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Classification of Priorities Such That Deferred Acceptance is Obviously Strategyproof

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  • Clayton Thomas

Abstract

We study the strategic simplicity of stable matching mechanisms where one side has fixed preferences, termed priorities. Specifically, we ask which priorities are such that the strategyproofness of deferred acceptance (DA) can be recognized by agents unable to perform contingency reasoning, that is, \emph{when is DA obviously strategyproof} (Li, 2017)? We answer this question by completely characterizing those priorities which make DA obviously strategyproof (OSP). This solves an open problem of Ashlagi and Gonczarowski, 2018. We find that when DA is OSP, priorities are either acyclic (Ergin, 2002), a restrictive condition which allows priorities to only differ on only two agents at a time, or contain an extremely limited cyclic pattern where all priority lists are identical except for exactly two. We conclude that, for stable matching mechanisms, the tension between understandability (in the sense of OSP) and expressiveness of priorities is very high.

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  • Clayton Thomas, 2020. "Classification of Priorities Such That Deferred Acceptance is Obviously Strategyproof," Papers 2011.12367, arXiv.org, revised Feb 2021.
    • Handle: RePEc:arx:papers:2011.12367
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    References listed on IDEAS

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    1. Troyan, Peter & Morrill, Thayer, 2020. "Obvious manipulations," Journal of Economic Theory, Elsevier, vol. 185(C).
    2. Haluk I. Ergin, 2002. "Efficient Resource Allocation on the Basis of Priorities," Econometrica, Econometric Society, vol. 70(6), pages 2489-2497, November.
    3. Ashlagi, Itai & Gonczarowski, Yannai A., 2018. "Stable matching mechanisms are not obviously strategy-proof," Journal of Economic Theory, Elsevier, vol. 177(C), pages 405-425.
    4. Bade, Sophie, 2019. "Matching with single-peaked preferences," Journal of Economic Theory, Elsevier, vol. 180(C), pages 81-99.
    5. Marek Pycia & Peter Troyan, 2021. "A theory of simplicity in games and mechanism design," ECON - Working Papers 393, Department of Economics - University of Zurich.
    6. Mackenzie, Andrew, 2020. "A revelation principle for obviously strategy-proof implementation," Games and Economic Behavior, Elsevier, vol. 124(C), pages 512-533.
    7. Shengwu Li, 2017. "Obviously Strategy-Proof Mechanisms," American Economic Review, American Economic Association, vol. 107(11), pages 3257-3287, November.
    8. Peter Troyan, 2019. "Obviously Strategy‐Proof Implementation Of Top Trading Cycles," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 60(3), pages 1249-1261, August.
    9. Mackenzie, Andrew, 2018. "A revelation principle for obviously strategy-proof implementation," Research Memorandum 014, Maastricht University, Graduate School of Business and Economics (GSBE).
    10. Jiangtao Li & Piotr Dworczak, 2020. "Are simple mechanisms optimal when agents are unsophisticated?," GRAPE Working Papers 42, GRAPE Group for Research in Applied Economics.
    11. 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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    Cited by:

    1. Pinaki Mandal & Souvik Roy, 2022. "Obviously Strategy‐Proof Implementation Of Assignment Rules: A New Characterization," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 63(1), pages 261-290, February.

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