On Theorem XXXXXXXXXX) (a) Consider a controlled capacitated network with a minimum cut, where all control games corresponding to the edges in this minimum cut (connecting vertices between the two...

On Theorem 20.6 (1)

(a) Consider a controlled capacitated network with a minimum cut, where all control games corresponding to the edges in this minimum cut (connecting vertices between the two sets in the cut) have veto players. Prove that the corresponding flow game is balanced.

(b) Show that the flow game, corresponding to Fig. 20.3, where the winning coalitions of
 where the winning coalitions of
 and where the capacities are 1, 10, 10 respectively, has a nonempty core. Note that there is no minimum cut where all control games have veto players.

Fig. 20.3