Strategy-Proof and Nonbossy Allocation of Indivisible Goods and Money

Which strategy-proof nonbossy mechanisms exist in a model with a finite number of indivisible goods (houses, jobs, positions) and a compensating perfectly divisible good (money)? The main finding is that only a finite number of distributions of the divisible good is consistent with strategy-proofness and nonbossiness. Under various additional assumptions - neutrality, individual rationality, object efficiency, weak decentralization - the distribution of the divisible good is further restricted. For instance, under neutrality the outcome of the mechanism can have only one distribution, which is hence independent of individual preferences. In this case the mechanism becomes serially dictatorial. On the other hand, individual rationality leads to a fixed-price equilibrium with a well defined rationing method (Gale's top trading cycle procedure).