Two Buyers and a Seller Players 1 and 2 are buyers, while player 3 is a seller. The seller owns an object that is worth nothing to him, but has value 1 for buyer 1 and value 2 for buyer 2. These are...

Two Buyers and a Seller

Players 1 and 2 are buyers, while player 3 is a seller. The seller owns an object that is worth nothing to him, but has value 1 for buyer 1 and value 2 for buyer 2. These are the prices that the buyers are willing to pay to the seller in order to get the object.

(a) Model this situation as a three-person TU-game, where the worth of each coalition is the maximal surplus it can create by a transaction between a buyer and the seller.

(b) Compute the core of this game.

(c) Compute the Shapley value of this game. Is it in the core?

(d) Compute the nucleolus of this game.