 | MNG | Mongolia |

19 | BLZ | Belize | 114 | MNE | Montenegro |

20 | BEN | Benin | 115 | MAR | Morocco |

21 | BMU | Bermuda | 116 | MOZ | Mozambique |

22 | BTN | Bhutan | 117 | MMR | Myanmar |

23 | BOL | Bolivia | 118 | NAM | Namibia |

24 | BIH | Bosnia and Herzegovina | 119 | NPL | Nepal |

25 | BWA | Botswana | 120 | NLD | Netherlands |

26 | BRA | Brazil | 121 | ANT | Netherlands Antilles |

27 | VGB | British Virgin Islands | 122 | NCL | New Caledonia |

28 | BRN | Brunei | 123 | NZL | New Zealand |

29 | BGR | Bulgaria | 124 | NIC | Nicaragua |

30 | BFA | Burkina Faso | 125 | NER | Niger |

31 | BDI | Burundi | 126 | NGA | Nigeria |

32 | KHM | Cambodia | 127 | NOR | Norway |

33 | CMR | Cameroon | 128 | PSE | Gaza Strip |

34 | CAN | Canada | 129 | OMN | Oman |

35 | CPV | Cape Verde | 130 | PAK | Pakistan |

36 | CYM | Cayman Islands | 131 | PAN | Panama |

37 | CAF | Central African Republic | 132 | PNG | Papua New Guinea |

38 | TCD | Chad | 133 | PRY | Paraguay |

39 | CHL | Chile | 134 | PER | Peru |

40 | CHN | China | 135 | PHL | Philippines |

41 | COL | Colombia | 136 | POL | Poland |

42 | COG | Congo | 137 | PRT | Portugal |

43 | CRI | Costa Rica | 138 | QAT | Qatar |

44 | HRV | Croatia | 139 | KOR | South Korea |

45 | CUB | Cuba | 140 | MDA | Moldova |

46 | CYP | Cyprus | 141 | ROU | Romania |

47 | CZE | Czech Republic | 142 | RUS | Russia |

48 | CIV | Cote d’Ivoire | 143 | RWA | Rwanda |

49 | PRK | North Korea | 144 | WSM | Samoa |

50 | COD | DR Congo | 145 | SMR | San Marino |

51 | DNK | Denmark | 146 | STP | Sao Tome and Principe |

52 | DJI | Djibouti | 147 | SAU | Saudi Arabia |

53 | DOM | Dominican Republic | 148 | SEN | Senegal |

54 | ECU | Ecuador | 149 | SRB | Serbia |

55 | EGY | Egypt | 150 | SYC | Seychelles |

56 | SLV | El Salvador | 151 | SLE | Sierra Leone |

57 | ERI | Eritrea | 152 | SGP | Singapore |

58 | EST | Estonia | 153 | SVK | Slovakia |

59 | ETH | Ethiopia | 154 | SVN | Slovenia |

60 | FJI | Fiji | 155 | SOM | Somalia |

61 | FIN | Finland | 156 | ZAF | South Africa |

62 | FRA | France | 157 | SDS | South Sudan |

63 | PYF | French Polynesia | 158 | ESP | Spain |

64 | GAB | Gabon | 159 | LKA | Sri Lanka |

65 | GMB | Gambia | 160 | SUD | Sudan |

66 | GEO | Georgia | 161 | SUR | Suriname |

67 | DEU | Germany | 162 | SWZ | Swaziland |

68 | GHA | Ghana | 163 | SWE | Sweden |

69 | GRC | Greece | 164 | CHE | Switzerland |

70 | GRL | Greenland | 165 | SYR | Syria |

71 | GTM | Guatemala | 166 | TWN | Taiwan |

72 | GIN | Guinea | 167 | TJK | Tajikistan |

73 | GUY | Guyana | 168 | THA | Thailand |

74 | HTI | Haiti | 169 | MKD | TFYR Macedonia |

75 | HND | Honduras | 170 | TGO | Togo |

76 | HKG | Hong Kong | 171 | TTO | Trinidad and Tobago |

77 | HUN | Hungary | 172 | TUN | Tunisia |

78 | ISL | Iceland | 173 | TUR | Turkey |

79 | IND | India | 174 | TKM | Turkmenistan |

80 | IDN | Indonesia | 175 | USR | Former USSR |

81 | IRN | Iran | 176 | UGA | Uganda |

82 | IRQ | Iraq | 177 | UKR | Ukraine |

83 | IRL | Ireland | 178 | ARE | United Arab Emirates |

84 | ISR | Israel | 179 | GBR | United Kingdom |

85 | ITA | Italy | 180 | TZA | Tanzania |

86 | JAM | Jamaica | 181 | USA | United States |

87 | JPN | Japan | 182 | URY | Uruguay |

88 | JOR | Jordan | 183 | UZB | Uzbekistan |

89 | KAZ | Kazakhstan | 184 | VUT | Vanuatu |

90 | KEN | Kenya | 185 | VEN | Venezuela |

91 | KWT | Kuwait | 186 | VNM | Viet Nam |

92 | KGZ | Kyrgyzstan | 187 | YEM | Yemen |

93 | LAO | Laos | 188 | ZMB | Zambia |

94 | LVA | Latvia | 189 | ZWE | Zimbabwe |

95 | LBN | Lebanon |

No. | Abbr. | Industrial Sector |
---|---|---|

1 | S1 | Agriculture |

2 | S2 | Fishing |

3 | S3 | Mining and Quarrying |

4 | S4 | Food & Beverages |

