Reallocative Auctions and Core Selection (with Marzena Rostek) (Online appendix)
Forthcoming, Review of Economic Studies
When selling goods like wireless spectrum or electricity contracts, designers often opt for core-selecting mechanisms — i.e., those that induce outcomes in the core — in order to balance revenue and efficiency goals. But increasingly, auctions — such as the FCC’s Incentive Auction and those explored for natural resources — seek to reallocate goods, not just sell them. We show that when bidders can both buy and sell, substitutability among goods is no longer sufficient or necessary for core selection. In particular, in these environments, core selection can fail even with a single good and positive revenue, and can succeed even when some or all bidders view goods as complements. Instead, we show that the key feature that determines core selection is heterogeneity among the bidders. With too much heterogeneity, reallocation mostly realizes pre-existing gains from trade among the bidders, and core selection fails. With limited heterogeneity, most gains from trade among the bidders are created by the quantity auctioned, and a core-selecting mechanism is possible.
Complementarity in Matching Markets and Exchange Economies (with Marzena Rostek)
Games and Economic Behavior, 150: 415-435 (2025)
The literature has shown that complementarity places significant structure on outcomes in matching markets and exchange economies. We examine the extent to which this structure, and the economic intuition underlying it, is common across these classes of environments. We show that transferable utility matching markets can be represented as exchange economies in a way that preserves competitive equilibria and gross complementarity. Unlike canonical representations that preserve substitutability, this representation must involve the addition of brokers whenever the matching market is not two-sided. We use our representation results to uncover the relationship (or lack thereof) between existence results in the literature that rely on complementarity, and to give a new existence result for matching markets with imperfectly transferable utility and net complementarity.
Designing Incentives for Heterogeneous Researchers (Online appendix)
Journal of Political Economy, 130 (8): 2018-2054 (2022)
A principal (e.g., the U.S. government) contracts with a researcher of unknown quality (e.g., a vaccine developer) to conduct a costly experiment. This contracting problem has a novel feature that captures the difference between the form of an experiment and the strength of its results: researchers face a problem of information design, rather than optimal effort. Using a novel comparative static for Bayesian persuasion settings, I characterize the optimal contract and show how experimentation is distorted by the need to screen researcher types. Moreover, I show that there is no loss from contracting on the experiment’s result rather than the experiment itself.
Matching with Complementary Contracts (with Marzena Rostek) (Supplementary Material)
Econometrica, 88 (5): 1793-1827 (2020) (lead article)
In this paper, we show that stable outcomes exist in matching environments with complementarities, such as social media platforms or markets for patent licenses. Our results apply to both nontransferable and transferable utility settings, and allow for multilateral agreements and those with externalities. In particular, we show that stable outcomes in these settings are characterized by the largest fixed point of a monotone operator, and so can be found using an algorithm; in the nontransferable utility case, this is a one-sided deferred acceptance algorithm, rather than a Gale-Shapley algorithm. We also give a monotone comparative statics result as well as a comparative static on the effect of bundling contracts together. These illustrate the impact of design decisions, such as increased privacy protections on social media, or the use of antitrust law to disallow patent pools, on stable outcomes.
Information Design for Differential Privacy (with Ian Schmutte) (Online appendix) (Extended abstract in EC '22: Proceedings of the 23rd ACM Conference on Economics and Computation) June 2025
Firms and statistical agencies must protect the privacy of the individuals whose data they collect, analyze, and publish. Increasingly, these organizations do so by using publication mechanisms that satisfy differential privacy. We consider the problem of choosing such a mechanism so as to maximize the value of its output to end users. We show that mechanisms which add conditionally independent noise to the statistic of interest — like most of those used in practice — are never without loss when the statistic is a sum or average of magnitude data (e.g., income). However, we also show that adding conditionally independent noise is always optimal when the statistic is a count of data entries with a certain characteristic, and the underlying database is drawn from a symmetric distribution (e.g., if individuals’ data are i.i.d.). When, in addition, data users have supermodular payoffs, we show that the simple geometric mechanism is always optimal by using a novel comparative static that ranks information structures according to their usefulness in supermodular decision problems.
