Title: Pricing, entry, and social learning

Abstract: I develop a two-period theoretical model to show how potential entry and competition in the future shapes the optimal learning speed for the Incumbent in period 1. As a result, the Incumbent might want to push the period 1 price beyond a static monopoly level if, a priori, the market is less optimistic; lower the price if the market is instead too optimistic.

Title: Privacy Preserving Signals

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.