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Strategyproof and fair matching mechanism for union of symmetric m-convex constraints

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  • Nathanaël Barrot
  • Kentaro Yahiro
  • Makoto Yokoo
  • Yuzhe Zhang

Abstract

We identify a new class of distributional constraints defined as a union of symmetric M-convex sets, which can represent a wide range of real-life constraints in two-sided matching settings. Since M-convexity is not closed under union, a union of symmetric M-convex sets does not belong to this well-behaved class of constraints. Consequently, devising a fair and strategyproof mechanism to handle this new class is challenging. We present a novel mechanism for it called Quota Reduction Deferred Acceptance (QRDA), which repeatedly applies the standard Deferred Acceptance mechanism by sequentially reducing artificially introduced maximum quotas. We show that QRDA is fair and strategyproof when handling a union of symmetric M-convex sets, which extends previous results obtained for a subclass of the union of symmetric M-convex sets: ratio constraints. QRDA always yields a weakly better matching for students than a baseline mechanism called Artificial Cap Deferred Acceptance (ACDA). We also experimentally show that QRDA outperforms ACDA in terms of nonwastefulness.

Suggested Citation

  • Nathanaël Barrot & Kentaro Yahiro & Makoto Yokoo & Yuzhe Zhang, 2024. "Strategyproof and fair matching mechanism for union of symmetric m-convex constraints," PLOS ONE, Public Library of Science, vol. 19(2), pages 1-31, February.
    • Handle: RePEc:plo:pone00:0289965
    DOI: 10.1371/journal.pone.0289965
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    References listed on IDEAS

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    1. Yuichiro Kamada & Fuhito Kojima, 2015. "Efficient Matching under Distributional Constraints: Theory and Applications," American Economic Review, American Economic Association, vol. 105(1), pages 67-99, January.
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