Research

**Working Papers**

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

**New**)*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 reside in 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 from political economy, Bayesian persuasion, industrial organization, econometrics, finance, and accounting.

* An earlier version focusing on gerrymandering

**Market-Minded Informational Intermediary and Unintended Welfare Loss. (Online Appendix) (with Wenji Xu)**

[Cowles Discussion Paper]*Abstract*This paper examines the welfare effects of informational intermediation. A (short-lived) seller sets the price of a product that is sold through a (long-lived) informational intermediary. The intermediary can disclose information about the product to consumers, earns a fixed percentage of the sales revenue in each period, and has concerns about its prominence---the market size it faces in the future, which in turn is increasing in past consumer surplus. We characterize the Markov perfect equilibria and the set of subgame perfect equilibrium payoffs of this game and show that when the

**market feedback**(i.e., how much past consumer surplus affects future market sizes) 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]*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")