5 | S5 | Textiles and Wearing Apparel |

6 | S6 | Wood and Paper |

7 | S7 | Petroleum, Chemical and Non-Metallic Mineral Products |

8 | S8 | Metal Products |

9 | S9 | Electrical and Machinery |

10 | S10 | Transport Equipment |

11 | S11 | Other Manufacturing |

12 | S12 | Recycling |

13 | S13 | Electricity, Gas and Water |

14 | S14 | Construction |

15 | S15 | Maintenance and Repair |

16 | S16 | Wholesale Trade |

17 | S17 | Retail Trade |

18 | S18 | Hotels and Restaurants |

19 | S19 | Transport |

20 | S20 | Post and Telecommunications |

21 | S21 | Financial Intermediation and Business Activities |

22 | S22 | Public Administration |

23 | S23 | Education, Health and Other Services |

24 | S24 | Private Households |

25 | S25 | Others |

26 | S26 | Re-export & Re-import |

Category | Sectors |
---|---|

Agriculture (SC1) | Agriculture; Fishing |

Mining (SC2) | Mining and Quarrying |

Manufacturing (SC3) | Food & Beverages; Textiles and Wearing Apparel; Wood and Paper; Petroleum, Chemical and Non-Metallic Mineral Products; Metal Products; Electrical and Machinery; Transport Equipment; Other Manufacturing; Recycling; Electricity, Gas and Water; Construction |

Services (SC4) | Maintenance and Repair; Wholesale Trade; Retail Trade; Hotels and Restaurants; Transport; Post and Telecommunications; Financial Intermediation and Business Activities; Public Administration; Education, Health and Other Services; Private Households; Others; Re-export & Re-import |

## Appendix B. Network Pruning

Procedure | Column Deletion of Input Relations | Row Deletion of Output Relations |
---|---|---|

Network | $W={\left({w}_{ij}\right)}_{N\times N}\xb7$$i,j\in \left[1,N\right]$ | |

Refactoring | ${\stackrel{\leftharpoonup}{w}}_{1}=desecend{\left({w}_{11},{w}_{21,}\cdots ,{w}_{N1}\right)}^{T}$ ${\stackrel{\leftharpoonup}{w}}_{2}=descend{\left({w}_{12},{w}_{22,}\cdots ,{w}_{N2}\right)}^{T}$ $\cdots $ ${\stackrel{\leftharpoonup}{w}}_{N}=descend{\left({w}_{1N},{w}_{2N,}\cdots ,{w}_{NN}\right)}^{T}$ $\stackrel{\leftharpoonup}{W}=\left({\stackrel{\leftharpoonup}{w}}_{1},{\stackrel{\leftharpoonup}{w}}_{2},\cdots ,{\stackrel{\leftharpoonup}{w}}_{N}\right)={\left({\stackrel{\leftharpoonup}{w}}_{sj}\right)}_{N\times N}$ $s,j\in \left[1,N\right]$ | ${\stackrel{\rightharpoonup}{w}}_{1}=desecend\left({w}_{11},{w}_{12,}\cdots ,{w}_{1N}\right)$ ${\stackrel{\rightharpoonup}{w}}_{2}=descend\left({w}_{21},{w}_{22,}\cdots ,{w}_{2N}\right)$ $\cdots $ ${\stackrel{\rightharpoonup}{w}}_{N}=descend\left({w}_{N1},{w}_{N2,}\cdots ,{w}_{NN}\right)$ $\stackrel{\rightharpoonup}{W}=\left(\begin{array}{c}{\stackrel{\rightharpoonup}{w}}_{1}\\ {\stackrel{\rightharpoonup}{w}}_{2}\\ \cdots \\ {\stackrel{\rightharpoonup}{w}}_{N}\end{array}\right)={\left({\stackrel{\rightharpoonup}{w}}_{it}\right)}_{N\times N}$ $i,t\in \left[1,N\right]$ |

Conditions | $\forall {a}_{1},{a}_{2},\cdots ,{a}_{j}\in \left[1,N\right]$ $\left\{\begin{array}{c}\frac{{{\displaystyle \sum}}_{s=1}^{{a}_{j}}{\stackrel{\leftharpoonup}{w}}_{sj}}{{{\displaystyle \sum}}_{s=1}^{N}{\stackrel{\leftharpoonup}{w}}_{sj}}\ge 1-\frac{{a}_{j}}{N}\\ \frac{{{\displaystyle \sum}}_{s=1}^{{a}_{j}-1}{\stackrel{\leftharpoonup}{w}}_{sj}}{{{\displaystyle \sum}}_{s=1}^{N}{\stackrel{\leftharpoonup}{w}}_{sj}}<1-\frac{{a}_{j}-1}{N}\end{array}\right.$ | $\forall {b}_{1},{b}_{2},\cdots ,{b}_{i}\in \left[1,N\right]$ $\left\{\begin{array}{c}\frac{{{\displaystyle \sum}}_{t=1}^{{b}_{i}}{\stackrel{\rightharpoonup}{w}}_{it}}{{{\displaystyle \sum}}_{t=1}^{N}{\stackrel{\rightharpoonup}{w}}_{it}}\ge 1-\frac{{b}_{i}}{N}\\ \frac{{{\displaystyle \sum}}_{t=1}^{{b}_{i}-1}{\stackrel{\rightharpoonup}{w}}_{it}}{{{\displaystyle \sum}}_{t=1}^{N}{\stackrel{\rightharpoonup}{w}}_{it}}<1-\frac{{b}_{i}-1}{N}\end{array}\right.$ |

