Voting (1) Suppose in Parliament there are four parties A; B;C; D with numbers of votes equal to 40; 30; 20; 10, respectively. To pass any law a two-third majority is needed. (a) Formulate this...

Voting (1)

Suppose in Parliament there are four parties A; B;C; D with numbers of votes equal to 40; 30; 20; 10, respectively. To pass any law a two-third majority is needed.

(a) Formulate this situation as a four-person cooperative game where winning coalitions have worth 1 and losing coalitions worth 0. Determine the Shapley value of this game.

(b) Determine also the core and the nucleolus of this game.