• This paper studies optimal mechanisms for collecting and trading data. Consumers benefit from revealing information about their taste to a service provider because this improves the service. However, the information is also valuable to a third party as it may extract more revenue from the consumer in another market called the product market. The paper characterizes the constrained optimal mechanism for the service provider subject to incentive feasibility. It is shown that the service provider sometimes sells no information or only partial information in order to preserve profits in the service market. Moreover, a ban on data trade may reduce social welfare because it makes it harder to price discriminate in the product market.

• We offer a search-theoretic model of statistical discrimination, in which firms treat identical groups unequally based on their occupational choices. The model admits symmetric equilibria in which the group characteristic is ignored, but also asymmetric equilibria in which a group is statistically discriminated against, even when symmetric equilibria are unique. Moreover, a robust possibility is that symmetric equilibria become unstable when the group characteristic is introduced. Unlike most previous literature, our model can justify affirmative action since it eliminates asymmetric equilibria without distorting incentives.

This paper studies the sellers’ differentiation and price competition before consumer costly learning about the preference in horizontal differentiated markets. We first characterize the unique symmetric pricing-learning equilibrium given choices of differentiation, and then investigate the sellers’ equilibrium choices of product differentiation. Moreover, we study the efficiency implication of the costly learning on the equilibrium differentiation and apply the model to study the industry-optimal differentiation. It is shown that the equilibrium market differentiation is inefficient: too much for small learning costs and too little for large learning costs. However, the industry-optimal differentiation can restore efficiency under some conditions on learning costs. 

• We consider the equilibrium interplay between sellers' price competition and consumers' perception of product differentiation. We analyze a situation where, before trading, consumers acquire information at a cost about their preferences between sellers' differentiated products. The incentive for information acquisition depends on the average value of products, the objective product differentiation, and their beliefs about sellers' prices. The acquired information shapes consumers' perceived product differentiation and sellers' equilibrium prices. We characterize the unique symmetric equilibrium and study comparative statics with respect to consumer information acquisition cost and sensitivity to product differentiation. We then apply our model to platform design.

• This paper studies stress tests as Bayesian persuasion within the fundamental bank run framework. It shows that the optimal disclosure policy depends on the liquidation cost of the long-term asset. In particular, when the liquidation cost is low, the optimal stress test fully discloses information about banks: it increases the likelihood of enjoying the high asset return. When the liquidation cost is high, the optimal stress test partially discloses information: it reduces the likelihood of costly bank runs. The central trade-off in stress test design is between the bank run cost and the high asset return. The theory suggests regulatory policy coordination and offers insights on different stress testing experiences across countries.