Research

Abstract: This paper studies a matching problem between doctors and patients affiliated with two distinct types of hospitals: resource-rich hospitals and under-resourced hospitals. The problem involves both cross-institutional assignments, where doctors from resource-rich hospitals provide support to patients from under-resourced hospitals, and internal assignments conducted within each hospital. Each resource-rich hospital is subject to a capacity constraint that limits the number of doctors it can allocate to external assistance. Its priority rule determines the order in which doctors are considered for such assignments. Conversely, each under-resourced hospital faces a capacity requirement specifying the minimum number of doctors needed to satisfy patient demand, while its priority rule determines the order in which patients are considered for external assistance. Within this framework, we refine the notion of stability by explicitly accounting for the interaction between capacity constraints and priority structures, thereby identifying multiple sources of blocking pairs. We then propose a Multi-stage Deferred Acceptance (MDA) mechanism that can find a feasible, stable, and Pareto efficient matching and achieve incentive compatibility for a subset of patients.

Abstract: Universities in England and many others elsewhere give first-year students priority over returning students in dormitory allocation, even when some returning students initially occupy university housing. Motivated by this practically important but, to the best of our knowledge, previously unstudied priority structure, we develop a model allowing indifferences in students’ preferences and dormitories’ priorities. Our stability concept retains standard individual and pairwise blocking logic while incorporating asymmetric student rights and coalitional blocks based on initial occupation. We propose the Proposal and Swapping Deferred Acceptance (PSDA) mechanism, which combines deferred acceptance for new students with priority-respecting cycles and paths for senior students. PSDA produces a stable and fair matching and is strategy-proof. Because stability may conflict with Pareto efficiency, we introduce coalition-sensitive weak stability. A modified Top Trading Cycles mechanism produces a core matching that is Pareto efficient and weakly stable and is coalition-strategy-proof.

Abstract:  This paper studies matching markets with endogenous constraints, motivated by squad-registration rules in professional sports such as football and wheelchair basketball. Unlike conventional type-specific constraints, which can be stated independently, endogenous constraints link roster composition to total capacity: a shortfall in a protected player type reduces the number of players a club may register. We formulate stability, group stability, and non-wastefulness for this environment and propose the Club-Proposing Multiple-Stages mechanism. Its outcome is feasible and group-stable, and hence stable, non-wasteful, and Pareto efficient. Truthful preference reporting is a dominant strategy for clubs. We extend the framework and mechanism to three or more player types, where endogenous constraints cannot be represented by separate type-specific quotas.

Abstract: We study product markets in which buyers can consult expert recommendations before purchasing. Buyers are matched with products whose fit is uncertain and decide whether to incur a privately known cost to obtain advice. Experts issue recommendations to buyers, while sellers post prices and may offer experts incentive payments. We show that the welfare effects of these incentive payments depend critically on contract types. Paid recommendations affect consumer welfare through two channels: an information channel, which always harms buyers at a fixed price, and a price channel, through which contracts can expand market coverage and benefit buyers. When no shift in pricing strategy occurs, the two channels reinforce each other and incentive contracts always hurt buyers, with attributed-sales contracts harming them less than direct contracts. When a shift in pricing strategy occurs, the two channels work in opposite directions. Attributed-sales contracts  introduce a capture-conversion trade-off that bounds the information loss, ensuring that the price channel dominates whenever it is activated. Direct contracts have no such guarantee, but their lower implementation cost activates the price channel more often. Neither contract type is uniformly better for consumers. When no shift in pricing strategy occurs, both a blanket ban and a targeted restriction on the more distortive type benefit consumers. When a shift in pricing strategy occurs, either intervention can foreclose a Pareto improvement. 

Abstract: We study a market design problem in many-to-one job matching markets with commitments. A worker-firm relationship may be newly created as a one-sided commitment, strengthened into a mutual commitment, or dissolved. This requires an outcome to specify not only who is matched with whom, but also which commitment relationships are attached to the matching. Firms have hiring capacities as well as commitment capacities. We formulate stability using blocking chains and cycles, and introduce committed-worker efficiency to capture the allocation of commitment slots. We then design a mechanism and show that it produces a stable core matching and satisfies committed-worker efficiency.

Abstract: Stability and nonbossiness are important properties in matching theory. We show that they are incompatible in senior-level matching markets with commitments, even though commitments weaken the standard stability requirement. The incompatibility holds both for standard nonbossiness and for a commitment-related version that accounts for commitment states.

Abstract: We revisit the framework of  Sun and Yang (2021) in a dynamic model with new entrants. Under the dynamic framework, agents who dissolve a committed relationship may be better off in the short term, but worse off in the final period. This generates a forward-looking incentive that makes commitments harder to dissolve than in a static environment, leading to the persistence of committed relationships. To formalize this observation, we study a dynamic senior-level job matching model under commitment and introduce a notion of dynamic stability. We show that commitment could be sustained under a dynamically stable multiperiod matching.