Kai Hao Yang

I am an assistant professor of economics at Yale School of Management.

My field of interest is microeconomic theory, in particular, mechanism design, information design and game theory

Research

Working Papers

(Last Update: 10/26/2021, R&R at American Economic Review) 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. Consequently, vertical integration between the data broker and the producer increases total surplus while leaving the consumer surplus unchanged and brokership improves total surplus compared with uniform pricing. Furthermore, the characterization of optimal mechanisms 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 obtains the exclusive right to sell to the consumers directly.

* An earlier version and its supplemental material with additional results

(Last Update: 08/12/2021) Abstract

The structure of a market describes the nature of competition between participating firms. This paper introduces a framework for designing market structures and characterizes the socially efficient ones. We define a market structure as the set of firms’ strategies and mappings from those strategies to market entry rules, an allocation of products to consumers, and firm revenues. We show that efficient market structures are equivalent to price competition with transfers and yardstick price caps that depend on the published prices of competing firms. Hence, efficient market structures can be implemented without prior knowledge of individual consumer preferences, firms' realized costs, or firm conduct. Further, if firms have any private information, any unregulated market is socially inefficient. Finally, if a regulator cannot administer the optimal market structure, a naive policy of restricting entry to the lowest-priced firms performs well for low-grade, outdated products (e.g., flip phones), but not for premium, state-of-the-art products (e.g., robotics).

(Last Update: 11/21/2019) 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.

(Last Update: 11/14/2019) Abstract

In an environment that features second-degree price discrimination, this paper fully characterizes the set of surplus divisions that can arise from all possible information consumers have about their valuation. By extending the techniques developed in a companion paper (Yang, 2019a), I show that the set of feasible surplus divisions can be characterized by a family of information structures that induce Pareto-distributed interim expected values. Unlike the linear model as in Roesler & Szentes (2017) where posted price is always optimal, the efficient frontier is generically not attainable under any information structures and there are environments in which a (nontrival) subset of the feasible surplus divisions collapses to a one-dimensional set. Nevertheless, the sets of feasible surplus divisions are stable around the linear environments.

(Last Update: 04/20/2017) Abstract

In this paper, without fully specifying the underlying game form, we showed that the probability of an inefficient breakdown in any bilateral crisis bargaining model is smaller when the more informed party has more bargaining power. Moreover, introduction of additional private information does not necessarily lead to extra efficiency loss. Several implications can be drawn from these results. Specifically, regarding international security, reducing incomplete information is not the only way to reduce the probability of war. Instead, reallocating bargaining power properly would also be effective in terms of preventing conflicts. Furthermore, these results also provide a formal justification for the power transition theory as the status-quo power can be interpreted as the party with more bargaining power when the information structure shifts due to power transition.

(Last Update: 04/20/2017) Abstract

This paper investigates the strategic interactions between the counter proliferator and the proliferator in a nuclear proliferation crisis, as well as their impacts on international security and stability. A baseline model of contest with interdependent values is established and its implications are discussed. Furthermore, we characterize the equilibria in a class of models in a "detail-free" fashion and analyze equilibrium outcomes, with particular attentions to international stability and likelihood of a successful development. It thus yields some results and implications that are robust to game forms and model details and provides several generalizations and insights to the effects of various counter-proliferation measures as well as the consequences of nuclear proliferation.

Publications

• 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. (Last Update: 10/27/2020) 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. (Last Update: 10/27/2020) 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.

In Progress

• Profiting from the Money Burnt: Optimal Advertisement Design and its Implications (Draft coming soon)
• Market-Minded Informational Intermediary and Unintended Welfare Loss (with Wenji Xu; Draft coming soon)
• Hyperstable Sequential Equilibria (with Philip Reny)
• Price Discrimination in Oligopoly: An Information Design Approach
• Revenue Maximization with Rich Allocation Space: Irrelevance of Contractibility