3. (4 points) (Shapley value, core) Consider a three person game with the characteristic function v(1)=8,v(2)=5,v(3)=6,v(12)=20,v(13)=24,v(23)=15 and v(N)=50 (i) Find the Shapley value of this game. (ii) Find the core of this game. (iii) Is the Shapley value in the core? (iv) Assuming that superadditivity must hold and that v(K) are fixed for all K=N, what is the lowest value to which v(N) can be changed? If v(N) is changed to this value, is the core empty or nonempty? 3. (4 points) (Shapley value, core) Consider a three person game with the characteristic function v(1)=8,v(2)=5,v(3)=6,v(12)=20,v(13)=24,v(23)=15 and v(N)=50 (i) Find the Shapley value of this game. (ii) Find the core of this game. (iii) Is the Shapley value in the core? (iv) Assuming that superadditivity must hold and that v(K) are fixed for all K=N, what is the lowest value to which v(N) can be changed? If v(N) is changed to this value, is the core empty or nonempty