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Incentive properties for ordinal mechanisms

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  • Cho, Wonki Jo

Abstract

We study three incentive properties for ordinal mechanisms: (i) strategy-proofness, which requires that no agent gain by misrepresenting his preferences; (ii) adjacent strategy-proofness, which requires that no agent gain by switching the rankings of two adjacent alternatives; and (iii) mistake monotonicity, which requires that the welfare of each agent weakly decrease as he reports increasingly bigger mistakes. Each of these properties has three versions, depending on whether preferences over sure alternatives are extended to preferences over lotteries by the stochastic dominance, downward lexicographic, or upward lexicographic extension. We identify conditions on the preference domain that guarantee the equivalence of these properties. The universal domain and the domains of single-dipped and single-peaked preferences satisfy our conditions.

Suggested Citation

  • Cho, Wonki Jo, 2016. "Incentive properties for ordinal mechanisms," Games and Economic Behavior, Elsevier, vol. 95(C), pages 168-177.
    • Handle: RePEc:eee:gamebe:v:95:y:2016:i:c:p:168-177
    DOI: 10.1016/j.geb.2015.12.003
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    Cited by:

    1. Chatterji, Shurojit & Zeng, Huaxia, 2018. "On random social choice functions with the tops-only property," Games and Economic Behavior, Elsevier, vol. 109(C), pages 413-435.
    2. Madhuparna Karmokar & Souvik Roy, 2023. "The structure of (local) ordinal Bayesian incentive compatible random rules," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 76(1), pages 111-152, July.
    3. Altuntaş, Açelya & Phan, William & Tamura, Yuki, 2023. "Some characterizations of Generalized Top Trading Cycles," Games and Economic Behavior, Elsevier, vol. 141(C), pages 156-181.
    4. Youngsub Chun & Kiyong Yun, 2020. "Upper-contour strategy-proofness in the probabilistic assignment problem," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 54(4), pages 667-687, April.
    5. Liu, Peng, 2020. "Random assignments on sequentially dichotomous domains," Games and Economic Behavior, Elsevier, vol. 121(C), pages 565-584.
    6. Liu, Peng, 2020. "Local vs. global strategy-proofness: A new equivalence result for ordinal mechanisms," Economics Letters, Elsevier, vol. 189(C).
    7. Kumar, Ujjwal & Roy, Souvik & Sen, Arunava & Yadav, Sonal & Zeng, Huaxia, 2021. "Local global equivalence for unanimous social choice functions," Games and Economic Behavior, Elsevier, vol. 130(C), pages 299-308.
    8. Roy, Souvik & Sadhukhan, Soumyarup, 2021. "A unified characterization of the randomized strategy-proof rules," Journal of Economic Theory, Elsevier, vol. 197(C).
    9. Harless, Patrick, 2016. "Solidarity in preference aggregation: Improving on a status quo," Games and Economic Behavior, Elsevier, vol. 95(C), pages 73-87.
    10. Liu, Peng & Zeng, Huaxia, 2019. "Random assignments on preference domains with a tier structure," Journal of Mathematical Economics, Elsevier, vol. 84(C), pages 176-194.
    11. Cho, Wonki Jo, 2016. "When is the probabilistic serial assignment uniquely efficient and envy-free?," Journal of Mathematical Economics, Elsevier, vol. 66(C), pages 14-25.
    12. Haris Aziz & Yoichi Kasajima, 2017. "Impossibilities for probabilistic assignment," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 49(2), pages 255-275, August.
    13. Aziz, Haris & Brandl, Florian & Brandt, Felix & Brill, Markus, 2018. "On the tradeoff between efficiency and strategyproofness," Games and Economic Behavior, Elsevier, vol. 110(C), pages 1-18.
    14. Chatterji, Shurojit & Zeng, Huaxia, 2019. "Random mechanism design on multidimensional domains," Journal of Economic Theory, Elsevier, vol. 182(C), pages 25-105.
    15. William Thomson, 2023. "Where should your daughter go to college? An axiomatic analysis," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 60(1), pages 313-330, January.
    16. Karmokar, Madhuparna & Roy, Souvik, 2020. "The structure of (local) ordinal Bayesian incentive compatible random rules," MPRA Paper 103494, University Library of Munich, Germany.
    17. Roy, Souvik & Sadhukhan, Soumyarup, 2022. "On the equivalence of strategy-proofness and upper contour strategy-proofness for randomized social choice functions," Journal of Mathematical Economics, Elsevier, vol. 99(C).
    18. Sulagna Dasgupta & Debasis Mishra, 2020. "Ordinal Bayesian incentive compatibility in random assignment model," Papers 2009.13104, arXiv.org, revised May 2021.
    19. Mennle, Timo & Seuken, Sven, 2021. "Partial strategyproofness: Relaxing strategyproofness for the random assignment problem," Journal of Economic Theory, Elsevier, vol. 191(C).
    20. Muto, Nozomu & Sato, Shin, 2017. "An impossibility under bounded response of social choice functions," Games and Economic Behavior, Elsevier, vol. 106(C), pages 1-15.
    21. Zhang, Jun, 2020. "When are efficient and fair assignment mechanisms group strategy-proof?," Games and Economic Behavior, Elsevier, vol. 119(C), pages 251-266.
    22. Cho, Wonki Jo & Doğan, Battal, 2016. "Equivalence of efficiency notions for ordinal assignment problems," Economics Letters, Elsevier, vol. 146(C), pages 8-12.
    23. Andrew McLennan & Shino Takayama & Yuki Tamura, 2024. "An Efficient, Computationally Tractable School Choice Mechanism," Discussion Papers Series 668, School of Economics, University of Queensland, Australia.

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    More about this item

    Keywords

    Ordinal mechanism; Strategy-proofness; Adjacent strategy-proofness; Mistake monotonicity;
    All these keywords.

    JEL classification:

    • C70 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - General
    • C78 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Bargaining Theory; Matching Theory
    • D71 - Microeconomics - - Analysis of Collective Decision-Making - - - Social Choice; Clubs; Committees; Associations

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