Recall that in a cost game (N, c), for a coalition SCN, the number c(S) is interpreted as the cost of coalition S, not a

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Recall That In A Cost Game N C For A Coalition Scn The Number C S Is Interpreted As The Cost Of Coalition S Not A 1 (211.65 KiB) Viewed 39 times

Recall that in a cost game (N, c), for a coalition SCN, the number c(S) is interpreted as the cost of coalition S, not as the gain of S. Hence, the Shapley value, the core, the nucleolus, of the cost game (N, c) is defined to be the negative of the Shapley value, the core, the nucleolus, of the ordinary TU game (N, v), where v = -c. Exercise 5. Let N = {1,...,4} and C = (12, 18, 24, 36) and consider the corresponding airport cost game (N, c) defined by c(S) = max{Ci | i € S} for all Ø ‡ S ≤ N and c(0) = 0. 1. Verify that the corresponding TU game (N, —c) is a convex game and find and describe the core. 2. Compute the Shapley value of (N, c). 3. Compute the nucleolus of (N, c). 4. Compute the modiclus of (N, c).