A professor is invited to visit three universities located in Chicago, New York and Washington, respectively. The round trip costs of visiting each city either separately or in combination are as follows: Chicago (C) 400 New York (N) 300 Washington (D) 300 C and N 600 C and D 500 N and D 450 C, N and D 750 The anti-core is a variation of the core suitable for allocating costs vs. benefits. Formally, the anti-core is the set of payoff vectors such that no coalition is charged more than its own cost, c(S), or ( ), .  n i i S x x cS S N       a. If the professor were to make a single trip to all three and allocate the costs equally among the hosts, is this in the anti-core? Explain. b. Is the allocation (350,200,200) to C, N and D, respectively, in the anti-core? Explain. c. If costs were allocation according to the Shapley value, what amount should each pay? Is this in the anti-core? Explain