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There is a cooperative game involving three persons (i.e., A, B, and C). The characteristic values of all possible coalitions are v($) = 0; "(A) = 5, v(B) = x, v(C) = 2; U(AB) = y, v(AC) =10, v(BC) = 12; v( ABC) = z. 1. In which ranges must the values of x, y, and z be to ensure that the grand coalition is stable? That is, if all conditions for the non-emptiness of the core are satisfied, what ranges should the values of x, y, and z be in? [12 Marks] 2. Suppose the values of x, y. and z are in the ranges obtained by you in part a. You are required to find the Shapley value in terms of x, y, and z. Under the Shapley value, the allocations to players A, B, and C are a(A). a(B), and a(C), respectively. You need to find the values of a(A), a(B). and a(C). [12 Marks] 3. Under what condition(s) will the Shapley value for player A is the highest fi.e., a(A) > a(B) and a(A) 2 a(C)}? You should find the condition(s) in terms of x, y, and z. [6 Marks]