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Variable Sum Games as Models of Public Goods in the International System - A Crtical Appraisal
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14
DD
DC
Possible Games - Given the Assumptions that MRSc = MRSc
The 4! possible ordinal preference orderings for the 2x2 variable sum game are shown
in table 1. All but four of these preference orderings can be eliminated from consideration due
to the requirements of theorems 1, 6, and 7 or corollary 7.1. That is, no permutation in which
CD>CC, DD>DC, (DC>CC and CD>DD), or (CC>DD and DD>CD) can be a preference
ordering given the assumptions of the model at this point and the arguments in the previous
discussion.
Permutation
Possible
Reason
not
Possible
Permutation
Possible
Reason
not
Possible
1. CC > CD > DC > DD
Yes
13. DC > CC > CD > DD
No
Theorem 7
2. CC > CD > DD > DC
No
Theorem 6
14. DC > CC > DD > CD
Yes
3. CC > DC > CD > DD
Yes
15. DC > CD > CC > DD
No
Theorem 1
4. CC > DC > DD > CD
No
Corollary 7.1
16. DC > CD > CC > DD
No
Theorem 1
5. CC > DD > CD > DC
No
Theorem 6
17. DC > DD > CC > CD
Yes
6. CC > DD > DC > CD
No
Theorem 6
18. DC > DD > CD > CC
No
Theorem 1
7. CD > CC > DC > DD
No
Theorem 1
19. DD > CC > CD > DC
No
Theorem 6
8. CD > CC > DD > DC
No
Theorem 1
20. DD > CC > DC > CD
No
Theorem 6
9. CD > DC > CC > DD
No
Theorem 1
21. DD > CD > CC > DC
No
Theorem 6
10. CD > DC > DD > CC
No
Theorem 1
22. DD > CD > DC > CC
No
Theorem 6
11. CD > DD > CC > DC
No
Theorem 1
23. DD > DC > CC > CD
No
Theorem 6
12. CD > DD > DC > CC
No
Theorem 1
24. DD > DC > CD > CC
No
Theorem 6
Table 1. The 24 permutations of the public goods preference orderings.
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14
DD
DC
Possible Games - Given the Assumptions that MRSc = MRSc
The 4! possible ordinal preference orderings for the 2x2 variable sum game are shown
in table 1. All but four of these preference orderings can be eliminated from consideration due
to the requirements of theorems 1, 6, and 7 or corollary 7.1. That is, no permutation in which
CD>CC, DD>DC, (DC>CC and CD>DD), or (CC>DD and DD>CD) can be a preference
ordering given the assumptions of the model at this point and the arguments in the previous
discussion.
Permutation
Possible
Reason
not
Possible
Permutation
Possible
Reason
not
Possible
1. CC > CD > DC > DD
Yes
13. DC > CC > CD > DD
No
Theorem 7
2. CC > CD > DD > DC
No
Theorem 6
14. DC > CC > DD > CD
Yes
3. CC > DC > CD > DD
Yes
15. DC > CD > CC > DD
No
Theorem 1
4. CC > DC > DD > CD
No
Corollary 7.1
16. DC > CD > CC > DD
No
Theorem 1
5. CC > DD > CD > DC
No
Theorem 6
17. DC > DD > CC > CD
Yes
6. CC > DD > DC > CD
No
Theorem 6
18. DC > DD > CD > CC
No
Theorem 1
7. CD > CC > DC > DD
No
Theorem 1
19. DD > CC > CD > DC
No
Theorem 6
8. CD > CC > DD > DC
No
Theorem 1
20. DD > CC > DC > CD
No
Theorem 6
9. CD > DC > CC > DD
No
Theorem 1
21. DD > CD > CC > DC
No
Theorem 6
10. CD > DC > DD > CC
No
Theorem 1
22. DD > CD > DC > CC
No
Theorem 6
11. CD > DD > CC > DC
No
Theorem 1
23. DD > DC > CC > CD
No
Theorem 6
12. CD > DD > DC > CC
No
Theorem 1
24. DD > DC > CD > CC
No
Theorem 6
Table 1. The 24 permutations of the public goods preference orderings.
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