101 research outputs found
A solution to matching with preferences over colleagues
We study many-to-one matchings, such as the assignment of students to colleges, where the students have preferences over the other students who would attend the same college. It is well known that the core of this model may be empty, without strong assumptions on agents' preferences. We introduce a method that finds all core matchings, if any exist. The method requires no assumptions on preferences. Our method also finds certain partial solutions that may be useful when the core is empty
A Solution to Matching with Preferences over Colleagues
We study many-to-one matchings, such as the assignment of students to colleges, where the students have preferences over the other students who would attend the same college. It is well known that the core of this model may be empty, without strong assumptions on agentsâ preferences. We introduce a method that finds all core matchings, if any exist. The method requires no assumptions on preferences. Our method also finds certain partial solutions that may be useful when the core is empty
How to Control Controlled School Choice
We characterize choice rules for schools that regard students as substitutes while expressing preferences for a diverse student body. The stable (or fair) assignment of students to schools requires the latter to regard the former as substitutes. Such a requirement is in conflict with the reality of schools' preferences for diversity. We show that the conflict can be useful, in the sense that certain unique rules emerge from imposing both considerations. We also provide welfare comparisons for students when different choice rules are employed
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
Median Stable Matching
We define the median stable matching for two-sided matching markets with side payments and prove constructively that it exists.
Efficient Market Design with Distributional Objectives
Given an initial matching and a policy objective on the distribution of agent
types to institutions, we study the existence of a mechanism that weakly
improves the distributional objective and satisfies constrained efficiency,
individual rationality, and strategy-proofness. We show that such a mechanism
need not exist in general. We introduce a new notion of discrete concavity,
which we call pseudo M-concavity, and construct a mechanism with
the desirable properties when the distributional objective satisfies this
notion. We provide several practically relevant distributional objectives that
are pseudo M-concave
Fair Allocation of Vaccines, Ventilators and Antiviral Treatments: Leaving No Ethical Value Behind in Health Care Rationing
COVID-19 has revealed limitations of existing mechanisms for rationing
medical resources under emergency scenarios. Many argue that these mechanisms
abandon various ethical values such as equity by discriminating against
disadvantaged communities. Illustrating that these limitations are aggravated
by a restrictive choice of mechanism, we formulate pandemic rationing of
medical resources as a new application of market design and propose a reserve
system as a resolution. We develop a general theory of reserve design,
introduce new concepts such as cutoff equilibria and smart reserves, extend
analysis of previously-known ones such as sequential reserve matching, relate
these concepts to current debates, and present preliminary policy impact.Comment: Keywords: ethical rationing, reserve system, COVID-19, vaccines,
ventilator
Stability and Median Rationalizability for Aggregate Matchings
We develop the theory of stability for aggregate matchings used in empirical studies and establish fundamental properties of stable matchings including the result that the set of stable matchings is a non-empty, complete, and distributive lattice. Aggregate matchings are relevant as matching data in revealed preference theory. We present a result on rationalizing a matching data as the median stable matching
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