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7. Consider the following cooperative game: N = { 1, 2, 3,4) and V([1)) = v(12)) =4, v(13)) = v(14)) =6 v({1,2)) = v({ 1,3]) = v({ 1,4)) = 8, v({2,3)) = 10, v({2,4)) = 10, v({3,4)) = 12, v({1,2,3]) = v({ 1,2,4)) = v({2,3,4]) = 14, v({1,2,3,4)) = 18 Is the core non-empty? 8. Consider the following cooperative game: N = {1, 2, 3) and v({1)) =10, v((2)) =8, v(13)) =6 v({1,2)) =24, v({1,3)) = 22, v({2,3)) = 18 v({1,2,3]) = 34 Find the Shapley value. 9. Consider the following cooperative game: N = {1, 2, 3 ) and v({1]) = 80, v((2)) = 60, v(13)) =30 v({1,2)) = 180, v({1,3)) = 160, v({2,3]) = 120 v({1,2,3]) = 260. Find the Shapley value 10. Consider again the game of Exercise 9. Is Player 1 a dummy player?1 1. Consider again the game of Exercise 9. Are Players I and 2 interchangeable? 12. Consider the following cooperative game: N = (1, 2, 3) and v((1)) = 2, v(12)) =4, v(13)) =2 v({1,2)) =8, v({1,3)) = 10. v(12,3]) = 8 v({1,2,3)) = 12 (a) Are Players 1 and 3 interchangeable? (b) Find the Shapley value. (c) Is the Shapley value in the core? 13. Consider the following cooperative game: N = (1, 2, 3) and V((1)) =2, v(12)) =4, v(13))=6 v({1,2)) =6, v([1,3)) =8, v(12,3)) = 12 v({1,2,3) ) = 14 (a) Are any two players interchangeable? (b) Is any player a dummy player? (c) Find the Shapley value. (d) Is the Shapley value in the core