In many auction settings the auctioneer must disclose the identity of the winner and the price he pays. We characterize the auction that minimizes the winner's privacy loss among those that maximize total surplus or the seller's revenue, and are strategy-proof. Privacy loss is measured with respect to what an outside observer learns from the disclosed price, and is quantified by the mutual information between the price and the winner's willingness to pay. When only interim individual-rationality is required, the most privacy preserving auction involves stochastic ex-post payments. Under ex-post individual rationality, and assuming the bidders' type distribution exhibits a monotone hazard rate, privacy loss is minimized by the second-price auction with deterministic payments.

A seller sells an object over time but is uncertain how the buyer learns their willingness-to-pay. We consider informational robustness under limited commitment, where the seller offers a price each period to maximize continuation profit against worst-case information arrival. Our formulation considers the worst case sequentially. Under general conditions, we characterize an essentially unique equilibrium. Furthermore, we identify a condition that ensures the equilibrium price path is "reinforcing," so even non-sequentially worst-case information arrival would not lower the seller's payoff below the equilibrium level.

Algorithms are increasingly used to guide consequential decisions, such as who should be granted bail or be approved for a loan. Motivated by growing empirical evidence, regulators are concerned about the possibility that the errors of these algorithms differ sharply across subgroups of the population. What are the tradeoffs between accuracy and fairness, and how do these tradeoffs depend on the inputs to the algorithm? We propose a model in which a designer chooses an algorithm that maps observed inputs into decisions, and introduce a fairness-accuracy Pareto frontier. We identify how the algorithm's inputs govern the shape of this frontier, showing (for example) that access to group identity reduces the error for the worse-off group everywhere along the frontier. We then apply these results to study an "input-design" problem where the designer controls the algorithm's inputs (for example, by legally banning an input), but the algorithm itself is chosen by another agent. We show that: (1) all designers strictly prefer to allow group identity if and only if the algorithm's other inputs satisfy a condition we call group-balance; (2) all designers strictly prefer to allow any input (including potentially biased inputs such as test scores) so long as group identity is permitted as an input, but may prefer to ban it when group identity is not.

The expectation is an example of a descriptive statistic that is monotone with respect to stochastic dominance, and additive for sums of independent random variables. We provide a complete characterization of such statistics, and explore a number of applications to models of individual and group decision-making. These include a representation of stationary, monotone time preferences, extending the work of Fishburn and Rubinstein (1982) to time lotteries, as well as a characterization of risk-averse preferences over monetary gambles that are invariant to mean-zero background risks.

An agent has access to multiple information sources, each modeled as a Brownian motion whose drift provides information about a different component of an unknown Gaussian state. Information is acquired continuously---where the agent chooses both which sources to sample from, and also how to allocate attention across them---until an endogenously chosen time, at which point a decision is taken. We demonstrate conditions on the agent's prior belief under which it is possible to exactly characterize the optimal information acquisition strategy. We then apply this characterization to derive new results regarding: (1) endogenous information acquisition for binary choice, (2) the dynamic consequences of attention manipulation, and (3) strategic information provision by biased news sources.

We develop a model of social learning from overabundant information: Agents have access to many sources of information, and observation of all sources is not necessary in order to learn the payoff-relevant state. Short-lived agents sequentially choose to acquire a signal realization from the best source for them. All signal realizations are public. Our main results characterize two starkly different possible long-run outcomes, and the conditions under which each obtains: (1) efficient information aggregation, where the community eventually achieves the highest possible speed of learning; (2) "learning traps," where the community gets stuck using a suboptimal set of sources and learns inefficiently slowly. A simple property of the correlation structure separates these two possibilities. In both regimes, we characterize which sources are observed in the long run and how often.

We consider the problem of optimal dynamic information acquisition from many correlated information sources. Each period, the decision-maker jointly takes an action and allocates a fixed number of observations across the available sources. His payoff depends on the actions taken and on an unknown state. In the canonical setting of jointly normal information sources, we show that the optimal dynamic information acquisition rule proceeds myopically after finitely many periods. If signals are acquired in large blocks each period, then the optimal rule turns out to be myopic from period 1. These results demonstrate the possibility of robust and "simple" optimal information acquisition, and simplify the analysis of dynamic information acquisition in a widely used informational environment.

We study the problem of designing a recommendation system for network goods under the constraint of differential privacy. Agents living on a graph face the introduction of a new good and undergo two stages of adoption. The first stage consists of private, random adoptions. In the second stage, remaining non-adopters decide whether to adopt with the help of a recommendation system A. The good has network complimentarity, making it socially desirable for A to reveal the adoption status of neighboring agents. The designer's problem, however, is to find the socially optimal A that preserves privacy. We derive feasibility conditions for this problem and characterize the optimal solution.