Competitive envy-free division

We are concerned with a fair division problem in which the indivisible "goods" to be distributed among a finite number of individuals have divisible "bads" associated with them. The problem is formulated and analyzed in terms of the housemates problem. We present an efficient procedure that decides whether an envy-free solution exists, and if so, finds one of them; otherwise finds a solution such that each envious housemate is assigned a room whose rent is zero.