My Aunt and I Auntie Betty can complete a certain job together with me or with any of my three brothers, with the payment for the work being $1,000, but she must choose one of the four of us. All four of us brothers together (without Auntie Betty) can also complete the same job.

(a) Describe this situation as a coalitional game.

(b) Compute the nucleolus of the game for the coalitional structure B = {N}.

(c) Compute the nucleolus of the game for the coalitional structure

B = {{Auntie Betty, Me},{Brother A},{Brother B},{Brother C}}.