The subjective likelihood of a contingency often depends on the manner in which it is described to the decision maker. To accommodate this dependence, we introduce a model of decision making under uncertainty that takes as primitive a family of preferences indexed by partitions of the state space. Each partition corresponds to a description of the state space. We characterize the following partition-dependent expected utility representation. The decision maker has a nonadditive set function ν over events. Given a partition of the state space, she computes expected utility with respect to her partition-dependent belief, which weights each cell in the partition by ν. Nonadditivity of ν allows the probability of an event to depend on the way in which the state space is described. We propose behavioral definitions for those events that are transparent to the decision maker and those that are completely overlooked, and connect these definitions to conditions on the representation.

We study preferences over menus which can be represented as if the individual is uncertain of her tastes, but is able to engage in costly contemplation before selecting an alternative from a menu. Since contemplation is costly, our key axiom, aversion to contingent planning, reflects the individual's preference to learn the menu from which she will be choosing prior to engaging in contemplation about her tastes for the alternatives. Our representation models contemplation strategies as subjective signals over a subjective state space. The subjectivity of the state space and the information structure in our representation makes it difficult to identify them from the preference. To overcome this issue, we show that each signal can be modeled in reduced form as a measure over ex post utility functions without reference to a state space. We show that in this reduced-form representation, the set of measures and their costs are uniquely identified. Finally, we provide a measure of comparative contemplation costs and characterize the special case of our representation where contemplation is costless.

In several school choice districts in the United States, the student proposing deferred acceptance algorithm is applied after indifferences in priority orders are broken in some exogenous way. Although such a tie-breaking procedure preserves stability, it adversely affects the welfare of the students since it introduces artificial stability constraints. Our main finding is a polynomial-time algorithm for the computation of a student-optimal stable matching when priorities are weak. The idea behind our construction relies on a new notion which we call a stable improvement cycle. We also investigate the strategic properties of the student-optimal stable mechanism. (JEL C78, D82, I21)

Liver exchange has been practiced in small numbers, mainly to overcome blood‐type incompatibility between patients and their living donors. A donor can donate either his smaller left lobe or the larger right lobe, although the former option is safer. Despite its elevated risk, right‐lobe transplantation is often utilized due to size‐compatibility requirement with the patient. We model liver exchange as a market‐design problem, focusing on logistically simpler two‐way exchanges, and introduce an individually rational, Pareto‐efficient, and incentive‐compatible mechanism. Construction of this mechanism requires novel technical tools regarding bilateral exchanges under partial‐order‐induced preferences. Through simulations we show that not only can liver exchange increase the number of transplants by more than 30%, it can also increase the share of the safer left‐lobe transplants.

Owing to the worldwide shortage of deceased‐donor organs for transplantation, living donations have become a significant source of transplant organs. However, not all willing donors can donate to their intended recipients because of medical incompatibilities. These incompatibilities can be overcome by an exchange of donors between patients. For kidneys, such exchanges have become widespread in the last decade with the introduction of optimization and market design techniques to kidney exchange. A small but growing number of liver exchanges have also been conducted. Over the last two decades, a number of transplantation procedures emerged where organs from two living donors are transplanted to a single patient. Prominent examples include dual‐graft liver transplantation, lobar lung transplantation, and simultaneous liver‐kidney transplantation. Exchange, however, has been neither practiced nor introduced in this context. We introduce dual‐donor organ exchange as a novel transplantation modality, and through simulations show that living‐donor transplants can be significantly increased through such exchanges. We also provide a simple theoretical model for dual‐donor organ exchange and introduce optimal exchange mechanisms under various logistical constraints.