Motivated by our collaboration with Food Rescue U.S. (FRUS), a food recovery organization that relies on volunteers to complete recurring tasks, we study how crowdsourcing platforms can use commitment to promote growth and engagement. Despite reducing match uncertainty, high levels of commitment can decrease the probability of forming new matches in the spot market, which in turn can suppress growth. To better understand this trade-off, we develop a model for two-sided random markets which repeatedly match volunteers with tasks. Our model incorporates match uncertainty as well as the negative impact of failing to match on future engagement. We study the optimal level of commitment to maximize the total discounted number of matches.

School choice mechanism designers use discrete choice models to understand and predict families' preferences. The most widely-used choice model, the multinomial logit (MNL), is linear in school and/or household attributes. While the model is simple and interpretable, it assumes the ranked preference lists arise from a choice process that is uniform throughout the ranking, from top to bottom. In this work, we introduce two strategies for rank-heterogeneous choice modeling tailored for school choice. First, we adapt a context-dependent random utility model (CDM), considering down-rank choices as occurring in the context of earlier up-rank choices. Second, we consider stratifying the choice modeling by rank, regularizing rank-adjacent models towards one another when appropriate. Using data on household preferences from the San Francisco Unified School District (SFUSD) across multiple years, we show that the contextual models considerably improve our out-of-sample evaluation metrics across all rank positions over the non-contextual models in the literature. Meanwhile, stratifying the model by rank can yield more accurate first-choice predictions while down-rank predictions are relatively unimproved. These models provide performance upgrades that school choice researchers can adopt to improve predictions and counterfactual analyses.

In the classic Bayesian Persuasion model studied by [Kamenica and Gentzkow, 2011], there are two players: the first, called Sender, wishes to persuade the second, called Receiver, to take a desired action. Provided that Sender is ex-post better informed about the underlying state of the world, Sender can leverage their informational advantage by communicating with Receiver via a signal mechanism. However, Sender's ability to effectively manage Receiver's beliefs largely hinges on the assumption that Sender can credibly commit to a signal mechanism. Usually, it is not ex-post optimal for Sender to follow the mechanism, but instead to deviate and send the message that generates the highest payoff. Consequently, Receiver may not have faith in Sender's ability to commit. In this case, all bets are off: persuasion devolves into cheap talk.

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We consider a model for repeated stochastic matching where compatibility is probabilistic, is realized the first time agents are matched, and persists in the future. Such a model has applications in the gig economy, kidney exchange, and mentorship matching. We ask whether adecentralized matching process can approximate the optimal online algorithm. In particular, we consider a decentralizedstable matching process where agents match with the most compatible partner who does not prefer matching with someone else, and known compatible pairs continue matching in all future rounds. We demonstrate that the above process provides a 0.316-approximation to the optimal online algorithm for matching on general graphs. We also provide a 1/7-approximation for many-to-one bipartite matching, a 1/11-approximation for capacitated matching on general graphs, and a 1/2k-approximation for forming teams of up to k agents. Our results rely on a novel coupling argument that decomposes the successful edges of the optimal online algorithm in terms of their round-by-round comparison with stable matching.

In the school choice market, where scarce public school seats are assigned to students, a key issue is how to reassign seats that are vacated after an initial round of centralized assignment. Every year around 10% of students assigned a seat in the NYC public high school system eventually do not use it, and their vacated seats can be reassigned. Practical solutions to the reassignment problem must be simple to implement, truthful and efficient. I propose and axiomatically justify a class of reassignment mechanisms, the Per- muted Lottery Deferred Acceptance (PLDA) mechanisms, which generalize the commonly used Deferred Acceptance (DA) school choice mechanism to a two-round setting and retain its desirable in- centive and efficiency properties. I also provide guidance to school districts as to how to choose the appropriate mechanism in this class for their setting. Centralized admissions are typically conducted in a single round using Deferred Acceptance, with a lottery used to break ties in each school’s prioritization of students. Our proposed PLDA mechanisms reassign vacated seats using a second round of DA with a lottery based on a suitable permutation of the first-round lottery numbers. I demonstrate that under a natural order condition on aggregate student demand for schools, the second-round tie-breaking lottery can be correlated arbitrarily with that of the first round without affecting allocative welfare. I also show how the identifying char- acteristic of PLDA mechanisms, their permutation, can be chosen to control reallocation. vacated after the initial round are reassigned using decentralized waitlists that create significant student movement after the start of the school year, which is costly for both students and schools. I show that reversing the lottery order between rounds minimizes reassignment among all PLDA mechanisms, allowing us to alleviate costly student movement between schools without affecting the ef- ficiency of the final allocation. In a setting without school priorities, I also characterize PLDA mechanisms as the class of mechanisms that provide students with a guarantee at their first-round assign- ment, respect school priorities, and are strategy-proof, constrained Pareto efficient, and satisfy some mild symmetry properties. Finally, I provide simulations of the performance of different PLDA mecha- nisms in the presence of school priorities. All simulated PLDAs have similar allocative efficiency, while the PLDA based on reversing the tie-breaking lottery between rounds minimizes the number of reassigned students. These results support our theoretical findings. This is based on joint work with Itai Feigenbaum, Yash Kanoria, and Jay Sethuraman.