Definition | $X{I}_{j}^{B}=\frac{{a}_{j}}{N}$ $X{I}^{B}={\left(X{I}_{j}^{B}\right)}_{N\times 1}$ | $X{I}_{i}^{F}=\frac{{b}_{i}}{N}$ $X{I}^{F}={\left(X{I}_{i}^{F}\right)}_{N\times 1}$ |

Pruning | ${\overleftarrow{w}}_{ij}=\left\{\begin{array}{ccc}{w}_{ij}& ,& {w}_{ij}={\stackrel{\leftharpoonup}{w}}_{sj}ands\le {a}_{j}\\ 0& ,& otherwise\end{array}\right.$ | ${\overrightarrow{w}}_{ij}=\left\{\begin{array}{ccc}{w}_{ij}& ,& {w}_{ij}={\stackrel{\rightharpoonup}{w}}_{it}andt\le {b}_{i}\\ 0& ,& otherwise\end{array}\right.$ |

Merging | ${\overleftrightarrow{w}}_{ij}=\left\{\begin{array}{ccc}{w}_{ij}& ,& {\overleftarrow{w}}_{ij}\ne 0or{\overrightarrow{w}}_{ij}\ne 0\\ 0& ,& otherwise\end{array}\right.$ | |

Result | $\overleftrightarrow{W}={\left({\overleftrightarrow{w}}_{ij}\right)}_{N\times N}$ |

**Figure A1.**Three possible situations in the application of XIFA algorithm. (

**a**) The source node has only one weighted edge connected to it, and 100% of its strength is allocated on it; (

**b**) Top 20% of weighted edges carry 80% of the strength of source node. (

**c**) Any 50% of weighted edges carry 50% of the strength of source node.

## Appendix C. Sorting Algorithms

- 1.
- SBD Algorithm

- 2.
- NTC Algorithm

**Figure A2.**Sorting Adjacency Matrix Based on SBD Algorithm. This is a schematic diagram of the process of ordering nodes by degree. The solid blue circles represent each industrial sector, the rows represent the upstream industrial sectors, the columns represent the downstream industry sectors, the blue squares represent the existence of interdependence between upstream and downstream industries, and the size of the solid circles is proportional to the node’s degree.

- 3.
- BIN Algorithm

- 4.
- FCA Algorithm

**Figure A3.**Sorting Adjacency Matrix of GVC Network Based on Three Algorithms and Its Corresponding NODF Variation Trend. (

**a**–

**c**) are the adjacency matrix ranking results obtained according to the SBD, BIN, and FCA algorithms, respectively. Where the vertical axis represents the upstream sector and the horizontal axis represents the downstream sector, and each non-empty position reflects the transfer of intermediate products from the upstream sector to the downstream sector. This input–output relationship between industrial sectors resembles predation in an ecosystem: the upstream sector, as the provider of energy (products and services), can be regarded as the prey; the downstream sector, as the consumer of energy (products and services), can be regarded as the predator, and each industry sector plays dual role in the industrial ecosystem.

## Appendix D. Complementary Econometric Analysis

Variables | Coef. | Robust Std. Err | t | p | 95% Confidence Interval |
---|---|---|---|---|---|

DTN-NODF | −9.49 | 2.64 | −3.60 | 0.000 *** | [−14.67, −4.32] |

ETN-NODF | 44.27 | 3.88 | 11.40 | 0.000 *** | [36.65, 51.90] |

ITN-NODF | 21.03 | 6.88 | 3.06 | 0.002 ** | [7.54, 34.52] |

Intercept Term | 71.97 | 180.36 | 0.40 | 0.690 | [−281.95, 425.89] |

${R}^{2}$(adjusted) | 0.411 | Root MSE | 867.68 |

Variables | Coef. | Robust Std. Err | t | p | 95% Confidence Interval |
---|---|---|---|---|---|

DTN-NODF | 0.40 | 1.99 | 0.20 | 0.840 | [−3.52, 4.33] |

Comp. | 43.27 | 45.56 | 0.95 | 0.343 | [−46.62, 133.17] |

Intercept Term | −538.56 | 712.27 | −0.76 | 0.451 | [−1943.92, 866.80] |

Variables | Coef. | Robust Std. Err | t | p | 95% Confidence Interval |
---|---|---|---|---|---|

