Designing marketplaces in complex settings requires both novel economic theory and real-world engineering, often drawing upon ideas from fields such as computer science and operations research. In Discovering Prices: Auction Design in Markets with Complex Constraints, Milgrom (2017) explains the theory and design of the United States’ “incentive auction” that reallocated wireless spectrum licenses from television broadcasters to telecoms. Milgrom’s account teaches us how economic designers can grapple with complexity both in theory and in practice. Along the way, we come to understand several different types of complexity that can arise in marketplace design.

We model spatial clusters of similar firms. Our model highlights how agglomerative forces lead to localized, individual connections among firms, while interaction costs generate a defined distance over which attraction forces operate. Overlapping firm interactions yield agglomeration clusters that are much larger than the underlying agglomerative forces themselves. Empirically, we demonstrate that our model’s assumptions are present in the structure of technology and labor flows within Silicon Valley. Our model further identifies how the lengths over which agglomerative forces operate influence the shapes and sizes of industrial clusters; we confirm these predictions using variations across patent technology clusters.

Holdout problems prevent private (voluntary and self-financing) assembly of complementary goods—such as land or dispersed spectrum—from many self-interested sellers. While mechanisms that fully respect sellers' property rights cannot alleviate these holdout problems, traditional solutions, such as the use of coercive government powers of “eminent domain” to expropriate property, can encourage wasteful and unfair assemblies. We discuss the problems holdout creates for the efficient operation of markets and how previous approaches have used regulated coercion to address these challenges. We then investigate when encouraging competition can partially or fully substitute for coercion, focusing particularly on questions of spectrum allocation.

High commissions in the U.S. residential real estate agency market pose a puzzle for economic theory because brokerage is not a concentrated industry. We model brokered markets as a game in which agents post prices for customers and then choose which other agents to work with. We show that there exists an equilibrium in which each agent conditions working with other agents on those agents' posted prices. Prices can therefore be meaningfully higher than the competitive level (for a fixed discount factor), regardless of the number of agents. Thus, brokered markets can remain uncompetitive even with low concentration and easy entry.

We characterize when a stable and strategy-proof mechanism is guaranteed to exist in the setting of many-to-one matching with contracts. We introduce three novel conditions—observable substitutability, observable size monotonicity, and non-manipulability via contractual terms—and show that when these conditions are satisfied, the cumulative offer mechanism is the unique mechanism that is stable and strategy-proof (for workers). Moreover, we show that our three conditions are, in a sense, necessary: if the choice function of some firm fails any of our three conditions, we can construct unit-demand choice functions for the other firms such that no stable and strategy-proof mechanism exists. Thus, our results provide a rationale for the ubiquity of cumulative offer mechanisms in practice.

Policymakers frequently use price regulations as a response to inequality in the markets they control. In this paper, we examine the optimal structure of such policies from the perspective of mechanism design. We study a buyer‐seller market in which agents have private information about both their valuations for an indivisible object and their marginal utilities for money. The planner seeks a mechanism that maximizes agents' total utilities, subject to incentive and market‐clearing constraints. We uncover the constrained Pareto frontier by identifying the optimal trade‐off between allocative efficiency and redistribution. We find that competitive‐equilibrium allocation is not always optimal. Instead, when there is inequality across sides of the market, the optimal design uses a tax‐like mechanism, introducing a wedge between the buyer and seller prices, and redistributing the resulting surplus to the poorer side of the market via lump‐sum payments. When there is significant same‐side inequality that can be uncovered by market behavior, it may be optimal to impose price controls even though doing so induces rationing.

Current refugee resettlement processes account for neither the preferences of refugees nor the priorities of hosting communities. We introduce a new framework for matching with multidimensional knapsack constraints that captures the (possibly multidimensional) sizes of refugee families and the capacities of communities. We propose four refugee resettlement mechanisms and two solution concepts that can be used in refugee resettlement matching under various institutional and informational constraints. Our theoretical results and simulations using refugee resettlement data suggest that preference-based matching mechanisms can improve match efficiency, respect priorities of communities, and incentivize refugees to report where they would prefer to settle.

Many scarce public resources are allocated at below-market-clearing prices and sometimes for free. Such “nonmarket” mechanisms sacrifice some surplus, yet they can potentially improve equity. We develop a model of mechanism design with redistributive concerns. Agents are characterized by a privately observed willingness to pay for quality, a publicly observed label, and a social welfare weight. A market designer controls allocation and pricing of a set of objects of heterogeneous quality and maximizes the expectation of a welfare function. The designer does not directly observe individuals’ social welfare weights. We derive structural insights about the form of the optimal mechanism, leading to a framework for determining how and when to use nonmarket mechanisms.

Many markets are syndicated, including those for initial public offerings, club deal leveraged buyouts, and debt issuances; in such markets, each winning bidder invites competitors to join a syndicate to complete production. We show that in syndicated markets, collusion may become easier as market concentration falls and market entry may facilitate collusion. In particular, firms can sustain collusion by refusing to syndicate with any firm that undercuts the collusive price, thereby raising that firm’s production costs. Our results can thus rationalize the paradoxical empirical observations that many real-world syndicated markets exhibit seemingly collusive pricing despite low levels of market concentration.