House Allocation with Existing Tenants: An Equivalence

In this paper we analyze two house allocation mechanisms each of which is designed to eliminate inefficiencies in real-life house allocation problems where there are both existing tenants and newcomers. The first mechanism chooses the unique core allocation of a "sister" exchange economy which is constructed by assigning each existing tenant her current house and randomly assigning each newcomer a vacant house. The second mechanism -top trading cycles mechanism- first chooses an ordering from a given distribution and next determines the final outcome as follows: Assign first agent her top choice, next agent her top choice among remaining houses and so on, until someone demands house of an existing tenant who is still in the line. At that point modify the queue by inserting her at the top and proceed. Similarly, insert any existing tenant who is not already served at the top of the queue once her house is demanded. Whenever a loop of existing tenants forms, assign each of them the house she demands and proceed. Our main result is that the core based mechanism is equivalent to an extreme case of the top trading cycles mechanism which orders newcomers before the existing tenants.

Course Bidding at Business Schools

Mechanisms that rely on course bidding are widely used at Business Schools in order to allocate seats at oversubscribed courses. Bids play two key roles under these mechanisms: Bids are used to infer student preferences and bids are used to determine who have bigger claims on course seats. We show that these two roles may easily conflict and preferences induced from bids may significantly differ from the true preferences. Therefore while these mechanisms are promoted as market mechanisms, they do not necessarily yield market outcomes. The two conflicting roles of bids is a potential source of efficiency loss part of which can be avoided simply by asking students to state their preferences in addition to bidding and thus "separating" the two roles of the bids. While there may be multiple market outcomes under this proposal, there is a market outcome which Pareto dominates any other market outcome.

Room Assignment-Rent Division: A Market Approach

A group of friends consider renting a house but they shall first agree on how to allocate its rooms and share the rent. We propose an auction mechanism for room assignment-rent division problems which mimics the market mechanism. Our auction mechanism is efficient, envy-free, individually-rational and it yields a non-negative price to each room whenever that is possible with envy-freeness.

Pairwise Kidney Exchange

The theoretical literature on exchange of indivisible goods finds natural application in organizing the exchange of live donor kidneys for transplant. However, in kidney exchange, there are constraints on the size of feasible exchanges. Initially, kidney exchanges are likely to be pairwise exchanges, between just two patient-donor pairs, as these are logistically simpler than larger exchanges. Furthermore, the experience of many American surgeons suggests to them that preferences over kidneys are approximately 0-1, i.e. that patients and surgeons should be largely indifferent among healthy donors whose kidneys are compatible with the patient. This is because, in the United States, transplants of compatible live kidneys have about equal graft survival probabilities, regardless of the closeness of tissue types between patient and donor. We show that, although the pairwise constraint eliminates some potential exchanges, there is a wide class of constrained-efficient mechanisms that are strategy-proof when patient-donor pairs and surgeons have 0-1 preferences. This class of mechanisms includes deterministic mechanisms that would accomodate the kinds of priority setting that organ banks currently use to allocate cadaver organs, as well as stochastic mechanisms that allow distributive justice issues to be

Kidney Exchange

Most transplanted kidneys are from cadavers, but there are also substantial numbers of transplants from live donors. Recently, there have started to be kidney exchanges involving two donor-patient pairs such that each donor cannot give a kidney to the intended recipient because of immunological incompatibility, but each patient can receive a kidney from the other donor. Exchanges are also made in which a donor-patient pair makes a donation to someone on the queue for a cadaver kidney, in return for the patient in the pair receiving the highest priority for a compatible cadaver kidney when one becomes available. We explore how such exchanges can be arranged efficiently and incentive compatibly. The problem resembles some of the housing' problems studied in the mechanism design literature for indivisible goods, with the novel feature that while live donor kidneys can be assigned simultaneously, the cadaver kidneys must be transplanted immediately upon becoming available. In addition to studying the theoretical properties of the design we propose for a kidney exchange, we present simulation results suggesting that the welfare gains would be substantial, both in increased number of feasible live donation transplants, and in improved match quality of transplanted kidneys.

