Research

**Working Papers**

**Privacy Preserving Signals.****(with Philipp Strack)**

*Abstract*

A signal is**privacy-preserving**with respect to a collection of**privacy sets**, if the posterior probability assigned to every privacy set remains unchanged conditional on any signal realization. We characterize the privacy-preserving signals for arbitrary state space and arbitrary privacy sets. A signal is privacy-preserving if and only if it is a garbling of a**reordered quantile signal**. These signals are equivalent to couplings, which in turn lead to a characterization of optimal privacy-preserving signals for a decision-maker. We demonstrate the applications of this characterization in the contexts of algorithmic fairness, price discrimination, and information design.**Extreme Points and First-Order Stochastic Dominance: Theory and Applications. (with Alex Zentefis)**

*R&R, American Economic Review; EC' 23*

*Abstract*We characterize the extreme points of first-order stochastic dominance (FOSD) intervals and show how these intervals are at the heart of many topics in economics. Using these extreme points, we characterize the distributions of posterior quantiles, leading to an analog of a classical result regarding the distributions of posterior means. We apply this analog to various subjects, including the psychology of judgement, political economy, and Bayesian persuasion. In addition, FOSD intervals provide a common structure to security design. We use the extreme points to unify and generalize seminal results in that literature when either adverse selection or moral hazard pertains.

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

**[Online Appendix] [SET Video]**

*R&R, RAND Journal of Economics*

*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.

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

[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.

**Published and Accepted Papers**

**On the Continuity of Outcomes in a Monopoly Market.**

[Working Paper Version]

*Journal of Mathematical Economics,*2023

*Abstract*

A monopolist with a constant marginal cost faces an arbitrary nondecreasing and upper-semicontinuous demand function on that takes a value in {0,1} outside of a fixed compact interval. This paper derives topological properties of outcomes induced by this monopolist's optimal pricing problem. Specifically, the monopolist's optimal profit is continuous in the marginal cost and the demand (under the weak-* topology); the optimal price and output correspondences are upper-hemicontinuous in the marginal cost and the demand; and the consumer surplus is upper (lower)-semicontinuous when the monopolist charges the lowest (highest) optimal price. These results further imply similar topological properties of outcomes in settings that feature either second-degree price discrimination or third-degree price discrimination.**Regulating Oligopolistic Competition. (with Alex Zentefis)**

**[Working Paper Version]**

**Journal of Economic Theory,****2023**

*Abstract*We consider the problem of how to regulate an oligopoly when firms have private information about their costs. In the environment, consumers make discrete choices over goods, and minimal structure is placed on the manner in which firms compete. In the optimal regulatory policy, firms compete on price margins, and based on firms' prices, the regulator charges them taxes or give them subsidies, and imposes on each firm a ``yardstick'' price cap that depends on the posted prices of competing firms.

**Selling Consumer Data for Profit: Optimal Market-Segmentation Design and its Consequences**.

**[Online Appendix] [Working Paper Version]**

*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.

**Efficient Demands in a Multi-Product Monopoly.**

**[Working Paper Version]**

**Journal of Economic Theory****, 2021.**

AbstractThis paper characterizes the efficient market demands among those with a fixed surplus level in a multi-product monopoly, where the monopolist is able to produce a continuum of quality-differentiated products with a cost function that is convex in quality. We show that any efficient market demand must be

**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 Generating Arbitrary Joint Distributions Using Partitions.***Abstract*

** Subsumed Papers**

**Distribution of Posterior Quantiles and Economic Applications.**(Subsumed by "Extreme Points of First-Order Stochastic Dominance Intervals: Theory and Applications") [VSET Video]

**Gerrymandering and the Limits of Representative Democracy.**(Partly subsumed by"Extreme Points of First-Order Stochastic Dominance Intervals: Theory and Applications") [Media: Election Law Blog, Yale Insight]

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