Large Matchings in Large Markets with Flexible Supply
87 Pages Posted: 14 Aug 2018 Last revised: 5 Nov 2018
Date Written: November 5, 2018
The size of a matching is defined as the expected number of agents who are matched to some objects. It is an important design objective in many applications, including refugee resettlement, daycare assignment, and mass vaccination campaigns. This paper studies the matching size achieved by strategy-proof mechanisms in a general model of matching with constraints. Our model generalizes a number of constraint structures considered in the extant literature. We show that naïve extensions of classical mechanisms may generate an arbitrarily small matching when we have such generalized constraints. Assuming a large market (in that the variety of objects is fixed but the capacities are large), we develop a technique to reshape a given resource constraint to a more structured one, called a polymatroidal constraint, with which a classical mechanism performs well. We propose a mechanism that (i) satisfies strategy-proofness, (ii) always achieves at least 1-1/e = 63.2% of the maximum size (which is the best approximation ratio a strategy-proof mechanism can achieve), (iii) respects agents' preferences, and (iv) is computationally efficient, for general instances.
Keywords: Random assignment, Strategy-proofness, Matching with constraints, Large market, Maximum matching
JEL Classification: C78, D47, D61, D82
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