Allocation of Disputable Zones in the Arctic Region
Fig. 1. Natural resources availability in Arctic region
Fig. 2. Areas allocation by distance (scenario 1) and utility (scenario 2)
Fig. 3. Areas allocation with respect to the satisfaction level
Fig. 4. Areas allocation according to scenarios 15-18
Fig. 5. Areas allocation by the modified adjusted winner procedure
Fig. 6. Areas allocation according to scenario 20
Table 1. Importance of shipping routes in Arctic region
|
ID |
Country |
Gross register tonnage (GRT) |
Importance of shipping routes |
|
1 |
USA |
22009 |
0.01 |
|
2 |
Russia |
751227 |
0.51 |
|
3 |
Canada |
40142 |
0.03 |
|
4 |
Denmark |
76311 |
0.05 |
|
5 |
Norway |
401676 |
0.27 |
|
6 |
Iceland |
12413 |
0.01 |
|
7 |
China |
217610 |
0.15 |
|
8 |
Japan |
200937 |
0.14 |
|
9 |
South Korea |
366232 |
0.25 |
Table 2. Envy-freeness for scenarios 3,5
|
Country in row envies country in column |
USA |
Russia |
Canada |
Denmark |
Norway |
Iceland |
China |
Japan |
South Korea |
Envy-freeness |
|
USA |
0 |
-514 |
-16 |
116 |
1119 |
1394 |
1394 |
1394 |
1394 |
-514 |
|
Russia |
919 |
0 |
540 |
498 |
1966 |
2467 |
2467 |
2467 |
2467 |
0 |
|
Canada |
268 |
-203 |
0 |
-178 |
1199 |
1521 |
1521 |
1521 |
1521 |
-203 |
|
Denmark |
775 |
335 |
303 |
0 |
374 |
1755 |
1755 |
1755 |
1755 |
0 |
|
Norway |
769 |
300 |
223 |
-71 |
0 |
1566 |
1566 |
1566 |
1566 |
-71 |
|
Iceland |
-105 |
-137 |
-434 |
-695 |
-1236 |
0 |
0 |
0 |
0 |
-1236 |
|
China |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
|
Japan |
-331 |
-434 |
-26 |
0 |
0 |
0 |
0 |
0 |
0 |
-434 |
|
South Korea |
-10 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
-10 |
Table 3. Envy-freeness for scenario 4
|
Country in row envies country in column |
USA |
Russia |
Canada |
Denmark |
Norway |
Iceland |
China |
Japan |
South Korea |
Envy-freeness |
|
USA |
0 |
-396 |
-98 |
129 |
1120 |
1404 |
1404 |
1404 |
1404 |
-396 |
|
Russia |
895 |
0 |
572 |
548 |
1960 |
2478 |
2478 |
2478 |
2478 |
0 |
|
Canada |
329 |
-208 |
0 |
-184 |
1200 |
1532 |
1532 |
1532 |
1532 |
-208 |
|
Denmark |
869 |
219 |
374 |
0 |
374.7 |
1765 |
1765 |
1765 |
1765 |
0 |
|
Norway |
853 |
146 |
331 |
-58 |
0 |
1576 |
1576 |
1576 |
1576 |
-58 |
|
Iceland |
-13 |
-287 |
-361 |
-710 |
-1237 |
0 |
0 |
0 |
0 |
-1237 |
|
China |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
|
Japan |
-398 |
-259 |
-135 |
0 |
0 |
0 |
0 |
0 |
0 |
-398 |
|
South Korea |
-6.5 |
-3.1 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
-6.5 |
Table 4. Envy-freeness for scenario 6
|
Country in row envies country in column |
USA |
Russia |
Canada |
Denmark |
Norway |
Iceland |
China |
Japan |
South Korea |
Envy-freeness |
|
USA |
0 |
-273 |
-154 |
