Competitive envy-free division (Q1767292)

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.