Vote trading:-

A legislature with three members decides, by majority vote, the fate of three bills, A, B, and C. Each legislator's preferences are represented by the sum of the values she attaches to the bills that pass. The value attached by each legislator to each bill is indicated in Figure.

For example, if bills A and B pass and C fails, then the three legislators' payoffs are 1, 3, and 0 respectively. Each majority coalition can achieve the passage of any set of bills, whereas each minority is powerless.

a. Find the core of the coalitional game that models this situation.

b. Find the core of the game in which the values the legislators attach to the payoff of each bill differ from those in Figure 1 only in that legislator 3 values the passage of bill C at 0.

c. Find the core of the game in which the values the legislators attach to the payoff of each bill differ from those in Figure 1 only in that each 1 is replaced by -1.