124 |
1127 |
1418 |
1418 |
1418 |
1418 |
-273 |
|
Russia |
920 |
0 |
545 |
609 |
1969 |
2491 |
2491 |
2491 |
2491 |
0 |
|
Canada |
330 |
-125 |
0 |
-201 |
1200 |
1545 |
1545 |
1545 |
1545 |
-201 |
|
Denmark |
892 |
238 |
403 |
0 |
372.2 |
1779 |
1779 |
1779 |
1779 |
0 |
|
Norway |
889 |
113 |
372 |
-34 |
0 |
1590 |
1590 |
1590 |
1590 |
-34 |
|
Iceland |
-4.3 |
-309 |
-323 |
-723 |
-1248 |
0 |
0 |
0 |
0 |
-1248 |
|
China |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
|
Japan |
-409 |
-204 |
-178 |
-0.2 |
0 |
0 |
0 |
0 |
0 |
-409 |
|
South Korea |
-8.2 |
-0.4 |
-0.9 |
-0.1 |
0 |
0 |
0 |
0 |
0 |
-8.2 |
Table 5. Envy-freeness for scenario 7
|
Country in row envies country in column |
USA |
Russia |
Canada |
Denmark |
Norway |
Iceland |
China |
Japan |
South Korea |
Envy-freeness |
|
USA |
0 |
-503 |
-16 |
117 |
1119 |
1397 |
1397 |
1397 |
1397 |
-503 |
|
Russia |
918 |
0 |
555 |
498 |
1965 |
2470 |
2470 |
2470 |
2470 |
0 |
|
Canada |
274 |
-197 |
0 |
-178 |
1199 |
1524 |
1524 |
1524 |
1524 |
-197 |
|
Denmark |
785 |
330 |
310 |
0 |
374.8 |
1758 |
1758 |
1758 |
1758 |
0 |
|
Norway |
778 |
290 |
236 |
-71 |
0 |
1569 |
1569 |
1569 |
1569 |
-71 |
|
Iceland |
-99 |
-143 |
-433 |
-696 |
-1236 |
0 |
0 |
0 |
0 |
-1236 |
|
China |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
|
Japan |
-337 |
-421 |
-33 |
-0.2 |
0 |
0 |
0 |
0 |
0 |
-421 |
|
South Korea |
-9.6 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
-9.6 |
Table 6. Envy-freeness for scenario 8
|
Country in row envies country in column |
USA |
Russia |
Canada |
Denmark |
Norway |
Iceland |
China |
Japan |
South Korea |
Envy-freeness |
|
USA |
0 |
-211 |
-202 |
89.4 |
1166 |
1422 |
1422 |
1422 |
1422 |
-211 |
|
Russia |
902 |
0 |
549 |
572 |
2036 |
2494 |
2494 |
2494 |
2494 |
0 |
|
Canada |
331 |
-103 |
0 |
-251 |
1244 |
1548 |
1548 |
1548 |
1548 |
-251 |
|
Denmark |
882 |
225 |
445 |
0 |
370.6 |
1782 |
1782 |
1782 |
1782 |
0 |
|
Norway |
872 |
78 |
433 |
-27 |
0 |
1593 |
1593 |
1593 |
1593 |
-27 |
|
Iceland |
-1.3 |
-353 |
-272 |
-707 |
-1273 |
0 |
0 |
0 |
0 |
-1273 |
|
China |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
|
Japan |
-406 |
-151 |
-234 |
0 |
0 |
0 |
0 |
0 |
0 |
-406 |
|
South Korea |
-9.6 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
-9.6 |
Table 7. Envy-freeness for scenario 9
|
Country in row envies country in column |
USA |
Russia |
Canada |
Denmark |
Norway |
Iceland |
China |
Japan |
South Korea |
Envy-freeness |
|
USA |
0 |
-581 |
90.1 |
32.4 |
1118 |
1385 |
1385 |
1385 |
1385 |
-581 |
|
Russia |
895 |
0 |
673 |
347 |
1962 |
2458 |
2458 |
2458 |
2458 |
0 |
|
Canada |
263 |
-244 |
0 |
-179 |
1201 |
1512 |
1512 |
1512 |
1512 |
-244 |
|
Denmark |
742 |
