A Flow Game Consider the network in Fig XXXXXXXXXXSuppose that this is a controlled capacitated network with player  suppose that all edges have capacity 1 and that  is the simple game where a...

A Flow Game

Consider the network in Fig. 20.2. Suppose that this is a controlled capacitated network with player
 suppose that all edges have capacity 1 and that
 is the simple game where a coalition is winning if, and only if, it contains player i.]

(a) Calculate the corresponding flow game
.

(b) Calculate

(c) The proof of Theorem 20.6 describes a way to find core elements by looking at minimum cuts and dividing the capacities of edges in the minimum cut in some way among the veto players of the corresponding control game. Which elements of
 can be obtained in this way?

Fig. 20.2