Core-selection is a crucial property of rules in the literature of resource allocation. It is also desirable, from the perspective of mechanism design, to address the incentive of agents to cheat by misreporting their preferences. This paper investigates the exchange problem where (i) each agent is initially endowed with (possibly multiple) indivisible goods, (ii) agents' preferences are assumed to be conditionally lexicographic, and (iii) side payments are prohibited. We propose an exchange rule called augmented top-trading-cycles (ATTC), based on the original TTC procedure. We first show that ATTC is core-selecting and runs in polynomial time with respect to the number of goods. We then show that finding a beneficial misreport under ATTC is NP-hard. We finally clarify relationship of misreporting with splitting and hiding, two different types of manipulations, under ATTC.

Kidney exchange is a type of barter market where patients exchange willing but incompatible donors. These exchanges are conducted via cycles---where each incompatible patient-donor pair in the cycle both gives and receives a kidney---and chains, which are started by an altruist donor who does not need a kidney in return. Finding the best combination of cycles and chains is hard. The leading algorithms for this optimization problem use either branch and price — a combination of branch and bound and column generation — or constraint generation. We show a correctness error in the leading prior branch-and-price-based approach [Glorie et al. 2014]. We develop a provably correct fix to it, which also necessarily changes the algorithm's complexity, as well as other improvements to the search algorithm. Next, we compare our solver to the leading constraint-generation-based solver and to the best prior correct branch-and-price-based solver. We focus on the setting where chains have a length cap. A cap is desirable in practice since if even one edge in the chain fails, the rest of the chain fails: the cap precludes very long chains that are extremely unlikely to execute and instead causes the solution to have more parallel chains and cycles that are more likely to succeed. We work with the UNOS nationwide kidney exchange, which uses a chain cap. Algorithms from our group autonomously make the transplant plans for that exchange. On that real data and demographically-accurate generated data, our new solver scales significantly better than the prior leading approaches.

In this paper we study the exchange of indivisible objects where agents’ possible preferences over the objects are strict and share a common structure among all of them, which represents a certain level of asymmetry among objects. A typical example of such an exchange model is a re-scheduling of tasks over several processors, since all task owners are naturally assumed to prefer that their tasks are assigned to fast processors rather than slow ones. We focus on designing exchange rules (a.k.a.mechanisms) that simultaneously satisfy strategyproofness, individual rationality, and Pareto efficiency. We first provide a general impossibility result for agents’ preferences that are determined in an additive manner, and then show an existence of such an exchange rule for further restricted lexicographic preferences. We finally find that for the restricted case, a previously known equivalence between the single-valuedness of the strict core and the existence of such an exchange rule does not carry over.

Core-selection is a crucial property of social choice functions, or rules, in social choice literature. It is also desirable to address the incentive of agents to cheat by misreporting their preferences. This paper investigates an exchange problem where each agent may have multiple indivisible goods, agents' preferences over sets of goods are assumed to be lexicographic, and side payments are not allowed. We propose an exchange rule called augmented top-trading-cycles (ATTC) procedure based on the original TTC procedure. We first show that the ATTC procedure is core-selecting. We then show that finding a beneficial misreport under the ATTC procedure is NP-hard. Under the ATTC procedure, we finally clarify the relationship between preference misreport and splitting, which is a different type of manipulation.