Consider the glove game in which there are four players; player 1 can supply one left glove and players 2, 3, and 4 can supply one right glove each.

Consider the glove game in which there are four players; player 1 can supply one left glove and players 2, 3, and 4 can supply one right glove each.

(a) Find v(S) for this game if the value of a coalition is the number of paired gloves in the coalition.
(b) Find C(0).
(c) What is the Shapley allocation?
(d) Now we change the problem a bit. Suppose there are two players, each with three gloves. Player 1 has two left-hand gloves and one right-hand glove; player 2 has two right-hand gloves and one left-hand glove. They can sell a pair of gloves for 10 dollars. How should they split the proceeds. Determine the nucleolus and the Shapley allocation.
Consider the glove game in which there are four players; player 1 can supply one left glove and players 2, 3, and 4 can supply one right glove each.