Kidney Exchange

Most transplanted kidneys are from cadavers, but there are also substantial numbers of transplants from live donors. Recently, there have started to be kidney exchanges involving two donor-patient pairs such that each donor cannot give a kidney to the intended recipient because of immunological incompatibility, but each patient can receive a kidney from the other donor. Exchanges are also made in which a donor- patient pair makes a donation to someone on the queue for a cadaver kidney, in return for the patient in the pair receiving the highest priority for a compatible cadaver kidney when one becomes available. We explore how such exchanges can be arranged efficiently and incentive compatibly. The problem resembles some of the "housing" problems studied in the mechanism design literature for indivisible goods, with the novel feature that while live donor kidneys can be assigned simultaneously, the cadaver kidneys must be transplanted immediately upon becoming available. In addition to studying the theoretical properties of the design we propose for a kidney exchange, we present simulation results suggesting that the welfare gains would be substantial, both in increased number of feasible live donation transplants, and in improved match quality of transplanted kidneys.

Efficient Kidney Exchange: Coincidence of Wants in a Structured Market

Patients needing kidney transplants may have willing donors who cannot donate to them because of blood or tissue incompatibility. Incompatible patient-donor pairs can exchange donor kidneys with other such pairs. The situation facing such pairs resembles models of the "double coincidence of wants," and relatively few exchanges have been consummated by decentralized means. As the population of available patient-donor pairs grows, the frequency with which exchanges can be arranged will depend in part on how exchanges are organized. We study the potential frequency of exchanges as a function of the number of patient-donor pairs, and the size of the largest feasible exchange. Developing infrastructure to identify and perform 3-way as well as 2-way exchanges will have a substantial effect on the number of transplants, and will help the most vulnerable patients. Larger than 3-way exchanges have much smaller impact. Larger populations of patient-donor pairs increase the percentage of patients of all kinds who can find exchanges.

Efficient Kidney Exchange: Coincidence of Wants in a Structured Market

Patients needing kidney transplants may have willing donors who cannot donate to them because of blood or tissue incompatibility. Incompatible patient-donor pairs can exchange donor kidneys with other such pairs. The situation facing such pairs resembles models of the “double coincidence of wants,” and relatively few exchanges have been consummated by decentralized means. As the population of available patient-donor pairs grows, the frequency with which exchanges can be arranged will depend in part on how exchanges are organized. We study the potential frequency of exchanges as a function of the number of patient-donor pairs, and the size of the largest feasible exchange. Developing infrastructure to identify and perform 3-way as well as 2-way exchanges will have a substantial effect on the number of transplants, and will help the most vulnerable patients. Larger than 3- way exchanges have much smaller impact. Larger populations of patient- donor pairs increase the percentage of patients of all kinds who can find exchanges.

Pairwise Kidney Exchange

In connection with an earlier paper on the exchange of live donor kidneys (Roth, S”nmez, and šnver 2004) the authors entered into discussions with New England transplant surgeons and their colleagues in the transplant community, aimed at implementing a Kidney Exchange program. In the course of those discussions it became clear that a likely first step will be to implement pairwise exchanges, between just two patient-donor pairs, as these are logistically simpler than exchanges involving more than two pairs. Furthermore, the experience of these surgeons suggests to them that patient and surgeon preferences over kidneys should be 0-1, i.e. that patients and surgeons should be indifferent among kidneys from healthy donors whose kidneys are compatible with the patient. This is because, in the United States, transplants of compatible live kidneys have about equal graft survival `robabilities, regardless of the closeness of tissue types between patient and dOnor (unless there is a rare perfect match). In the present paper we show that, although thd pairwise constraint eliminates some potential exchanges, there is a wide class of constrained-efficient mechanisms 4hat are strategy-proof when patient-donor pairs and surgeons have 0-1 preferences. This class of meahanisms includes deterministic mechanisms that would accomodate the kinds of priority setting that organ banks currently use for the allocation of cadaver organs, as well as stochastic mechanisms that allow considerations of distributive justice to be addressed.