DTN-NODF | 0.40 | 2.19 | 0.18 | 0.854 | [−3.91, 4.72] |

Comp. | 43.27 | 50.14 | 0.86 | 0.389 | [−55.65, 142.20] |

country | |||||

AFG | 346.87 | 353.84 | 0.98 | 0.328 | [−351.2987, 1045.033] |

AGO | 281.05 | 257.66 | 1.09 | 0.277 | [−227.3288, 789.4262] |

ALB | 216.71 | 218.33 | 0.99 | 0.322 | [−214.0759, 647.4973] |

AND | 236.70 | 238.52 | 0.99 | 0.322 | [−233.9195, 707.3123] |

ARE | 422.05 | 276.65 | 1.53 | 0.129 | [−123.7993, 967.9091] |

ARG | −346.32 | 749.44 | −0.46 | 0.645 | [−1825.031, 1132.375] |

ARM | 214.61 | 231.28 | 0.93 | 0.355 | [−241.7304, 670.9555] |

ATG | 202.95 | 188.93 | 1.07 | 0.284 | [−169.8275, 575.7282] |

AUS | −477.86 | 1384.80 | −0.35 | 0.73 | [−3210.196, 2254.469] |

AUT | −134.15 | 501.67 | −0.27 | 0.789 | [−1123.986, 855.6903] |

AZE | 211.72 | 206.19 | 1.03 | 0.306 | [−195.0985, 618.5441] |

BDI | 197.72 | 179.91 | 1.1 | 0.273 | [−157.2522, 552.6847] |

BEL | −1179.98 | 1749.33 | −0.67 | 0.501 | [−4631.553, 2271.592] |

BEN | 266.94 | 276.91 | 0.96 | 0.336 | [−279.4249, 813.3128] |

BFA | 197.92 | 209.44 | 0.94 | 0.346 | [−215.324, 611.1616] |

BGD | 463.47 | 441.16 | 1.05 | 0.295 | [−406.9706, 1333.907] |

BGR | 322.55 | 330.76 | 0.98 | 0.331 | [−330.0761, 975.1704] |

BHR | 321.21 | 341.12 | 0.94 | 0.348 | [−351.8472, 994.2654] |

BHS | 263.53 | 275.51 | 0.96 | 0.34 | [−280.0784, 807.1395] |

BIH | 303.62 | 310.98 | 0.98 | 0.33 | [−309.9727, 917.2204] |

BLR | 109.25 | 102.04 | 1.07 | 0.286 | [−92.07386, 310.582] |

BLZ | 142.7 | 156.80 | 0.91 | 0.364 | [−166.6857, 452.0805] |

BMU | 163.46 | 161.68 | 1.01 | 0.313 | [−155.5533, 482.4662] |

BOL | 80.53 | 84.62 | 0.95 | 0.343 | [−86.4349, 247.4872] |

BRA | 527.65 | 715.03 | 0.74 | 0.462 | [−883.1721, 1938.471] |

BRB | 282.83 | 291.34 | 0.97 | 0.333 | [−292.0029, 857.6546] |

BRN | 334.04 | 351.24 | 0.95 | 0.343 | [−358.9823, 1027.066] |

BTN | 79.27 | 88.60 | 0.89 | 0.372 | [−95.53579, 254.075] |

BWA | 285.04 | 305.34 | 0.93 | 0.352 | [−317.4236, 887.4988] |

CAF | 265.57 | 260.87 | 1.02 | 0.31 | [−249.161, 780.2916] |

CAN | 770.19 | 341.90 | 2.25 | 0.025 * | [95.58298, 1444.791] |

CHE | −909.9 | 1534.75 | −0.59 | 0.554 | [−3938.092, 2118.301] |

CHL | −60.5 | 228.66 | −0.26 | 0.792 | [−511.6715, 390.6751] |

CHN | 1503.19 | 2459.50 | 0.61 | 0.542 | [−3349.617, 6355.998] |

CIV | 346.24 | 367.63 | 0.94 | 0.348 | [−379.13, 1071.614] |

CMR | 360.41 | 378.99 | 0.95 | 0.343 | [−387.3771, 1108.196] |

COD | 265.26 | 265.10 | 1 | 0.318 | [−257.8036, 788.316] |

COG | 290.82 | 307.71 | 0.95 | 0.346 | [−316.319, 897.9642] |

COL | 81.02 | 76.04 | 1.07 | 0.288 | [−69.00603, 231.0458] |

CPV | 219 | 208.95 | 1.05 | 0.296 | [−193.2711, 631.2752] |

CRI | 390.24 | 414.36 | 0.94 | 0.348 | [−427.3227, 1207.812] |

CUB | 381.23 | 369.91 | 1.03 | 0.304 | [−348.6375, 1111.096] |

CYP | 342.62 | 366.80 | 0.93 | 0.352 | [−381.1153, 1066.35] |

CZE | −172.23 | 317.34 | −0.54 | 0.588 | [−798.369, 453.9041] |

DEU | 198.25 | 2855.59 | 0.07 | 0.945 | [−5436.072, 5832.577] |

DJI | 163.01 | 138.96 | 1.17 | 0.242 | [−111.1765, 437.1888] |

DNK | −703.72 | 1088.11 | −0.65 | 0.519 | [−2850.657, 1443.218] |

DOM | 416.84 | 427.58 | 0.97 | 0.331 | [−426.8171, 1260.502] |

DZA | 408.18 | 350.16 | 1.17 | 0.245 | [−282.7166, 1099.085] |

