Fair allocation of items and money
Fair allocation of items and money is a class of fair item allocation problems in which, during the allocation process, it is possible to give or take money from some of the participants. Without money, it may be impossible to allocate indivisible items fairly. For example, if there is one item and two people, and the item must be given entirely to one of them, the allocation will be unfair towards the other one. Monetary payments make it possible to attain fairness, as explained below. Two agents and one item With two agents and one item, it is possible to attain fairness using the following simple algorithm (which is a variant of cut and choose): Alice says a price p that she is willing to pay for the item. George chooses whether to take the item and pay p, or leave the item to Alice so that Alice pays p. This algorithm assumes that the agents have quasilinear utilities, that is, their utility is the value of items plus the amount of money that they have. If George thinks that Alice's price is low (he is willing to pay more than p), then he takes the item and pay p,