333 |
289 |
0 |
375.9 |
1746 |
1746 |
1746 |
1746 |
0 |
|
Norway |
724 |
325 |
222 |
-98 |
0 |
1557 |
1557 |
1557 |
1557 |
-98 |
|
Iceland |
-116 |
-125 |
-490 |
-647 |
-1229 |
0 |
0 |
0 |
0 |
-1229 |
|
China |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
|
Japan |
-314 |
-457 |
-8.4 |
-11 |
0 |
0 |
0 |
0 |
0 |
-457 |
|
South Korea |
-0.3 |
-9.3 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
-9.3 |
Table 8. Envy-freeness for scenario 10
|
Country in row envies country in column |
USA |
Russia |
Canada |
Denmark |
Norway |
Iceland |
China |
Japan |
South Korea |
Envy-freeness |
|
USA |
0 |
-608 |
92 |
49.3 |
1117 |
1384 |
1384 |
1384 |
1384 |
-608 |
|
Russia |
886 |
0 |
675 |
351 |
1958 |
2457 |
2457 |
2457 |
2457 |
0 |
|
Canada |
279 |
-278 |
0 |
-172 |
1201 |
1510 |
1510 |
1510 |
1510 |
-278 |
|
Denmark |
759 |
306 |
290 |
0 |
376.5 |
1744 |
1744 |
1744 |
1744 |
0 |
|
Norway |
736 |
312 |
223 |
-104 |
0 |
1555 |
1555 |
1555 |
1555 |
-104 |
|
Iceland |
-94 |
-145 |
-490 |
-651 |
-1226 |
0 |
0 |
0 |
0 |
-1226 |
|
China |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
|
Japan |
-329 |
-452 |
-9.4 |
-0.6 |
0 |
0 |
0 |
0 |
0 |
-452 |
|
South Korea |
0 |
-9.6 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
-9.6 |
Table 9. Envy-freeness for scenario 11
|
Country in row envies country in column |
USA |
Russia |
Canada |
Denmark |
Norway |
Iceland |
China |
Japan |
South Korea |
Envy-freeness |
|
USA |
0 |
-506 |
-3 |
105 |
1120 |
1397 |
1397 |
1397 |
1397 |
-506 |
|
Russia |
902 |
0 |
596 |
476 |
1959 |
2469 |
2469 |
2469 |
2469 |
0 |
|
Canada |
299 |
-226 |
0 |
-177 |
1202 |
1524 |
1524 |
1524 |
1524 |
-226 |
|
Denmark |
806 |
301 |
313 |
0 |
376 |
1757 |
1757 |
1757 |
1757 |
0 |
|
Norway |
790 |
269 |
246 |
-75 |
0 |
1568 |
1568 |
1568 |
1568 |
-75 |
|
Iceland |
-59 |
-185 |
-441 |
-690 |
-1233 |
0 |
0 |
0 |
0 |
-1233 |
|
China |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
|
Japan |
-357 |
-389 |
-43 |
-1 |
0 |
0 |
0 |
0 |
0 |
-389 |
|
South Korea |
0 |
-10 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
-10 |
Table 10. Envy-freeness for scenario 12
|
Country in row envies country in column |
USA |
Russia |
Canada |
Denmark |
Norway |
Iceland |
China |
Japan |
South Korea |
Envy-freeness |
|
USA |
0 |
-340 |
-86 |
84 |
1125 |
1410 |
1410 |
1410 |
1410 |
-340 |
|
Russia |
904 |
0 |
584 |
542 |
1972 |
2483 |
2483 |
2483 |
2483 |
0 |
|
Canada |
323 |
-159 |
0 |
-199 |
1199 |
1537 |
1537 |
1537 |
1537 |
-199 |
|
Denmark |
862 |
263 |
369 |
0 |
372 |
1771 |
1771 |
1771 |
1771 |
0 |
|
Norway |
850 |
166 |
329 |
-46 |
0 |
1582 |
1582 |
1582 |
1582 |
-46 |
|
Iceland |
-16 |
-273 |
-374 |
-699 |
-1246 |
0 |
0 |
0 |
0 |