ECU | −118.3 | 175.10 | −0.68 | 0.5 | [−463.7915, 227.1998] |

EGY | 511.76 | 410.13 | 1.25 | 0.214 | [−297.4581, 1320.971] |

ERI | 235.58 | 222.08 | 1.06 | 0.29 | [−202.6103, 673.7649] |

ESP | −609.87 | 1790.20 | −0.34 | 0.734 | [−4142.082, 2922.346] |

EST | −48.19 | 69.35 | −0.69 | 0.488 | [−185.0211, 88.64208] |

ETH | −107.18 | 134.83 | −0.79 | 0.428 | [−373.2024, 158.8407] |

FIN | −20.37 | 245.53 | −0.08 | 0.934 | [−504.8219, 464.0865] |

FJI | 276.83 | 299.98 | 0.92 | 0.357 | [−315.0676, 868.72] |

FRA | −1.51 | 2245.24 | 0 | 0.999 | [−4431.562, 4428.534] |

GAB | 314.42 | 332.34 | 0.95 | 0.345 | [−341.3062, 970.1512] |

GBR | −1022.55 | 3512.17 | −0.29 | 0.771 | [−7952.356, 5907.252] |

GEO | −178.73 | 200.24 | −0.89 | 0.373 | [−573.8264, 216.3583] |

GHA | 323.03 | 336.75 | 0.96 | 0.339 | [−341.3976, 987.4673] |

GIN | 264.45 | 280.28 | 0.94 | 0.347 | [−288.5671, 817.4742] |

GMB | 203.94 | 205.10 | 0.99 | 0.321 | [−200.7466, 608.6262] |

GRC | 100.46 | 91.75 | 1.09 | 0.275 | [−80.57459, 281.495] |

GRL | 375.57 | 432.99 | 0.87 | 0.387 | [−478.7589, 1229.897] |

GTM | 400.99 | 420.56 | 0.95 | 0.342 | [−428.8063, 1230.781] |

GUY | 403.69 | 444.55 | 0.91 | 0.365 | [−473.4424, 1280.816] |

HKG | −172.88 | 417.98 | −0.41 | 0.68 | [−997.5889, 651.824] |

HND | 351.7 | 384.12 | 0.92 | 0.361 | [−406.2073, 1109.612] |

HRV | 393.84 | 411.64 | 0.96 | 0.34 | [−418.3654, 1206.055] |

HTI | 322.38 | 338.26 | 0.95 | 0.342 | [−345.0331, 989.8003] |

HUN | −39.7 | 165.92 | −0.24 | 0.811 | [−367.0765, 287.6826] |

IDN | −204.47 | 695.67 | −0.29 | 0.769 | [−1577.078, 1168.141] |

IND | −405.95 | 1554.43 | −0.26 | 0.794 | [−3472.961, 2661.06] |

IRL | 61.82 | 107.64 | 0.57 | 0.566 | [−150.5622, 274.2033] |

IRN | −367.70 | 704.14 | −0.52 | 0.602 | [−1757.034, 1021.625] |

IRQ | 287.09 | 163.82 | 1.75 | 0.081 | [−36.13326, 610.32] |

ISL | 336.34 | 362.54 | 0.93 | 0.355 | [−378.9751, 1051.662] |

ISR | −403.11 | 647.93 | −0.62 | 0.535 | [−1681.534, 875.3045] |

ITA | −358.7 | 2247.07 | −0.16 | 0.873 | [−4792.36, 4074.952] |

JAM | 351.8 | 378.13 | 0.93 | 0.353 | [−394.2818, 1097.891] |

JOR | 325.8 | 359.43 | 0.91 | 0.366 | [−383.3841, 1034.987] |

JPN | 2047.56 | 3094.29 | 0.66 | 0.509 | [−4057.734, 8152.856] |

KAZ | −244.62 | 362.13 | −0.68 | 0.5 | [−959.1294, 469.8803] |

KEN | −197.97 | 244.35 | −0.81 | 0.419 | [−680.0901, 284.1591] |

KGZ | −455.86 | 512.61 | −0.89 | 0.375 | [−1467.283, 555.5592] |

KHM | 289.57 | 316.28 | 0.92 | 0.361 | [−334.4798, 913.6205] |

KOR | −313.24 | 1286.85 | −0.24 | 0.808 | [−2852.31, 2225.822] |

KWT | −154.41 | 235.90 | −0.65 | 0.514 | [−619.8692, 311.0498] |

LAO | 270.07 | 289.50 | 0.93 | 0.352 | [−301.147, 841.2839] |

LBN | 323.88 | 326.75 | 0.99 | 0.323 | [−320.815, 968.5826] |

LBR | 184.38 | 192.94 | 0.96 | 0.341 | [−196.318, 565.0694] |

LBY | 365.12 | 357.11 | 1.02 | 0.308 | [−339.4948, 1069.737] |

LIE | 302.74 | 309.76 | 0.98 | 0.33 | [−308.4337, 913.9225] |

LKA | 355.78 | 375.62 | 0.95 | 0.345 | [−385.3557, 1096.923] |

LSO | 134.13 | 131.54 | 1.02 | 0.309 | [−125.4121, 393.6786] |

LTU | −77.57 | 124.47 | −0.62 | 0.534 | [−323.162, 168.0136] |

LUX | 3.05 | 33.70 | 0.09 | 0.928 | [−63.45578, 69.54905] |

LVA | −70.4 | 97.66 | −0.72 | 0.472 | [−263.0863, 122.2896] |

