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Level-$k$ Mechanism Design

Author

Listed:
  • Geoffroy de Clippel
  • Rene Saran
  • Roberto Serrano

Abstract

Non-equilibrium models of choice (e.g. level-$k$ reasoning) have significantly different, sometimes more accurate, predictions in games than does Nash equilibrium. When it comes to the maximal set of functions that are implementable in mechanism design, however, they turn out to have similar implications. Focusing on single-valued rules, we discuss the role and implications of different behavioural anchors (arbitrary level-0 play), and prove a level-$k$ revelation principle. If a function is level-$k$ implementable given any level-0 play, it must obey a slight weakening of standard strict incentive constraints. Further, the same condition is also sufficient for level-$k$ implementability, although the role of specific level-0 anchors is more controversial for the sufficiency argument. Nonetheless, our results provide tight characterizations of level-$k$ implementable functions under a variety of level-0 play, including truthful, uniform, and atomless anchors.

Suggested Citation

  • Geoffroy de Clippel & Rene Saran & Roberto Serrano, 2019. "Level-$k$ Mechanism Design," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 86(3), pages 1207-1227.
    • Handle: RePEc:oup:restud:v:86:y:2019:i:3:p:1207-1227.
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    File URL: http://hdl.handle.net/10.1093/restud/rdy031
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    Citations

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    Cited by:

    1. Li, Fei & Song, Yangbo & Zhao, Mofei, 2023. "Global manipulation by local obfuscation," Journal of Economic Theory, Elsevier, vol. 207(C).
    2. Itzhak Rasooly, 2021. "Going... going... wrong: a test of the level-k (and cognitive hierarchy) models of bidding behaviour," Papers 2111.05686, arXiv.org.
    3. Itzhak Rasooly, 2022. "Going...going...wrong: a test of the level-k (and cognitive hierarchy) models of bidding behaviour," Economics Series Working Papers 959, University of Oxford, Department of Economics.
    4. de Clippel, Geoffroy & Saran, Rene & Serrano, Roberto, 2023. "Continuous level-k mechanism design," Games and Economic Behavior, Elsevier, vol. 140(C), pages 481-501.
    5. T. Hayashi & R. Jain & V. Korpela & M. Lombardi, 2023. "Behavioral strong implementation," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 76(4), pages 1257-1287, November.
    6. Crawford, Vincent P., 2021. "Efficient mechanisms for level-k bilateral trading," Games and Economic Behavior, Elsevier, vol. 127(C), pages 80-101.
    7. Ritesh Jain & Michele Lombardi, 2019. "Virtual implementation by bounded mechanisms: Complete information," IEAS Working Paper : academic research 19-A001, Institute of Economics, Academia Sinica, Taipei, Taiwan.
    8. Yi-Chun Chen & Richard Holden & Takashi Kunimoto & Yifei Sun & Tom Wilkening, 2023. "Getting Dynamic Implementation to Work," Journal of Political Economy, University of Chicago Press, vol. 131(2), pages 285-387.
    9. Giacomo Rubbini, 2023. "Mechanism Design without Rational Expectations," Papers 2305.07472, arXiv.org, revised Nov 2023.
    10. Kneeland, Terri, 2022. "Mechanism design with level-k types: Theory and an application to bilateral trade," Journal of Economic Theory, Elsevier, vol. 201(C).
    11. Caballero, William N. & Lunday, Brian J. & Uber, Richard P., 2021. "Identifying behaviorally robust strategies for normal form games under varying forms of uncertainty," European Journal of Operational Research, Elsevier, vol. 288(3), pages 971-982.
    12. Kneeland, Terri, 2017. "Mechanism design with level-k types: Theory and an application to bilateral trade," Discussion Papers, Research Unit: Economics of Change SP II 2017-303, WZB Berlin Social Science Center.
    13. Sylvain Chassang & Lucia Del Carpio & Samuel Kapon, 2020. "Making the Most of Limited Government Capacity: Theory and Experiment," Working Papers 2020-7, Princeton University. Economics Department..

    More about this item

    Keywords

    Mechanism design; Bounded rationality; Level-k reasoning; Revelation principle; Incentive compatibility;
    All these keywords.

    JEL classification:

    • C72 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Noncooperative Games
    • D70 - Microeconomics - - Analysis of Collective Decision-Making - - - General
    • D78 - Microeconomics - - Analysis of Collective Decision-Making - - - Positive Analysis of Policy Formulation and Implementation
    • D82 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Asymmetric and Private Information; Mechanism Design

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