Institutions care both about whom they select and the composition of the resulting group. We identify an upper-bound property and two exchange properties on distributional preferences. Conditional on the upper-bound property, the exchange properties are jointly necessary and sufficient for two results under every priority ranking: the greedy rule is the unique choice rule that is non-wasteful, distributionally maximal, and free of justified envy; and it is also path independent. In matching markets, deferred acceptance is the unique mechanism satisfying the three axioms, individual rationality, and strategy-proofness. Our framework accommodates intersectional identities and subsumes models based on reserves and matroids.

Medical ``Crisis Standards of Care'' call for a utilitarian allocation of scarce resources in public emergencies, whereas standards of care under normal conditions place relatively greater priority on the worst-off. Inspired by such triage rules, we study social welfare criteria whose distributive trade-offs depend on society's well-being, as captured by aggregate welfare. Because the welfare level determines the applicable aggregation criterion, while that criterion in turn determines welfare, the resulting criteria are self-referential. We provide an axiomatic foundation for a family of welfare criteria that become more utilitarian as aggregate welfare falls and more Rawlsian as it rises, thereby formalizing triage guidelines. We also characterize the converse case, in which priority to the worst-off increases as aggregate welfare falls.

This paper analyzes the strategic interactions between a profit-maximizing monopolist and a free, capacity-constrained public option. By restricting its own supply, the monopolist intentionally congests the public option and induces rationing, which increases consumers' willingness to pay for guaranteed access. Counterintuitively, expanding the public option's capacity may raise the monopoly price and lower consumer welfare. However, I derive conditions under which all buyer types benefit from a capacity expansion, and extend these results to a setting where an oligopoly competes with a public option. These findings have implications for mixed public-private markets, such as housing, education, and healthcare.

How does competition in markets for information affect the creation and division of surplus? We study this question in a  search environment in which an agent searches sequentially for a high-quality good and learns about the quality of sampled goods by repeatedly purchasing signals from profit-maximizing information brokers. Brokers design and price signals but can commit only to spot contracts. We characterize the equilibrium payoff set as a function of the market structure---the number of competing brokers. When search costs are low, market structure affects neither surplus generation nor its division. When costs are high, however, competition benefits the agent but reduces total surplus relative to monopoly. Methodologically, we extend repeated-games theory to stopping problems such as sequential search.

We use majorization to model comparative diversity in school choice. A population of agents is more diverse than another population of agents if its distribution over groups is less concentrated: being less concentrated takes a specific mathematical meaning borrowed from the theory of majorization. We adapt the standard notion of majorization in order to favor arbitrary distributional objectives, such as population-level distributions over race/ethnicity or socioeconomic status. With school admissions in mind, we axiomatically characterize choice rules that are consistent with modified majorization, and constitute a principled method for admitting a diverse population of students into a school. Two important advantages of our approach is that majorization provides a natural notion of diversity, and that our axioms are independent of any exogenous priority ordering. We compare our choice rule to the leading proposal in the literature, ``reserves and quotas,'' and find ours to be more flexible.

I study a continuous time principal-agent model in which an unknown parameter and the agent's hidden effort affect the distribution of observable outcomes. The principal and the agent learn about the parameter by observing past outcomes. The agent's current effort has an implicit long-term effect through the belief dynamics and a deviation in effort creates a persistent disparity between the principal's and the agent's beliefs. This disparity affects the rate of learning as well as how the two evaluate the expected distribution of future outcomes which in turn affects their evaluation of future payoffs. Placing minimal restrictions on how effort and the parameter interact, I derive necessary and sufficient conditions for incentive compatible contracts. In addition to the agent's promised utility, the covariance between the on-path posterior beliefs and the agent's total payoff serves as a second state variable capturing the marginal long-run effects of effort.

This paper studies how ex-ante information affects consumer welfare in a search market where buyers search and match to sellers of a vertically differentiated product. In a random search market, a buyer gets no informative signal about the quality of a seller's product prior to matching, whereas in a directed search market, a buyer observes a perfectly informative signal. I derive the unique equilibrium outcome in each type of market and show that consumers are worse off in a directed search market when sellers are scarce and prices are bilaterally ex-post efficient.