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An alternative characterization of the deferred acceptance algorithm

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  • Thayer Morrill

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Abstract

Kojima and Manea (Econometrica 78(2):633–653, 2010 ) present two characterizations of when an allocation rule corresponds to the agent-proposing deferred acceptance (DA) algorithm for some substitutable priority rule of the objects being assigned. Building on their results we characterize when an allocation rule is outcome equivalent to the DA algorithm for every substitutable priority rule. In particular, an assignment rule satisfies mutual best (MB) if an agent is always assigned her most preferred object whenever she has the highest priority for it. This mild requirement is a necessary but far from sufficient condition for an assignment rule to be stable. We demonstrate that any allocation mechanism that satisfies MB along with non-wastefulness, population monotonicity and either individually rational monotonicity or weak Maskin monotonicity not only is a stable assignment mechanism but is equivalent to the agent proposing DA algorithm. Copyright Springer-Verlag 2013

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  • Thayer Morrill, 2013. "An alternative characterization of the deferred acceptance algorithm," International Journal of Game Theory, Springer;Game Theory Society, vol. 42(1), pages 19-28, February.
  • Handle: RePEc:spr:jogath:v:42:y:2013:i:1:p:19-28
    DOI: 10.1007/s00182-011-0311-9
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    3. Mustafa Oğuz Afacan & Umut Mert Dur, 2020. "Constrained stability in two-sided matching markets," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 55(3), pages 477-494, October.
    4. Burak Can & Mohsen Pourpouneh & Ton Storcken, 2020. "Cost of transformation: a measure on matchings," IFRO Working Paper 2020/10, University of Copenhagen, Department of Food and Resource Economics.
    5. Pycia, Marek & Ünver, M. Utku, 2017. "Incentive compatible allocation and exchange of discrete resources," Theoretical Economics, Econometric Society, vol. 12(1), January.
    6. Can, Burak & Pourpouneh, Mohsen & Storcken, Ton, 2017. "Cost of transformation: a measure on matchings," Research Memorandum 015, Maastricht University, Graduate School of Business and Economics (GSBE).
    7. Lars Ehlers & Bettina Klaus, 2013. "House Allocation via Deferred-Acceptance (N.B.: This paper has been extended and results are now contained in working paper 14.08.)," Cahiers de Recherches Economiques du Département d'économie 13.10, Université de Lausanne, Faculté des HEC, Département d’économie.
    8. Sasaki, Yasuo & Ura, Masahiro, 2016. "Serial dictatorship and unmatch reduction: A problem of Japan’s nursery school choice," Economics Letters, Elsevier, vol. 147(C), pages 38-41.
    9. Lars Ehlers & Bettina Klaus, 2014. "Strategy-Proofness Makes the Difference: Deferred-Acceptance with Responsive Priorities," Mathematics of Operations Research, INFORMS, vol. 39(4), pages 949-966, November.
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    12. Raghavan, Madhav, 2020. "Swap-flexibility in the assignment of houses," Journal of Mathematical Economics, Elsevier, vol. 91(C), pages 1-10.
    13. Harless, Patrick, 2014. "A School Choice Compromise: Between Immediate and Deferred Acceptance," MPRA Paper 61417, University Library of Munich, Germany.
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