Research

Ongoing research projects

• Walrasian Mechanisms for Non-convex Economies and the Bound-Form First Welfare Theorem (with Paul Milgrom)
  • Revise and Resubmit, Review of Economic Studies
  • Previously “Linear Pricing Mechanisms for Market without Convexity”
  • We introduce two extensions of the Walrasian mechanism for quasilinear economies to allow agents to report non-concave values and non-convex costs. The extended mechanisms, which always deliver feasible, near-efficient allocations with no budget deficit, are computationally undemanding and nearly incentive-compatible. We also introduce an extension of the First Welfare Theorem allowing us to upper bound the welfare losses from these mechanisms.
  • Accepted to EC’22
  • Presented at 32nd Stony Brook International Conference on Game Theory by Paul Milgrom as part of Auction Research Evolving: Theorems and Market Designs.
  • Presented at the NBER Market Design Working Group Meeting, Fall 2021.
  • See a two-minute technical preview of the paper here:
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• Strong monotonicity and perturbation-proofness of Walrasian equilibrium
  • Preliminary draft
  • 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.
• A bandit model of trade with two-sided learning (with Yunus Aybas)
  • Draft soon
  • We study a model of trade with repeated interaction between a single buyer and many sellers. The buyer is initially uninformed about her valuation 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. Similarly to Braverman et al. (2019), 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. We then show that 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.

Academic Publications

Mathematical Notes

• Concavity and convexity of order statistics in sample size
  • We 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.

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.