Eduardo M. Azevedo

A Supply and Demand Framework for Two-Sided Matching Markets

This paper develops a price-theoretic framework for matching markets with heterogeneous preferences. The model departs from the Gale and Shapley model by assuming that a finite number of agents on one side (colleges) are matched to a continuum of agents on the other side (students). We show that stable matchings correspond to solutions of supply and demand equations, with the selectivity of each college playing a role similar to that of prices. We apply the model to an analysis of how competition induced by school choice gives schools incentives to invest in quality and to asymptotics of school choice mechanisms.

Hierarchical cheap talk

We investigate situations in which agents can communicate to each other only through a chain of intermediators, for example because they have to obey institutionalized communication protocols. We assume that all involved in the communication are strategic, and might want to influence the action taken by the final receiver. The set of pure strategy equilibrium outcomes is simple to characterize, monotonic in each intermediators bias, does not depend on the order of intermediators, and intermediation in these equilibria cannot improve information transmission. However, none of these conclusions hold for mixed equilibria. We provide a partial characterization of mixed equilibria, and offer an economically relevant sufficient condition for every equilibrium to be outcome-equivalent to a pure equilibrium and hence the simple characterization and comparative statics results to hold for the set of all equilibria.

Strategy-Proofness in the Large

We propose a criterion of approximate incentive compatibility, strategy-proofness in the large (SP-L), and argue that it is a useful second-best to exact strategy-proofness (SP) for market design. Conceptually, SP-L requires that an agent who regards a mechanism’s “prices” as exogenous to her report—be they traditional prices as in an auction mechanism, or price-like statistics in an assignment or matching mechanism—has a dominant strategy to report truthfully. Mathematically, SP-L weakens SP in two ways: (1) truth-telling is required to be approximately optimal (within epsilon in a large enough market) rather than exactly optimal, and (2) incentive compatibility is evaluated ex interim, with respect to all full-support i.i.d. probability distributions of play, rather than ex post with respect to all possible realizations of play. This places SP-L in between the traditional notion of approximate SP, which evaluates incentives to manipulate ex post and as a result is too strong to obtain our main results in support of SP-L, and the traditional notion of approximate Bayes-Nash incentive compatibility, which, like SP-L, evaluates incentives to manipulate ex interim, but which imposes common knowledge and strategic sophistication assumptions that are often viewed as unrealistic.

Walrasian Equilibrium in Large, Quasilinear Markets

In an economy with indivisible goods, a continuum of agents, and quasilinear utility, we show that equilibrium exists regardless of the nature of agents’ preferences over bundles. This contrasts with results for economies with a finite number of agents, which require restrictions on preferences (such as substitutability) to guarantee existence. When the distribution of preferences has full support, equilibrium prices are unique.

Perfect Competition in Markets with Adverse Selection

This paper proposes a perfectly competitive model of a market with adverse selection. Prices are determined by zero‐profit conditions, and the set of traded contracts is determined by free entry. Crucially for applications, contract characteristics are endogenously determined, consumers may have multiple dimensions of private information, and an equilibrium always exists. Equilibrium corresponds to the limit of a differentiated products Bertrand game. We apply the model to establish theoretical results on the equilibrium effects of mandates. Mandates can increase efficiency but have unintended consequences. With adverse selection, an insurance mandate reduces the price of low‐coverage policies, which necessarily has indirect effects such as increasing adverse selection on the intensive margin and causing some consumers to purchase less coverage.

Imperfect competition in two-sided matching markets ✩

This paper considers a simple equilibrium model of an imperfectly competitive two-sided matching market. Firms and workers may have heterogeneous preferences over matches on the other side, and the model allows for both uniform and personalized wages or contracts. To make the model tractable, I use the Azevedo and Leshno (2013) framework, in which a finite number of firms is matched to a continuum of workers.

The college admissions problem with a continuum of students

In many two-sided matching markets, agents on one side are matched to a large number of agents on the other side (e.g. college admissions). Yet little is known about the structure of stable matchings when there are many agents on one side. We propose a variation of the Gale and Shapley [3] college admissions model where a finite number of colleges is matched to a continuum of students. It is shown that, generically (though not always) (i) there is a unique stable matching, (ii) this stable matching varies continuously with the underlying economy, and (iii) it is the limit of the set of stable matchings of approximating large discrete economies.

Matching markets in the digital age

Digital markets make it easier to match companies and customers Recent advances in information technology are enabling new markets and revolutionizing many existing markets. For example, taxicabs used to find passengers through chance drive-bys or slow central dispatching (see the photo). Location tracking, computer navigation, and dynamic pricing now enable ride-sharing services such as Uber to offer low and consistent delay times of only a few minutes. In a recent study, Cramer and Krueger (1) show that ride-sharing has dramatically increased the usage of drivers and their cars, cutting costs for riders. The results highlight the opportunities provided by digital markets. Further efficiency gains may come from academia-industry collaborations, which could also help to ensure that the markets develop in ways that further the public interest.

Risk-neutral firms can extract unbounded profits from consumers with prospect theory preferences

This paper considers the problem of a risk-neutral firm offering a gamble to consumers with preferences given by prospect theory. Under conditions satisfied by virtually all functional forms used in the literature, firms can extract arbitrarily high expected values from consumers. Moreover, for any given lottery, there exists another lottery that makes both the firm and the consumer better off. As a consequence, equilibria and Pareto optimal allocations do not exist in standard monopolistic or competitive models.

Existence of stable matchings in large markets with complementarities

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