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A classic game is the garbage game. Suppose that there are n property owners, each with one bag of garbage that needs to be dumped on somebody’s property (one of the n). If n bags of garbage are dumped on a coalition S of property owners, the coalition receives a reward of −n. The characteristic function is taken to be the best that the members of a coalition S can do, which is to dump all their garbage on the property of the owners not in S. (a) Explain why the characteristic function should be v(S) = −(n − |S|), v(N) = −n, v(∅) = 0, where |S| is the number of members in S.

(b) Show that the core of the game is empty if n > 2.