MAC | 235.37 | 247.68 | 0.95 | 0.343 | [−253.3254, 724.0649] |

MAR | 426.86 | 415.58 | 1.03 | 0.306 | [−393.1085, 1246.832] |

MCO | 228.67 | 228.95 | 1 | 0.319 | [−223.0632, 680.4089] |

MDA | 26.78 | 37.72 | 0.71 | 0.479 | [−47.63299, 101.1987] |

MDG | 293.64 | 318.76 | 0.92 | 0.358 | [−335.2989, 922.5689] |

MDV | 88.83 | 87.04 | 1.02 | 0.309 | [−82.90518, 260.5718] |

MEX | 374.19 | 398.69 | 0.94 | 0.349 | [−412.467, 1160.84] |

MKD | −157.69 | 179.44 | −0.88 | 0.381 | [−511.7428, 196.361] |

MLI | 275.04 | 271.87 | 1.01 | 0.313 | [−261.3773, 811.4663] |

MLT | −125.21 | 149.46 | −0.84 | 0.403 | [−420.1182, 169.6895] |

MMR | 456.09 | 479.59 | 0.95 | 0.343 | [−490.168, 1402.357] |

MNE | 32.86 | 22.77 | 1.44 | 0.151 | [−12.06697, 77.78323] |

MNG | 209.38 | 216.84 | 0.97 | 0.336 | [−218.4693, 637.2248] |

MOZ | 277.65 | 287.27 | 0.97 | 0.335 | [−289.1506, 844.4498] |

MRT | 136.57 | 144.52 | 0.94 | 0.346 | [−148.5807, 421.7112] |

MUS | −221.78 | 246.34 | −0.9 | 0.369 | [−707.8259, 264.269] |

MWI | 265.54 | 286.68 | 0.93 | 0.356 | [−300.1154, 831.1903] |

MYS | −432.16 | 665.46 | −0.65 | 0.517 | [−1745.172, 880.8547] |

NAM | 282.94 | 314.23 | 0.9 | 0.369 | [−337.0612, 902.9311] |

NCL | 285.79 | 312.88 | 0.91 | 0.362 | [−331.5583, 903.1301] |

NER | 211.67 | 211.31 | 1 | 0.318 | [−205.2679, 628.5985] |

NGA | 462.42 | 328.72 | 1.41 | 0.161 | [−186.1661, 1111.009] |

NIC | 298.84 | 323.29 | 0.92 | 0.357 | [−339.0496, 936.7254] |

NLD | −1257.85 | 2128.45 | −0.59 | 0.555 | [−5457.455, 2941.764] |

NOR | 171.77 | 144.10 | 1.19 | 0.235 | [−112.5632, 456.0975] |

NPL | 322.12 | 342.61 | 0.94 | 0.348 | [−353.8727, 998.1114] |

NZL | −324.92 | 491.89 | −0.66 | 0.51 | [−1295.46, 645.6192] |

OMN | 306.8 | 306.43 | 1 | 0.318 | [−297.7998, 911.4071] |

PAK | 493.49 | 426.25 | 1.16 | 0.248 | [−347.5393, 1334.529] |

PAN | 366.84 | 392.24 | 0.94 | 0.351 | [−407.0808, 1140.766] |

PER | 271.73 | 222.84 | 1.22 | 0.224 | [−167.9554, 711.4218] |

PHL | −104.64 | 262.64 | −0.4 | 0.691 | [−622.8616, 413.5793] |

PNG | 297.34 | 316.28 | 0.94 | 0.348 | [−326.6992, 921.381] |

POL | 297.22 | 20.63 | 14.4 | 0 *** | [256.5053, 337.9304] |

PRT | −41.92 | 222.84 | −0.19 | 0.851 | [−481.6021, 397.7661] |

PRY | −60.38 | 68.79 | −0.88 | 0.381 | [−196.1178, 75.3495] |

PSE | 250.98 | 256.15 | 0.98 | 0.328 | [−254.4312, 756.3853] |

PYF | 300.49 | 308.45 | 0.97 | 0.331 | [−308.1146, 909.092] |

QAT | 207.47 | 166.47 | 1.25 | 0.214 | [−120.9961, 535.9267] |

ROU | −172.6 | 299.78 | −0.58 | 0.565 | [−764.0896, 418.8857] |

RUS | 55.24 | 861.24 | 0.06 | 0.949 | [−1644.06, 1754.53] |

RWA | 205.69 | 207.25 | 0.99 | 0.322 | [−203.2454, 614.611] |

SAU | 678.99 | 400.19 | 1.7 | 0.091 | [−110.6093, 1468.596] |

SDN | 678.37 | 630.08 | 1.08 | 0.283 | [−564.8316, 1921.575] |

SEN | 213.10 | 229.29 | 0.93 | 0.354 | [−239.313, 665.5046] |

SGP | −1055.88 | 1389.32 | −0.76 | 0.448 | [−3797.131, 1685.373] |

SLE | 236.47 | 236.93 | 1 | 0.32 | [−231.0028, 703.9444] |

SLV | 371.88 | 399.40 | 0.93 | 0.353 | [−416.1667, 1159.925] |

SMR | 211.90 | 195.89 | 1.08 | 0.281 | [−174.6041, 598.398] |

SOM | 300.16 | 297.33 | 1.01 | 0.314 | [−286.5072, 886.8234] |

SRB | 94.44 | 55.08 | 1.71 | 0.088 | [−14.23795, 203.1249] |

SSD | 400.82 | 407.84 | 0.98 | 0.327 | [−403.8719, 1205.521] |

