Kai Hao Yang

Research

Working Papers

Extreme Points and First-Order Stochastic Dominance: Theory and Applications. (with Alex Zentefis)
(New) 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. (Online Appendix) (with Wenji Xu)
[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) (R&R, Journal of Economic Theory) 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
This 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 Topological Properties of Outcomes in a Monopoly Market. Abstract
A monopolist with a nonnegative constant marginal cost faces an arbitrary nondecreasing and upper-semicontinuous demand function on $\mathbb{R_+}$ that takes a value in {0,1} outside of a fixed compact interval. This note derives topological properties of outcomes induced by this monopolist's optimal pricing problem. Specifically, the monopolist's optimal profit is continuous in both the marginal cost and the demand (under the weak-* topology); the induced output is lower (upper)-semicontinuous in both the marginal cost and the demand when the monopolist always charges the highest (lowest) optimal price; the optimal price correspondence is upper-hemicontinuous in both the marginal cost and the demand, which in turn implies that the consumer surplus is upper (lower)-semicontinuous in both the marginal cost and the demand when the monopolist always 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.

A Note on Generating Arbitrary Joint Distributions Using Partitions. Abstract
Consider a probability space $(\Theta,\mathcal{F},\mathbb{P})$ , two standard Borel spaces $(V,\mathcal{V})$ , $(S,\mathcal{S})$ , and a random variable $\mathbf{V}:\Theta \to V$ . This note shows that for any probability measure $\mu \in \Delta(V \times S, \mathcal{V}\otimes \mathcal{S})$ with $\mathrm{marg}_V \mu=\mathbb{P}\circ\mathbf{V}^{-1}$ , there exists a random variable $\mathbf{S}:\Theta \to S$ such that $(\mathbf{V},\mathbf{S})$ has law $\mu$ , provided that $(\Theta,\mathcal{F})$ is rich relative to $\mathbf{V}$ . This result has applications in generating market segmentations using consumer characteristics; segmenting the residual demand by only partitioning the consumers according their values in a multi-firm, multi-product setting; and connects back to well known results in information economics.