Matching with Externalities

We incorporate externalities into the stable matching theory of two-sided markets. Extending theclassical substitutes condition to markets with externalities, we establish that stable matchings exist whenagent choices satisfy substitutability. We show that substitutability is a necessary condition for the existenceof a stable matching in a maximal-domain sense and provide a characterization of substitutable choicefunctions. In addition, we extend the standard insights of matching theory, like the existence of side-optimal stable matchings and the deferred acceptance algorithm, to settings with externalities even thoughthe standard fixed-point techniques do not appl

Outside options in neutral allocation of discrete resources

Serial dictatorships have emerged as the canonical simple mechanisms in the literature on the allocation of indivisible goods without transfers. They are the only neutral and group-strategy-proof mechanisms in environments in which agents have no outside options and hence no individual rationality constraints (Svensson in Soc Choice Welfare 16:557–567, 1999). Accounting for outside options and individual rationality constraints, our main result constructs the class of group-strategy-proof, neutral, and non-wasteful mechanisms. These mechanisms are also Pareto efficient and we call them binary serial dictatorships. The abundance of the outside option - anybody who wants can opt out to get it - is crucial for our result

The Mechanism Design Approach to Student Assignment

The mechanism design approach to student assignment involves the theoretical, empirical, and experimental study of systems used to allocate students into schools around the world. Recent practical experience designing systems for student assignment has raised new theoretical questions for the theory of matching and assignment. This article reviews some of this recent literature, highlighting how issues from the field motivated theoretical developments and emphasizing how the dialogue may be a road map for other areas of applied mechanism design. Finally, it concludes with some open questions.National Science Foundation (U.S.

Incentives and Implementation in Marriage Markets with Externalities

We study the implementability of stable correspondences in marriage markets with externalities. We prove that, contrary to what happens in markets without externalities, no stable revelation mechanism makes a dominant strategy for the agents on one side of the market to reveal their preferences. However, the stable correspondence is implementable in Nash equilibrium

Incentive compatible allocation and exchange of discrete resources

The allocation and exchange of discrete resources, such as transplant organs, public housing, dormitory rooms, and many other resources for which agents have single-unit demand, is often conducted via direct mechanisms without monetary transfers. Incentive compatibility and efficiency are primary concerns when designing such mechanisms. We construct the full class of group strategy-proof and Pareto efficient mechanisms and show that each of them can be implemented by endowing agents with control rights over resources. This new class, which we call trading cycles, contains new mechanisms as well as known mechanisms such as top trading cycles, serial dictatorships, and hierarchical exchange. We illustrate how one can use our construction to show what can and what cannot be achieved in a variety of allocation and exchange problems, and we provide an example in which the new trading-cycles mechanisms are more Lorenz equitable than all previously known mechanisms

Arrovian efficiency and auditability in the allocation of discrete resources

In environments where heterogeneous indivisible resources are being allocated without monetary transfers and each agent has a unit demand, we show that an allocation mechanism is individually strategy-proof and Arrovian efficient, i.e., it always selects the best outcome with respect to some Arrovian social welfare function if, and only if, the mechanism is group strategy-proof and Pareto efficient. Re-interpreting Arrow's Independence of Irrelevant Alternatives in terms of auditability of the mechanism, we further show that these are precisely the mechanisms that are strategy-proof, Pareto efficient, and auditable