STP | 193.51 | 198.63 | 0.97 | 0.331 | [−198.4036, 585.4259] |

SUR | 243.73 | 262.98 | 0.93 | 0.355 | [−275.149, 762.6014] |

SVK | −247.02 | 326.19 | −0.76 | 0.45 | [−890.6272, 396.5884] |

SVN | 19.56 | 13.68 | 1.43 | 0.155 | [−7.434995, 46.55195] |

SWE | −393.60 | 866.62 | −0.45 | 0.65 | [−2103.527, 1316.32] |

SWZ | 242.6 | 251.98 | 0.96 | 0.337 | [−254.5818, 739.7901] |

SYC | 132.13 | 125.70 | 1.05 | 0.295 | [−115.8824, 380.1409] |

SYR | 359.9 | 377.63 | 0.95 | 0.342 | [−385.2012, 1104.996] |

TCD | 188.54 | 157.18 | 1.2 | 0.232 | [−121.5861, 498.6678] |

TGO | 238.09 | 240.84 | 0.99 | 0.324 | [−237.107, 713.2928] |

THA | −888.23 | 1271.91 | −0.7 | 0.486 | [−3397.813, 1621.363] |

TJK | 244.53 | 256.35 | 0.95 | 0.341 | [−261.2624, 750.32] |

TKM | 241.53 | 249.09 | 0.97 | 0.334 | [−249.9408, 732.9929] |

TTO | 233.84 | 258.47 | 0.9 | 0.367 | [−276.1362, 743.8105] |

TUN | 390.26 | 415.38 | 0.94 | 0.349 | [−429.3194, 1209.847] |

TUR | 151.52 | 355.53 | 0.43 | 0.67 | [−549.9788, 853.0178] |

TZA | 363.15 | 384.23 | 0.95 | 0.346 | [−394.9798, 1121.274] |

UGA | 338.52 | 352.60 | 0.96 | 0.338 | [−357.1915, 1034.23] |

UKR | −625.16 | 818.54 | −0.76 | 0.446 | [−2240.213, 989.8846] |

URY | −251.19 | 310.16 | −0.81 | 0.419 | [−863.1708, 360.7852] |

USA | 8620.85 | 3545.36 | 2.43 | 0.016 * | [1625.561, 15616.13] |

UZB | −500.93 | 603.00 | −0.83 | 0.407 | [−1690.688, 688.8321] |

VEN | −229.32 | 437.64 | −0.52 | 0.601 | [−1092.822, 634.1773] |

VNM | −357.61 | 489.28 | −0.73 | 0.466 | [−1323.01, 607.7872] |

VUT | 180.37 | 171.08 | 1.05 | 0.293 | [−157.189, 517.9312] |

WSM | 146.34 | 140.63 | 1.04 | 0.299 | [−131.1335, 423.8183] |

YEM | 343.20 | 357.33 | 0.96 | 0.338 | [−361.8306, 1048.234] |

ZAF | −490.76 | 832.22 | −0.59 | 0.556 | [−2132.81, 1151.288] |

ZMB | 194.33 | 185.64 | 1.05 | 0.297 | [−171.9579, 560.6236] |

ZWE | 272.31 | 291.27 | 0.93 | 0.351 | [−302.3891, 847.0155] |

_cons | −701.87 | 663.58 | −1.06 | 0.292 | [−2011.17, 607.42] |

Variables | Coef. | Robust Std. Err | Z | p | 95% Confidence Interval |
---|---|---|---|---|---|

DTN-NODF | −1.89 | 1.33 | −1.42 | 0.156 | [−4.50, 0.72] |

Comp. | 46.55 | 13.81 | 3.37 | 0.001 ** | [19.49, 73.61] |

Intercept Term | −430.93 | 188.57 | −2.29 | 0.022 * | [−800.53, −61.33] |

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**Figure 1.**Comparison between Mutualistic System and Global Production System. (

**a**) There exists a mutually beneficial symbiosis relationship between plants and pollinators. In simple terms, pollinators pollinate plants to promote the formation of their fruits and take in the nutrients they need at the same time. Among pollinators, there is not only competition for plants but also collaboration to complete the process of collecting pollination, which will be beneficial to both sides as their population grows. (

**b**) Refers to the global production system where the orange circles represent the upstream sectors and the blue circles the downstream sectors. The numerous upstream and downstream sectors on the GVC cooperate to complete the industrial division of labor, while the upstream sectors not only compete for the same buyers but also collaborate to make sure these buyers can get what they need in the production process.

