Research

**Working Papers**

**Distributions of Posterior Quantiles and Economic Applications. (Online Appendix) (with Alex Zentefis)**(

**Updated**)**[Cowles Discussion Paper]****[VSET Video]****[Media: Election Law Blog, Yale Insight]***Abstract*We characterize the distributions of posterior quantiles under a given prior. Unlike the distributions of posterior means, which are known to be mean-preserving contractions of the prior, the distributions of posterior quantiles coincide with a first-order stochastic dominance interval bounded by an upper and a lower truncation of the prior. We apply this characterization to several environments, ranging across political economy, Bayesian persuasion, industrial organization, econometrics, finance, and accounting.

* An earlier version focusing on gerrymandering

**Informational Intermediation, Market Feedback, and Welfare Losses. (Online Appendix) (with Wenji Xu)**(

**Updated**)**[SET Video]***Abstract*This paper examines the welfare implications of third-party informational intermediation. A seller sets the price of a product that is sold through an informational intermediary. The intermediary can disclose information about the product to consumers and earns a fixed percentage of sales revenue in each period. The intermediary's market base grows at a rate that increases with past consumer surplus. We characterize the stationary equilibria and the set of subgame perfect equilibrium payoffs. When

**market feedback**(i.e., the extent to which past consumer surplus affects future market bases) increases, welfare may decrease in the Pareto sense.

**Efficient Market Structures under Incomplete Information. (with Alex Zentefis)***Abstract*In economies with incomplete information,

*laissez-faire*price competition is not, in general, constrained Pareto efficient. But which market structures are? We consider an environment in which firms have private information about costs and consumers make discrete choices over goods. Surveying an expansive class of market structures, we show that the constrained efficient ones are equivalent to price competition, but with lump-sum transfers and yardstick price ceilings that depend on the prices of competing firms.

**Equivalence in Business Models for Informational Intermediaries.**

[SSRN] [TSE Online Seminar]*Abstract*An intermediary has the technology to provide information about a product to consumers and serves as a platform through which transactions between a monopoly and consumers take place. This paper explores the intermediary's revenue maximization problem across all possible business models. By examining the revenue maximizing solutions under three critical business models, I discover that the market outcomes---consumers' expected surplus, producer's expected profit and the intermediary's expected revenue---are equivalent across all business models if and only if the gains from trade are large enough, which provides some insights into, and implications for online selling platforms.

**Publications**

**Selling Consumer Data for Profit: Optimal Market-Segmentation Design and its Consequences****(Online Appendix),**

*American Economic Review, *2022. *Abstract*

A data broker sells market segmentations to a producer with private cost who sells a product to a unit mass of consumers. This paper characterizes the revenue-maximizing mechanisms for the data broker. Every optimal mechanism induces **quasi-perfect price discrimination**---all the consumers with values above a cost-dependent cutoff buy by paying their values while the rest of consumers do not buy. The characterization implies that market outcomes remain unchanged even if the data broker becomes more powerful---either by gaining the ability to sell access to consumers or by becoming a retailer who purchases the product and sells to the consumers exclusively.

* An earlier version and its supplemental material with additional results

**Efficient Demands in a Multi-Product Monopoly,***Journal of Economic Theory*, 2021.*Abstract***affine-unit-elastic**. This further reduces the problem of characterizing the efficient frontier to a finite dimensional constraint optimization problem. From this characterization, it follows that deadweight losses are positive even under efficient demands; that both consumer surplus and total welfare are nonmonotonic in cost; and that the monopolist sells at most two distinct quality levels under any efficient market demand.

**Short Notes**

**A Note on Topological Properties of Outcomes in a Monopoly Market.***Abstract*

**A Note on Generating Arbitrary Joint Distributions Using Partitions.***Abstract*

**Inactive Projects & Subsumed Papers**

**Informationally Robust Welfare Predictions under Second-Degree Price Discrimination.**(Partly subsumed by "Efficient Demands in a Multi-Product Monopoly")