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Royal Processions: Incentives, Efficiency and Fairness in Two-sided Matching

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  • Sophie Bade
  • Joseph Root

Abstract

We study the set of incentive compatible and efficient two-sided matching mechanisms. We classify all such mechanisms under an additional assumption -- "gender-neutrality" -- which guarantees that the two sides be treated symmetrically. All group strategy-proof, efficient and gender-neutral mechanisms are recursive and the outcome is decided in a sequence of rounds. In each round, two agents are selected, one from each side. These agents are either "matched-by-default" or "unmatched-by-default." In the former case either of the selected agents can unilaterally force the other to match with them while in the latter case they may only match together if both agree. In either case, if this pair of agents is not matched together, each gets their top choice among the set of remaining agents. As an important step in the characterization, we first show that in one-sided matching all group strategy-proof and efficient mechanisms are sequential dictatorships. An immediate corollary is that there are no individually rational, group strategy-proof and efficient one-sided matching mechanisms.

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  • Sophie Bade & Joseph Root, 2023. "Royal Processions: Incentives, Efficiency and Fairness in Two-sided Matching," Papers 2301.13037, arXiv.org.
    • Handle: RePEc:arx:papers:2301.13037
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    References listed on IDEAS

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    1. Joseph Root & David S. Ahn, 2020. "Incentives and Efficiency in Constrained Allocation Mechanisms," Papers 2006.06776, arXiv.org, revised Nov 2023.
    2. Bogomolnaia, Anna & Moulin, Herve, 2001. "A New Solution to the Random Assignment Problem," Journal of Economic Theory, Elsevier, vol. 100(2), pages 295-328, October.
    3. Satterthwaite, Mark Allen, 1975. "Strategy-proofness and Arrow's conditions: Existence and correspondence theorems for voting procedures and social welfare functions," Journal of Economic Theory, Elsevier, vol. 10(2), pages 187-217, April.
    4. Federico Echenique & Joseph Root & Fedor Sandomirskiy, 2022. "Efficiency in Random Resource Allocation and Social Choice," Papers 2203.06353, arXiv.org, revised Aug 2022.
    5. Sophie Bade, 2020. "Random Serial Dictatorship: The One and Only," Mathematics of Operations Research, INFORMS, vol. 45(1), pages 353-368, February.
    6. Gibbard, Allan, 1973. "Manipulation of Voting Schemes: A General Result," Econometrica, Econometric Society, vol. 41(4), pages 587-601, July.
    7. Alvin E. Roth, 1982. "The Economics of Matching: Stability and Incentives," Mathematics of Operations Research, INFORMS, vol. 7(4), pages 617-628, November.
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