Research

Research Papers

Optimal Redistribution Through Subsidies (Job Market Paper, with Zi Yang Kang)

We develop a model of redistribution where a social planner, seeking to maximize weighted total surplus, can subsidize consumers who participate in a private market. We identify when subsidies can strictly improve upon the laissez-faire outcome, which depends on the correlation between consumers’ demand and need. We characterize the optimal nonlinear subsidy by quantifying when—and for which units of the good—the social planner uses a full subsidy (i.e., free provision) rather than a partial subsidy or no subsidy. Our findings provide justifications for (i) free provision of a baseline quantity and (ii) subsidizing goods for which demand and need are positively correlated.

Optimal In-Kind Redistribution (with Zi Yang Kang)

This paper develops a model of in-kind redistribution where consumers participate in either a private market or a government-designed program, but not both. We characterize when a social planner, seeking to maximize weighted total surplus, can strictly improve upon the laissez-faire outcome. We show that the optimal mechanism consists of three components: a public option, nonlinear subsidies, and laissez-faire consumption. We quantify the resulting distortions and relate them to the correlation between consumer demand and welfare weights. Our findings reveal that while private market access constrains the social planner’s ability to redistribute, it also strengthens the rationale for non-market allocations.

A Walrasian Mechanism with Markups for Nonconvex Economies (with Paul Milgrom)

Revise and Resubmit at Review of Economic Studies Previously “Linear Pricing Mechanisms for Market without Convexity” and “Walrasian Mechanisms for Non-convex Economies and the Bound-Form First Welfare Theorem”

We introduce Markup equilbrium, an extension of Walrasian equilibrium that adds a markup to the prices that consumers pay to ensure existence even in nonconvex quasilinear economies. Markup equilibria are resource-feasible, incur no budget deficit, and require little more communication and computation than the Walrasian equilibrium. The Markup direct mechanism is large-market incentive-compatible. Our Bound-Form First Welfare Theorem states that for any feasible allocation and price vector, the welfare loss compared to a first-best allocation is at most the sum of (i) the budget surplus and (ii) any rationing losses suffered by the participants. This implies that any Markup equilibrium with a small markup is nearly efficient.

Abstract appeared in EC’22 as “Linear Pricing Mechanisms for Market without Convexity.” Also presented at the NBER Market Design Working Group Meeting, Fall 2021, at 32nd Stony Brook International Conference on Game Theory by Paul Milgrom as part of Auction Research Evolving: Theorems and Market Designs, and at the Simons Laufer Mathematical Sciences Institute Workshop on Algorithms, Approximation, and Learning in Market and Mechanism Design.

See a two-minute technical preview of the paper here:

Strong monotonicity and perturbation-proofness of Walrasian equilibrium

Awarded Best Paper by Young Researcher at the 2023 Econometric Society Australasian Meeting.

We study the price impact of small perturbations to Walrasian equilibrium, as might be caused by changes in the supply vector, changes in the set of participants, or misreports by an agent. A (nested) sequence of markets is perturbation-proof if, given any supply vector, the price impact of any bounded perturbation is inversely proportional to the number of agents. Perturbation-proofness implies good incentive properties of Walrasian equilibrium in large markets and robustness of prices to small misspecifications. Replica economies are perturbation-proof if and only if the base economy’s demand correspondence is strongly monotone. When buyers’ preferences are drawn identically and independently from a type distribution with a strongly monotone expected demand correspondence, the resulting sequence of economies is perturbation-proof with high probability. We argue that strong monotonicity of the expected demand correspondence is a realistic assumption in economic models with indivisibilities, reflecting variety in the set of possible preferences and uncertainty about reservation prices associated with demand changes.

Congestion in Labor Markets (with Shoshana Vasserman and John J. Horton)

Link coming soon

We report the results of a field experiment on an online labor market platform that introduced a ``soft’’ cap on the number of applications that could be received for a job opening and the number of days applications were accepted. Despite reducing the number of applications per opening, the intervention did not reduce the hiring probability or reported match quality. We interpret this as evidence of inefficient congestion: before the intervention, applicants submitted too many applications to popular jobs and too few to less popular ones. We show that inefficient congestion can arise due to a “missing market” for job applications and the associated failure of applicants to internalize their effects on the hiring probability of competing applicants. We find that application fees introduced by the platform reduced hire rates and competition among candidates, suggesting that these fees may have been miscalibrated or higher than socially efficient.

Risk aversion and auction design: Theoretical and empirical evidence (with Shoshana Vasserman )

International Journal of Industrial Organization, 79 (2021)

Auctions are inherently risky: bidders face uncertainty about their prospects of winning and payments, while sellers are unsure about revenue and chances of a successful sale. Auction rules influence the allocation of risk among agents and the behavior of risk-averse bidders, leading to a breakdown of payoff and revenue equivalence and a heightened significance of auction design decisions by sellers. In this paper, we review the literature on risk aversion in auctions, with an emphasis on what can be learned about auction design from theoretical modeling and empirical studies. We survey theoretical results relating to the behavior of risk-averse agents in auctions, the comparison of standard auction formats in the presence of risk aversion and implications for auction design. We discuss standard and more recent approaches to identifying risk preferences in empirical studies and evidence for the significance of risk aversion in auction applications. Finally, we identify areas where existing evidence is relatively scant and ask what questions empirical research might ask given the theory and where further theoretical research may be beneficial given existing empirical results.

Concavity and convexity of order statistics in sample size

I show that the expectation of the $k$th-order statistic of an i.i.d. sample of size $n$ from a monotone reverse hazard rate (MRHR) distribution is convex in $n$ and that the expectation of the $(n-k+1)$th-order statistic from a monotone hazard rate (MHR) distribution is concave in $n$ for $n \geq k$. We apply this result to the analysis of independent private value auctions in which the auctioneer faces a convex cost of attracting bidders.

Work In Progress

Who Gets What and When: Dynamic Allocation without Transfers (slides)

A principal is endowed with a stream of items to be allocated to a fixed population of agents. Items arrive with random quality—some items are “goods,” desired by all agents, while others are “bads,” conferring negative flow payoffs to agents—and no transfers are allowed. The principal seeks to allocate as many items as possible while respecting the agents’ participation constraints. I characterize the optimal allocation, which involves incentivizing undesirable allocations today using promises of improved future allocations. The principal is optimally “loyal” to agents with worse historical allocations, assigning them priority for the best arriving goods. I discuss the implications of these results for the design of markets for ridesharing and the centralized allocation of teachers to schools.

A Bandit Model of Trade with Two-Sided Learning (with Yunus Aybas, slides)

We study a model of trade with repeated interaction between a single buyer and many sellers. The buyer is initially uninformed about her valuations for the various goods and sellers are uninformed about the buyer’s demand. We model this interaction as a multi-armed bandit problem with strategic arms and seek to understand the welfare consequences of various models of buyer behavior. We show that a buyer using a no-regret (contextual) learning algorithm may be exploited by colluding sellers in an approximate Nash equilibrium for the sellers. However, a buyer with commitment power may extract almost all the gains from trade from the sellers in an approximate dominant strategy equilibrium for the sellers.

Other Published Work

Paul Milgrom and Mitchell Watt (2020) Commentary on Effective Allocation of Affordable Housing by Nick Arnosti and Peng Shi. Management Science Blog.

Mitchell Watt and Hubert Wu (2018) Trust mechanisms and online platforms: A regulatory response. Harvard Mossavar-Rahmani Center for Business and Governance Associate Working Paper Series No. 97.

Jim Chalmers and Mitchell Watt (2013) Labor should fight for economic mobility. Chifley Research Centre Blog.