Consider a market with 2 sellers and b buyers labelled 1; 2; 3; : : : b+2, where the first two players are sellers. Assume each buyer wants to buy an identical good worth 0 to each seller and worth 1 to each buyer. Also assume that each seller has k
identical goods, where k < b < 2k.
i) Write down the characteristic function for the above problem.
ii) Is the Gillies’ core for the above problem non-empty? If yes, display one vector in it.
iii) Find the Shapley values if k = 3 and b = 5.