Competitive Fair Division.

The analysis is developed in the context of the "housemates problem," in which the rent for a house (the bad) must be apportioned among several housemates, each of whom is entitled to receive one room (the good). Each housemate is assumed to have the same endowment, so the auction of rooms is a "relativized" one--only relative, not absolute, bids for each room matter. Other applications of the Gap Procedure, in which player endowments and entitlements may be different, or the procedure may be carried out in rounds, are discussed.