We study Prioritized Selection Problems in which an organization is presented with a set of individuals, and must choose which subset to accept. The organization makes a selection based on a priority ranking of individuals as well as other observable characteristics. We study outcome based selection rules, which are defined by a collection of feasible selections and a greedy processing algorithm.

We model the problem facing a policymaker who must allocate rapid rehousing support to people experiencing homelessness and wishes to minimize the steady-state size of the homeless population. Typically, support is given to the most vulnerable applicants, or to applicants most likely to remain housed. We show that these approaches may result in a homeless population that is arbitrarily larger than what could be achieved by an optimal policy, and propose an alternative priority queue that is approximately optimal.

This paper introduces a unified framework for stable matching, which nests the traditional definition of stable matching in finite markets and the continuum definition of stable matching from Azevedo and Leshno (2016) as special cases. Within this framework, I identify a novel continuum model, which makes individual-level probabilistic predictions.

We consider a model with k identical tickets. The set of agents (N) is partitioned into a set of groups, and agents have dichotomous preferences: an agent is successful if and only if members of her group receive enough tickets for everyone in the group. We treat the group structure as private information, unknown to the designer. Because there are only k tickets, there can be at most k successful agents. We define the efficiency of a lottery allocation to be the expected number of successful agents, divided by k. If this is at least β, then the allocation is β-efficient. A lottery allocation is fair if each agent has the same success probability, and β-fair if for any pair of agents, the ratio of their success probabilities is at least β.

In theprophet secretary problem, n values are drawn independently from known distributions, and presented in a uniformly random order. A decision-maker must accept or reject each value when it is presented, and may accept at most k values in total. The objective is to maximize the expected sum of accepted values.

We analyze the parallel lottery, which is used to allocate hunting permits in the state of Alaska. Each participant is given tickets to distribute among lotteries for different types of items. Participants who win multiple items receive their favorite, and new winners are drawn from the lotteries with unclaimed items. When supply is scarce, equilibrium outcomes of parallel lotteries approximate a competitive equilibrium from equal incomes (CEEI), which is Pareto efficient. When supply is moderate, parallel lotteries exhibit two sources of inefficiency. First, some agents may benefit from trading probability shares. Second, outcomes may be "wasteful": agents may receive nothing even if acceptable items remain unallocated. We bound both sources of inefficiency, and show that each is eliminated by giving applicants a suitable number of tickets k: trades are never beneficial when $k = 1$, and waste is eliminated as k approaches infinity.

We consider a setting in which agents and items match dynamically over time. We show that repeated independent lotteries with unlimited entry (which are commonly used in practice) encourage agents to enter many lotteries, and may result in low match value.

Stable matching mechanisms are used to clear many two-sided markets. In most settings, frictions cause participants to submit short preference lists (even if there are many potentially acceptable matches). This paper studies the consequences of this fact, and focuses on two broad questions. First, when lists are short, what is the quantity and quality of matches formed through the clearinghouse? Second, what are the effects of introducing an aftermarket which allows agents left unmatched by the clearinghouse to find one another? The answers to these questions depend crucially on the extent and form of correlations in agent preferences. I consider three canonical preference structures: fully independent (or idiosyncratic) preferences, vertical preferences (agents agree on the attractiveness of those on the opposite side), and aligned preferences (potential partners agree on the attractiveness of their match).

We model an online display advertising environment with brand advertisers and better-informed performance advertisers, and seek an auction mechanism that is strategy-proof, anonymous and insulates brand advertisers from adverse selection. We find that the only such mechanism that is also false-name proof assigns the item to the highest bidding performance advertiser only when the ratio of the highest bid to the second highest bid is sufficiently large. For fat-tailed match-value distributions, this new mechanism captures most of the gains from good matching and improves match values substantially compared to the common practice of setting aside impressions in advance.

We consider two-sided matching markets, and study the incentives of agents to circumvent a centralized clearing house by signing binding contracts with one another. It is well-known that if the clearing house implements a stable match and preferences are known, then no group of agents can profitably deviate in this manner. We ask whether this property holds even when agents have incomplete information about their own preferences or the preferences of others. We find that it does not. In particular, when agents are uncertain about the preferences of others, every mechanism is susceptible to deviations by groups of agents. When, in addition, agents are uncertain about their own preferences, every mechanism is susceptible to deviations in which a single pair of agents agrees in advance to match to each other. These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

We consider a decentralized two-sided matching market in which agents arrive and depart asynchronously. As a result, it is possible that an agent on one side of the market (a "buyer") identifies an agent on the other side of the market (a "seller") who is a suitable match, only to find that the seller is already matched. We find using a mean field approach that lack of knowledge about availability can create large welfare losses to both buyers and sellers. We consider a simple intervention available to the platform: limiting visibility of sellers. We find that this intervention can significantly improve the welfare of agents on both sides of the market; sellers pay lower application costs, while buyers are less likely to find that the sellers they screen have already matched. Somewhat counterintuitively, the benefits of showing fewer sellers to each buyer are greatest in markets in which there is a shortage of sellers.