-1246 |
|
China |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
|
Japan |
-393 |
-267 |
-131 |
0 |
0 |
0 |
0 |
0 |
0 |
-393 |
|
South Korea |
-4 |
-6 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
-6 |
Table 11. Envy-freeness for scenario 13
|
Country in row envies country in column |
USA |
Russia |
Canada |
Denmark |
Norway |
Iceland |
China |
Japan |
South Korea |
Envy-freeness |
|
USA |
0 |
-252 |
-182 |
128 |
1125 |
1417 |
1417 |
1417 |
1417 |
-252 |
|
Russia |
898 |
0 |
556 |
616 |
1967 |
2490 |
2490 |
2490 |
2490 |
0 |
|
Canada |
327 |
-126 |
0 |
-200 |
1198 |
1544 |
1544 |
1544 |
1544 |
-200 |
|
Denmark |
871 |
214 |
444 |
0 |
372 |
1778 |
1778 |
1778 |
1778 |
0 |
|
Norway |
858 |
82 |
430 |
-33 |
0 |
1590 |
1590 |
1590 |
1590 |
-33 |
|
Iceland |
-22 |
-343 |
-270 |
-724 |
-1248 |
0 |
0 |
0 |
0 |
-1248 |
|
China |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
|
Japan |
-398 |
-167 |
-226 |
0 |
0 |
0 |
0 |
0 |
0 |
-398 |
|
South Korea |
-8 |
0 |
-1 |
0 |
0 |
0 |
0 |
0 |
0 |
-8 |
Table 12. Envy-freeness for scenario 14
|
Country in row envies country in column |
USA |
Russia |
Canada |
Denmark |
Norway |
Iceland |
China |
Japan |
South Korea |
Envy-freeness |
|
USA |
0 |
-260 |
104 |
-332 |
1134 |
1383 |
1383 |
1383 |
1383 |
-332 |
|
Russia |
912 |
0 |
770 |
141 |
2043 |
2456 |
2456 |
2456 |
2456 |
0 |
|
Canada |
312 |
-172 |
0 |
-348 |
1235 |
1510 |
1510 |
1510 |
1510 |
-348 |
|
Denmark |
844 |
185 |
337 |
0 |
363 |
1743 |
1743 |
1743 |
1743 |
0 |
|
Norway |
831 |
58 |
310 |
-38 |
0 |
1554 |
1554 |
1554 |
1554 |
-38 |
|
Iceland |
-32 |
-354 |
-467 |
-499 |
-1256 |
0 |
0 |
0 |
0 |
-1256 |
|
China |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
|
Japan |
-379 |
-176 |
-99 |
-138 |
0 |
0 |
0 |
0 |
0 |
-379 |
|
South Korea |
-3 |
0 |
-6 |
0 |
0 |
0 |
0 |
0 |
0 |
-6 |
Table 13. Envy-freeness for scenario 15
|
Country in row envies country in column |
USA |
Russia |
Canada |
Denmark |
Norway |
Iceland |
China |
Japan |
South Korea |
Envy-freeness |
|
USA |
0 |
-5825 |
-343 |
12 |
28 |
28 |
28 |
28 |
28 |
-5825 |
|
Russia |
7805 |
0 |
7287 |
7802 |
7827 |
7827 |
7827 |
7827 |
7827 |
0 |
|
Canada |
573 |
-5268 |
0 |
575 |
600 |
600 |
600 |
600 |
600 |
-5268 |
|
Denmark |
64 |
-5163 |
-512 |
0 |
-966 |
82 |
82 |
82 |
82 |
-5163 |
|
Norway |
1212 |
-3558 |
703 |
1142 |
0 |
1222 |
1222 |
1222 |
1222 |
-3558 |
|
Iceland |
-4 |
-1142 |
-274 |
-56 |
-1132 |
0 |
0 |
0 |
0 |
-1142 |
|
China |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
|
Japan |
-6 |
-784 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
-784 |
|
South Korea |
0 |
-10 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
-10 |
Table 14. Envy-freeness for scenario 16
