We examine the evolution of the decentralized clearinghouse mechanisms that were in use throughout Europe from the thirteenth century to the eighteenth century; in particular, we explore the clearing of nontradable or limited-tradable debts such as bills of exchange. We construct a theoretical model of these clearinghouse mechanisms and show that the specific decentralized multilateral clearing algorithms known as rescontre, skontrieren, or virement des parties, used by merchants in this period, were efficient in specific historical contexts. Our analysis contributes to the understanding of these mechanisms during late medieval and early modern fairs and their robustness during the seventeenth and eighteenth centuries.

Hatfield and Milgrom (2005) present a unified model of matching with contracts phrased in terms of hospitals and doctors, which subsumes the standard two-sided matching and some package auction models. They show that a stable allocation exists if contracts are substitutes for each hospital. They further claim that if a hospital's preferences violate the substitutes condition, there exist singleton preferences for the other hospitals and doctors such that no stable allocation exists. We show this last claim does not hold in general. We further present a weaker condition that is necessary to guarantee the existence of stable allocations.

We develop a model of matching with contracts which incorporates, as special cases, the college admissions problem, the Kelso-Crawford labor market matching model, and ascending package auctions. We introduce a new “law of aggregate demand” for the case of discrete heterogeneous workers and show that, when workers are substitutes, this law is satisfied by profit-maximizing firms. When workers are substitutes and the law is satisfied, truthful reporting is a dominant strategy for workers in a worker-offering auction/matching algorithm. We also parameterize a large class of preferences satisfying the two conditions.

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.

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.

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.

We introduce a framework of matching with flexible allotments that can be used to model firms with cross-division hiring restrictions. Our framework also allows us to nest some prior models of matching with distributional constraints. Building upon our recent work on observable substitutability, we show that multi-division choice functions with flexible allotments enable stable and strategy-proof matching; these results illustrate the value of clearly mapping when stable and strategy-proof matching is possible.

We provide an illustration of how the design of labor market clearing mechanisms can affect incentives for human capital acquisition. Specifically, we extend the labor market matching model (with discrete transfers) of Kelso and Crawford (1982) to incorporate the possibility that agents may invest in human capital before matching. We show that in this setting, the worker-optimal stable matching mechanism incentivizes workers to make (nearly) efficient human capital investments. En route to our main result, we show that so long as the space of salaries is sufficiently rich, every stable outcome in the Kelso and Crawford (1982) setting is approximately efficient.

We develop a quality competition model to understand how price controls affect market outcomes in buyer-seller markets with discrete goods of varying quality. While competitive equilibria do not necessarily exist in such markets when price controls are imposed, we show that stable outcomes do exist and characterize the set of stable outcomes in the presence of price restrictions. In particular, we show that price controls induce non-price competition: price floors induce the trade of inefficiently high quality goods, while price ceilings induce the trade of inefficiently low quality goods.