Problems in market design with dynamic populations
Keywords: Economics.

This dissertation studies the problems of market design that arise from the interaction between information asymmetries and dynamically changing populations. In many markets, agents arrive and depart over time, and a first-order question is how the design of the market affects this ebb and flow. For example, in online marketplaces, agents' propensities to arrive or depart are their private information, and thinking about how to incentivize these agents leads to new questions in Mechanism Design. In other markets, such as mergers and acquisitions, the arrival of new players is modulated by the release of private information about existing players; this raises new questions in bargaining and information design, aside from providing another angle on questions of market transparency. In Chapter 1, "Privacy in Bargaining: The Case of Endogenous Entry, " I study the role of privacy in bargaining. A seller makes offers every instant, without commitment, to a privately informed buyer. There are potential competing buyers (entrants) who observe something about the negotiation and can choose to interrupt it by triggering a bidding war. As entrants learn about ongoing disagreement, they update their beliefs about the type of the buyer. The seller's lack of commitment reverses the seemingly intuitive effects of publicity. If learning that the buyer's type is lower encourages entrants, so that the seller ''should'' want to make publicly observable offers that lure in entrants against the incumbent buyer, then in equilibrium the seller typically prefers private bargaining. If learning that the buyer's type is lower discourages entrants, so that the seller ''should'' want to hide her offers to avoid frightening away entrants, then in equilibrium the seller prefers public bargaining. Chapter 2, "When to Hold An Auction?, " (joint with Shota Ichihashi) we study the optimal timing of an auction in a setting where bidders arrive and depart stochastically over time. First, we compare the revenue-maximizing timing and welfare-maximizing timing. We show that sellers hold auctions too late or too early whenever (censored at 0) virtual values are more or less right-skewed than values. We connect the relative right-skewness of virtual values to the ''price elasticity of demand'' of the bidder's valuation distribution. In particular, we show that sellers typically hold auctions inefficiently late. Second, we prove that the use of simple timing rules (i.e., a fixed deadline chosen in advance) can lose an arbitrarily large fraction of the revenue from the optimal stopping rule. This underscores the importance of taking timing seriously for good auction market design. Chapter 3, "Pricing Responses to Platform Leakage: Optimal Platform Design When Matches Are Irrevocable" focuses on a market design application where the two features of private information and dynamically evolving populations collide. Many for-profit matching platforms face the problem that the matches they make can be given, but not taken away. Once a platform like UpWork introduces a freelance developer to a firm for an initial transaction, the pair can exchange contact details and contract privately again while avoiding UpWork's fees on further transactions. Practitioners call this "platform leakage." I analyze this issue through a two-period model of a monopolist platform running a two-sided one-to-one matching market between workers and firms, where (i) agents can contract privately off the platform once they are matched (matches are irrevocable); (ii) they differ in how likely they are to want further business with a match (their durability); and (iii) firms have private information about their durability. I characterize the profit-maximizing matching and pricing policies. I show that the platform typically wants to impose a novel kind of distortion. In the first period, the platform wants to give firms either extremely high durability matches, or extremely low durability ones, but it would rather leave more firms unmatched than give any of them ''medium'' durability matches. This is in contrast to a seemingly related static model where a platform matches agents with privately known taste for quality to goods of different quality: in that case, the platform might price the bottom tier of agents out of the market, but it would never sell a low quality good before a medium quality one.