**Figure 2.**Relationship between MRIO Table and Network. Typical MRIO table includes three different areas, namely value-added, intermediate use and final demand. It is possible that the whole global economic system can be abstracted to a multilayer network as shown in Figure 2b, which includes three layers: the value-added layer, the intermediate use layer, and the final demand layer. The intermediate use layer can be further treated as a puzzle that is made of many single-layer networks out of a multilayer network, in which the nodes are the countries/regions, the layers are the industrial sectors, and links can be established from sellers to buyers within and across industrial sectors. If necessary, we can change the one-mode MRIO network into a two-mode network to separate the inner identity of each sector and prepare for the projection. In Figure 2d, the same sector distributes on the two sides of the dotted line, which means it belongs to both the upper stream and the lower stream. In other words, the upper stream sector in the MRIO table could be referred to as the object nodes in the bipartite graph, while the lower stream sector could be the participant nodes. Now, the self-loop is transformed into an edge between the two identities of this sector.

**Figure 3.**Topology of Different Regions after Sorting the Adjacency Matrix of GVC Network Based on SBD Algorithm. (

**A**) The IO relationship between the upstream and downstream generalist sectors; (

**B**) The IO relationship between the upstream generalist sectors and the downstream specialist sectors; (

**C**) The IO relationship between the upstream specialist sectors and the downstream generalist sectors; (

**D**) The IO relationship between the upstream and downstream specialist sectors.

**Figure 5.**The NODF of Removing a Certain Industrial Sector of GVC Network. The horizontal gray lines represent the NODF of the nested network sorted by the SBD algorithm, and the red scatter points represent the correspondence between the generalist degree after removing a certain industrial sector (the size of the outdegree or indegree) and the new NODF of the nested network.

**Figure 6.**The NODF of Proportionally Removing Industry Sectors of GVC Network. The gray lines represent the variation in the value of network nestedness after randomly removing a certain proportion of industrial sectors from the aligned adjacency matrix; the blue lines represent the variation in the value of network nestedness after removing industrial sectors from the aligned adjacency matrix in the descending order of generalist degree; the green lines represent the variation in the value of network nestedness after removing industrial sectors from the aligned adjacency matrix in the descending order of specialist.

**Figure 7.**The Formation Process of Nested Structure of GVC Network. The orange circle 1 in (

**a**) represents the developed countries initially at the center of the world economic system, while the yellow circles are the developing countries at the periphery, and the size of the circles reflects the degree of centrality of the countries; (

**b**,

**c**) indicate the gradual migration process of peripheral country 4 and peripheral country 6 to the central position, respectively. Besides, the ratio of outdegree of upstream sectors to indegree of downstream ones is designed to reflect the heterogeneity of development level of economies. Accordingly, the absolute value of slope of linear fitting increasing in (

**d**,

**e**) means our world is flattened by the economic integration.

**Figure 8.**Correlation of DTN-NODF, ETN-NODF, ITN-NODF and GDP. Three countries with large differences in GDP are selected, with red representing China, blue the United States and green Sierra Leone. Data source: World Bank—https://data.worldbank.org.cn/indicator, accessed on 14 January 2021.

Variables | Coef. | Robust Std. Err | t | p | 95% Confidence Interval |
---|---|---|---|---|---|

DTN-NODF | −9.49 | 2.64 | −3.60 | 0.000 | [−14.67, −4.32] |

ETN-NODF | 44.27 | 3.88 | 11.40 | 0.000 | [36.65, 51.90] |

ITN-NODF | 21.03 | 6.88 | 3.06 | 0.002 | [7.54, 34.52] |

Intercept Term | 71.97 | 180.36 | 0.40 | 0.690 | [−281.95, 425.89] |

${R}^{2}$ (adjusted) | 0.411 | Root MSE | 867.68 |

Component | Eigenvalue | Difference | Proportion | Cumulative | KMO | SMC |
---|---|---|---|---|---|---|

ETN-NODF | 233.326 | 220.745 | 0.9488 | 0.9488 | 0.9999 | 0.7410 |

ITN-NODF | 12.581 | - | 0.0512 | 1.0000 | 0.9999 | 0.7410 |

Variables | Coef. | Robust Std. Err | t | p | 95% Confidence Interval |
---|---|---|---|---|---|

DTN-NODF | −9.63 | 2.60 | −3.71 | 0.000 | [−14.72, −4.54] |

Comp. | 48.99 | 1.83 | 26.74 | 0.000 | [45.39, 52.58] |

Intercept Term | 74.09 | 180.14 | 0.41 | 0.681 | [−279.40, 427.57] |

${R}^{2}$ (adjusted) | 0.411 | Root MSE | 867.3 |

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## Share and Cite

**MDPI and ACS Style**

Ren, J.; Xing, L.; Han, Y.; Dong, X.
Nestedness-Based Measurement of Evolutionarily Stable Equilibrium of Global Production System. *Entropy* **2021**, *23*, 1077.
https://doi.org/10.3390/e23081077

**AMA Style**

Ren J, Xing L, Han Y, Dong X.
Nestedness-Based Measurement of Evolutionarily Stable Equilibrium of Global Production System. *Entropy*. 2021; 23(8):1077.
https://doi.org/10.3390/e23081077

**Chicago/Turabian Style**

Ren, Jiaqi, Lizhi Xing, Yu Han, and Xianlei Dong.
2021. "Nestedness-Based Measurement of Evolutionarily Stable Equilibrium of Global Production System" *Entropy* 23, no. 8: 1077.
https://doi.org/10.3390/e23081077