We study matching markets in which institutions may have minimum and maximum quotas. Minimum quotas are important in many settings, such as hospital residency matching, military cadet matching, and school choice, but current mechanisms are unable to accommodate them, leading to the use of ad hoc solutions. We introduce two new classes of strategyproof mechanisms that allow for minimum quotas as an explicit input and show that our mechanisms improve welfare relative to existing approaches. Because minimum quotas cause a theoretical incompatibility between standard fairness and nonwastefulness properties, we introduce new second-best axioms and show that they are satisfied by our mechanisms. Last, we use simulations to quantify (1) the magnitude of the potential efficiency gains from our mechanisms and (2) how far the resulting assignments are from the first-best definitions of fairness and nonwastefulness. Combining both the theoretical and simulation results, we argue that our mechanisms will improve the performance of matching markets with minimum quota constraints in practice.

Distributional constraints are important in many market design settings. Prominent examples include the minimum manning requirements at each Army branch in military cadet matching and diversity considerations in school choice, whereby school districts impose constraints on the demographic distribution of students at each school. Standard assignment mechanisms implemented in practice are unable to accommodate these constraints. This leads policymakers to resort to ad hoc solutions that eliminate blocks of seats ex ante (before agents submit their preferences) to ensure that all constraints are satisfied ex post (after the mechanism is run). We show that these current solutions ignore important information contained in the submitted preferences, resulting in avoidable inefficiency. We then introduce new dynamic quotas mechanisms that result in Pareto superior allocations while at the same time respecting all distributional constraints and satisfying important fairness and incentive properties. We expect the use of our mechanisms to improve the performance of matching markets with distributional constraints in the field. We are extremely grateful to Fuhito Kojima, Muriel Niederle, and Al Roth for numerous conversations regarding this project. We would like to thank

We characterize the full class of obviously strategy-proof mechanisms in environments without transfers as clinch-or-pass games that we call millipede games. Some millipede games are simple and widely used in practice, while others may be complex, requiring agents to perform lengthy backward induction, and are rarely observed. We introduce a natural strengthening of obvious strategy-proofness called strong obvious strategy-proofness, which eliminates these complex millipede games. We use our definition to characterize the well-known Random Priority mechanism as the unique mechanism that is efficient, fair, and simple to play, thereby explaining its popularity in practical applications.

Although there is a rich theoretical literature extolling the virtues of the top trading cycles (TTCs) mechanism, it is rarely used in practice. Anecdotal evidence suggests that one possible explanation is that TTC is difficult for participants to understand. This article formalizes this intuition by asking whether it is possible to implement TTC in an obviously strategy‐proof (OSP) way. I identify an acyclicity condition that is both necessary and sufficient for OSP implementation of TTC. The condition is unlikely to hold in most applications, which may explain why TTC is rarely used, despite its many appealing theoretical properties.

We introduce a general class of simplicity standards that vary the foresight abilities required of agents in extensive-form games. Rather than planning for the entire future of a game, agents are presumed to be able to plan only for those histories they view as simple from their current perspective. Agents may update their so-called strategic plan as the game progresses, and, at any point, for the called-for action to be simply dominant, it must lead to unambiguously better outcomes, no matter what occurs at non-simple histories. We use our gradated approach to simplicity to provide characterizations of simple mechanisms. While more demanding simplicity standards may reduce the flexibility of the designer in some cases, this is not always true, and many well-known mechanisms are simple, including ascending auctions, posted prices, and serial dictatorship-style mechanisms. In particular, we explain the widespread popularity of the well-known Random Priority mechanism by characterizing it as the unique mechanism that is efficient, fair, and simple to play.