Explaining Models (with Kai Hao Yang and Alex Zentefis) (Extended abstract in EC '25: Proceedings of the 26th ACM Conference on Economics and Computation) May 2025
We consider the problem of explaining models to a decision maker (DM) whose payoff depends on a state of the world described by inputs and outputs. A true model specifies the relationship between these inputs and outputs, but is not intelligible to the DM. Instead, the true model must be explained via a simpler model. If the DM maximizes their average payoff, then an explanation using ordinary least squares is as good as understanding the true model itself. However, if the DM maximizes their worst-case payoff, then any explanation is no better than no explanation at all. We discuss how these results apply to policy evaluation and explainable AI.
Delegating Experiments (with Cole Wittbrodt) May 2025
A principal wants information to help her decide whether or not to approve a project. She delegates costly experimentation to an agent, who wants her to approve the project and has private information about the state. The principal can influence experimentation only by restricting the experiments that the agent can undertake: she cannot commit to approval, and no transfers are possible. For example, the FDA may select a set of clinical trials that are acceptable for testing a new drug, but cannot pay drug companies or weaken its threshold for approval. We show that the principal can screen the agent -- and thus learn his private information -- by offering a menu of experiments that differ in conditional expected payoffs across states. Doing so is always optimal: screening dominates pooling. Private information distorts the optimal menu by making the false negative rate inefficiently high. In our drug approval application, too many good drugs are rejected.
Matching with Strategic Consistency (with Marzena Rostek) (Online appendix) June 2025
In many environments, agents form agreements that have externalities or are multilateral, and may view some agreements as substitutable and others as complementary. This paper presents an approach that ensures the existence of stable outcomes in any environment, including those with arbitrary externalities, preferences, and market structures. It does so by endogenizing the agents' choice functions while employing the standard stability concept. Instead of assuming that each agent chooses their favorite set of contracts, we require agents to choose optimally given correct beliefs about the choices of others. We show that stable outcomes are uniquely pinned down by agents' beliefs, which can be microfounded by their relative bargaining power. Our results provide new tools for the counterfactual analysis of stable outcomes and allow the use of matching-theoretic stability in new applications.
Matching with Costly Interviews: The Benefits of Asynchronous Offers (with Akhil Vohra) March 2025
In many matching markets, matches are formed after costly interviews. We develop a model of worker-firm matching that incorporates this feature, and examine the trade-offs between a centralized matching system and a decentralized one, where matches can occur at any time. Centralized matching with a common offer date leads to coordination issues in the interview stage. Each firm must incorporate the externality imposed by the interview decisions of the firms ranked above it when deciding on its interview list. As a result, low-ranked firms often fail to interview some candidates that ex-ante have high match quality. In a decentralized setting with exploding offers, the set of candidates who receive interviews differs, but the welfare generated is weakly greater than in the centralized setting. Total welfare is highest with a system that ensures firms interview and match in sequence, clearing the market for the next firm. Such asynchronicity reduces interview congestion. This system can be implemented by encouraging top firms to interview and match early and allowing candidates to renege on offers.
Counterfactual Analysis in Bargaining with Externalities: A Matching-Theoretic Foundation (with Marzena Rostek) June 2025
We show how matching-theoretic stability can be used to perform counterfactual analysis in environments with externalities. Our approach sidesteps the well-known existence problems faced by stability in these environments by endowing agents with correct beliefs about the choices of others. This facilitates a procedure that mirrors the one commonly used with the Nash-in-Nash solution concept, with beliefs playing the same role as bargaining weights: Like profiles of bargaining weights in Nash-in-Nash, each profile of beliefs predicts a unique outcome, but different profiles predict different outcomes.
Strategic Consistency in Two-Sided Markets (with Marzena Rostek) December 2023
In this note, we focus on two-sided markets where externalities are present — such as those between doctors and hospitals, or firms and consumers — and consider a notion of strategic sophistication weaker than the one we explore in Rostek and Yoder (2023): Each agent forms correct beliefs about others on the same side of the market, rather than all other agents. We show that together with substitutability, this within-side strategic consistency ensures that stable outcomes exist. Moreover, we show that there is a profile of choice functions and beliefs that satisfies it whenever agents' underlying preferences satisfy the standard substitutability and monotone externalities conditions from Pycia and Yenmez (2023).
Extended Real-Valued Information Design September 2023
This note shows that Bayesian persuasion problems still have solutions when the cost of inducing some posteriors is infinite, e.g., when information has a constant marginal cost. Consequently, the concavification approach of Gentzkow and Kamenica (2011) can be applied to these settings.