|
Country in row envies country in column |
USA |
Russia |
Canada |
Denmark |
Norway |
Iceland |
China |
Japan |
South Korea |
Envy-freeness |
|
USA |
0 |
-5825 |
-343 |
12 |
28 |
28 |
28 |
28 |
28 |
-5825 |
|
Russia |
7805 |
0 |
7287 |
7802 |
7827 |
7827 |
7827 |
7827 |
7827 |
0 |
|
Canada |
573 |
-5268 |
0 |
575 |
600 |
600 |
600 |
600 |
600 |
-5268 |
|
Denmark |
66 |
-5161 |
-510 |
0 |
-962 |
84 |
84 |
84 |
84 |
-5161 |
|
Norway |
1210 |
-3560 |
701 |
1138 |
0 |
1220 |
1220 |
1220 |
1220 |
-3560 |
|
Iceland |
-4 |
-1142 |
-274 |
-58 |
-1130 |
0 |
0 |
0 |
0 |
-1142 |
|
China |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
|
Japan |
-6 |
-784 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
-784 |
|
South Korea |
0 |
-10 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
-10 |
Table 15. Envy-freeness for scenario 17
|
Country in row envies country in column |
USA |
Russia |
Canada |
Denmark |
Norway |
Iceland |
China |
Japan |
South Korea |
Envy-freeness |
|
USA |
0 |
-5825 |
-343 |
12 |
28 |
28 |
28 |
28 |
28 |
-5825 |
|
Russia |
7805 |
0 |
7287 |
7802 |
7827 |
7827 |
7827 |
7827 |
7827 |
0 |
|
Canada |
573 |
-5268 |
0 |
575 |
600 |
600 |
600 |
600 |
600 |
-5268 |
|
Denmark |
63 |
-5164 |
-513 |
0 |
-969 |
81 |
81 |
81 |
81 |
-5164 |
|
Norway |
1213 |
-3557 |
704 |
1145 |
0 |
1223 |
1223 |
1223 |
1223 |
-3557 |
|
Iceland |
-4 |
-1142 |
-274 |
-55 |
-1133 |
0 |
0 |
0 |
0 |
-1142 |
|
China |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
|
Japan |
-6 |
-784 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
-784 |
|
South Korea |
0 |
-10 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
-10 |
Table 16. Envy-freeness for scenario 18
|
Country in row envies country in column |
USA |
Russia |
Canada |
Denmark |
Norway |
Iceland |
China |
Japan |
South Korea |
Envy-freeness |
|
USA |
0 |
-5825 |
-343 |
12 |
28 |
28 |
28 |
28 |
28 |
-5825 |
|
Russia |
7805 |
0 |
7287 |
7802 |
7827 |
7827 |
7827 |
7827 |
7827 |
0 |
|
Canada |
573 |
-5268 |
0 |
575 |
600 |
600 |
600 |
600 |
600 |
-5268 |
|
Denmark |
66 |
-5161 |
-510 |
0 |
-962 |
84 |
84 |
84 |
84 |
-5161 |
|
Norway |
1210 |
-3560 |
701 |
1138 |
0 |
1220 |
1220 |
1220 |
1220 |
-3560 |
|
Iceland |
-4 |
-1142 |
-274 |
-58 |
-1130 |
0 |
0 |
0 |
0 |
-1142 |
|
China |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
|
Japan |
-6 |
-784 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
-784 |
|
South Korea |
0 |
-10 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
-10 |
Authors: Fuad Aleskerov, Sergey Shvydun
Have you spotted a typo?
Highlight it, click Ctrl+Enter and send us a message. Thank you for your help!
To be used only for spelling or punctuation mistakes.