Consider the following transferable utility cooperative game: N = {1,2,3} and v({1})= 2, v({2}) = 4, v({3}) = 2 v({1, 2}) = 8, v({1,3})= 10, v({2,3}) = 8 v({1,2,3}) = 12 = (a) Two players i and j are interchangeable if for all S that contains neither i nor j,v(SU {i})= v(SU{j}). Rewrite/explain this definition with your own words. (b) Are there any players that are interchangeable? If so, which ones?

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Cooperative Games - Game Theory

Consider the following transferable utility cooperative game: N = {1,2,3} and
v({1})= 2, v({2}) = 4, v({3}) = 2
v({1, 2})=8, v({1,3}) = 10, v({2,3}) = 8
v({1,2,3}) = 12
(a) Two players i and j are interchangeable if for all S that contains neither i nor j,v(SU {i})=
v(SU {j}).
Rewrite/explain this definition with your own words.
(b) Are there any players that are interchangeable? If so, which ones?
Transcribed Image Text:Consider the following transferable utility cooperative game: N = {1,2,3} and v({1})= 2, v({2}) = 4, v({3}) = 2 v({1, 2})=8, v({1,3}) = 10, v({2,3}) = 8 v({1,2,3}) = 12 (a) Two players i and j are interchangeable if for all S that contains neither i nor j,v(SU {i})= v(SU {j}). Rewrite/explain this definition with your own words. (b) Are there any players that are interchangeable? If so, which ones?
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