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Efficient mechanisms for level-k bilateral trading

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  • Crawford, Vincent P

Abstract

This paper revisits Myerson and Satterthwaite's (1983) classic analysis of mechanism design for bilateral trading, replacing equilibrium with a level-k model of strategic thinking and focusing on direct mechanisms. The revelation principle fails for level-k models, so restricting attention to direct mechanisms and imposing incentive-compatibility are not without loss of generality. If, however, only direct, level-k-incentive-compatible mechanisms are feasible and traders' levels are observable, Myerson and Satterthwaite's characterization of mechanisms that maximize traders' total surplus subject to incentive constraints generalizes qualitatively to level-k models. If only direct, level-k-incentive-compatible mechanisms are feasible but traders' levels are not observable, generically a particular posted-price mechanism maximizes traders' total expected surplus subject to incentive constraints. If direct, non-level-k-incentive-compatible mechanisms are feasible and traders best respond to them, total expected surplus-maximizing mechanisms may take completely different forms.
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Suggested Citation

  • Crawford, Vincent P, 2021. "Efficient mechanisms for level-k bilateral trading," University of California at San Diego, Economics Working Paper Series qt4748b7r2, Department of Economics, UC San Diego.
    • Handle: RePEc:cdl:ucsdec:qt4748b7r2
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    Cited by:

    1. Jean-Michel Benkert, 2025. "Bilateral trade with loss-averse agents," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 79(2), pages 519-560, March.
    2. Li, Fei & Song, Yangbo & Zhao, Mofei, 2023. "Global manipulation by local obfuscation," Journal of Economic Theory, Elsevier, vol. 207(C).
    3. de Clippel, Geoffroy & Saran, Rene & Serrano, Roberto, 2023. "Continuous level-k mechanism design," Games and Economic Behavior, Elsevier, vol. 140(C), pages 481-501.
    4. Malachy James Gavan & Antonio Penta, 2022. "Safe Implementation," Working Papers 1363, Barcelona School of Economics.
    5. Gavan, Malachy James & Penta, Antonio, 2022. "Safe Implementation," TSE Working Papers 22-1369, Toulouse School of Economics (TSE).
    6. Rivera Mora, Ernesto, 2024. "Mechanism design with belief-dependent preferences," Journal of Economic Theory, Elsevier, vol. 216(C).
    7. Lin, Po-Hsuan & Palfrey, Thomas R., 2024. "Cognitive hierarchies for games in extensive form," Journal of Economic Theory, Elsevier, vol. 220(C).
    8. Giacomo Rubbini, 2023. "Mechanism Design without Rational Expectations," Papers 2305.07472, arXiv.org, revised Nov 2023.
    9. Kneeland, Terri, 2022. "Mechanism design with level-k types: Theory and an application to bilateral trade," Journal of Economic Theory, Elsevier, vol. 201(C).
    10. Ballester, Coralio & Rodriguez-Moral, Antonio & Vorsatz, Marc, 2024. "Cognitive reflection in experimental anchored guessing games," Games and Economic Behavior, Elsevier, vol. 148(C), pages 179-195.
    11. Possajennikov, Alex & Saran, Rene, 2023. "(In)efficiency in private value bargaining with naive players: Theory and experiment," Journal of Economic Behavior & Organization, Elsevier, vol. 216(C), pages 42-61.

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    JEL classification:

    • C70 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - General
    • D02 - Microeconomics - - General - - - Institutions: Design, Formation, Operations, and Impact

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