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Title : Matching with complex constraints
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Matching with complex constraints

At the NBER market design conference yesterday, Fuhito Kojima spoke about his paper with Yuchiro Kamada on matching with 'upper bound' constraints of the kind that occur in matching children to day care in Japan.

Here's the paper:

FAIR MATCHING UNDER CONSTRAINTS: THEORY AND
APPLICATIONS by YUICHIRO KAMADA AND FUHITO KOJIMA

Abstract. This paper studies a general model of matching with constraints. Observing that a stable matching typically does not exist, we focus on feasible, individually rational, and fair matchings. We characterize such matchings by fixed points of a certain function. Building on this result, we characterize the class of constraints on individual schools under which there exists a student-optimal fair matching (SOFM), the matching that is the most preferred by every student among those satisfying the three desirable properties. We study the numerical relevance of our theory using data on governmentorganized
daycare allocation.

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