1. Consider the following three-person cooperative game C = (N,v()) where the characteristic function v() is...

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1. Consider the following three-person cooperative game C = (N,v()) where the characteristic function v() is defined by v({i}) = 2, i = 1,2,3; v({1,2}) = 50 v({1, 3)} = 80 v({2,3}) = 90 v(N) = 100. (a) Is the above game essential? Explain your answer. (b) Obtain the characteristic function v' () of the game in 0 - 1 normal form which is strategically equivalent to C. What is the value of the payoff for each two-person coalition in this equivalent game? (c) Determine the core of the game (N, v'()). (d) Determine the Shapley value for Player 2 in the game (N, v'()). (4+6+4+6= 20 marks) 1. Consider the following three-person cooperative game C = (N,v()) where the characteristic function v() is defined by v({i}) = 2, i = 1,2,3; v({1,2}) = 50 v({1, 3)} = 80 v({2,3}) = 90 v(N) = 100. (a) Is the above game essential? Explain your answer. (b) Obtain the characteristic function v' () of the game in 0 - 1 normal form which is strategically equivalent to C. What is the value of the payoff for each two-person coalition in this equivalent game? (c) Determine the core of the game (N, v'()). (d) Determine the Shapley value for Player 2 in the game (N, v'()). (4+6+4+6= 20 marks)