A designer offers vertically differentiated positions to agents in the absence of transfers. Agents have private outside options and may reject their offers ex-post. The designer has preferences over the quantity of agents who accept each position. We show that under a general condition on the distribution of outside options, an optimal mechanism for the designer offers all agents an identical lottery, and we characterize this mechanism. When our condition does not hold, the optimal mechanism may require screening agents by offering a menu of distinct lotteries. Our results follow from a decomposition of agents' participation probabilities in any feasible mechanism. 

In many auctions, bidders may value keeping their information private from the auctioneer and other bidders. Among deterministic bilateral communication protocols, revealing less information to bidders requires revealing more information to the auctioneer, and vice versa. A protocol implementing a choice rule is on the Privacy Frontier if no alternative protocol reveals less to both bidders and the auctioneer. The sealed-bid first-price auction, the descending auction and the ascending auction are on the Privacy Frontier, but the sealed-bid second-price auction is not. We provide sufficient conditions for protocols to be on the Privacy Frontier and devise alternative frontier protocols.

We study the effect of providing information to agents who queue before a scarce good is distributed at a fixed time. When agents have quasi-linear utility in time spent waiting, they choose entry times as they would bids in a descending auction. An information designer can influence their behavior by providing updates about the length of the queue. Many natural information policies release sudden bad news, which occurs when agents learn that the queue is longer than previously believed. We show that sudden bad news can cause assortative inefficiency by prompting a mass of agents to simultaneously attempt to join the queue. As a result, if the value distribution has an increasing (decreasing) hazard rate, information policies that release sudden bad news increase (decrease) total surplus, relative to releasing no information. When agents face entry costs to join the queue and the value distribution has a decreasing hazard rate, an information designer maximizes total surplus by announcing only when the queue is full.