Abstract: I examine two types of mechanisms, preference revelation mechanisms and demand revelation mechanisms, in many-to-one matching problems.  As in Hatfield and Milgrom (2005), I consider general matching problems with contracts.  First, I show that Nash equilibrium outcomes of the preference revelation game induced by the deferred acceptance algorithm coincide with the set of individually rational allocations.  This is a generalization of Alcalde (1996)'s result for one-to-one matching problems without contracts.  In addition, I show that there exists a stable Nash equilibrium outcome with respect to the true preferences.  Second, I consider demand revelation mechanisms in which agents can submit a list of consumptions without indicating priorities.  I show that the core correspondence is not Nash-implementable by any demand revelation mechanism, regardless of the lengths of announcements.  A strong version of Maskin monotonicity plays a crucial role for this impossibility result.

Abstract:  Several school choice districts in the United States adopt the student-proposing  deferred acceptance algorithm as a centralized matching procedure to assign students to schools. It is well-known that it is a dominant strategy for students to truthfully reveal their preferences under the preference revelation game induced by the deferred acceptance algorithm. In this paper, we show that there exists no other dominant strategy equilibrium outcome of this game. In other words, the deferred acceptance algorithm is dominant strategy implementable by the associated direct mechanism.

Abstrat:  The paper builds a theoretical model of firm competition via nonlinear pricing.  To capture certain documented features of actual markets, the model permits firms to be asymmetric and allows for asymmetric information.  I show that for a delegated common agency game in this framework, an equilibrium exists and any equilibrium outcome (specifying allocation rules and who sells to which markets) is implementable by two-part tariffs.  In addition, I show that there exists a Nash equilibrium outcome in which the allocation rules exhibit pooling in an intermediate region of the type space, and quality distortions disappear at the top and the bottom of the set of consumer types served by each principal.  McManus (2006) empirically finds that distortions decrease toward zero at the top and the bottom of the product menu in a specialty coffee market.

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