House Allocation With Fractional Endowments

 

Stergios Athanassoglou

 

   In this paper we study a generalization of the well known house allocation problem. In contrast to the classical Shapley-Scarf model and its various extensions, agents are not restricted to own a full house. Rather, we assume that agents may own fractions of different houses summing to an arbitrary quantity, but that they have use for only the equivalent of one unit of a house. We also depart from the classical model by assuming that arbitrary quantities of each house may be available to the market. Justified envy considerations arise when two agents have the same initial endowment, or when an agent is in some sense disproportionately rewarded in comparison to her peers. In this context we provide an efficient algorithm that computes a fractional allocation of houses to agents that satisfies ordinal efficiency, individual rationality, and no justified envy. Our results extend to the full preference domain. We show that individual rationality, ordinal efficiency, and no justified envy conflict with weak strategy-proofness in the strict preference domain. We also show that individual rationality, ordinal efficiency and strategy-proofness are incompatible in the strict preference domain. Finally, we show that the strict core of the associated cooperative game is empty and that the weak core conflicts with individual rationality.