Expressive mechanisms for equitable rent division on a budget

We study the incentive properties of envy-free mechanisms for the allocation of rooms and payments of rent among financially constrained roommates. Each agent reports her values for rooms, her housing earmark (soft budget), and an index that reflects the difficulty the agent experiences from having to pay over this amount. Then an envy-free allocation for these reports is recommended. The complete information non-cooperative outcomes of each of these mechanisms are exactly the envy-free allocations with respect to true preferences if and only if the admissible budget violation indices have a bound.