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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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  • 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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    2. Geoffroy de Clippel & Rene Saran & Roberto Serrano, 2021. "Continuous Level-k Mechanism Design," Working Papers 2021-002, Brown University, Department of Economics.
    3. Malachy James Gavan & Antonio Penta, 2022. "Safe Implementation," Working Papers 1363, Barcelona School of Economics.
    4. Gavan, Malachy James & Penta, Antonio, 2022. "Safe Implementation," TSE Working Papers 22-1369, Toulouse School of Economics (TSE).
    5. de Clippel, Geoffroy & Saran, Rene & Serrano, Roberto, 2023. "Continuous level-k mechanism design," Games and Economic Behavior, Elsevier, vol. 140(C), pages 481-501.
    6. Giacomo Rubbini, 2023. "Mechanism Design without Rational Expectations," Papers 2305.07472, arXiv.org, revised Nov 2023.
    7. Kneeland, Terri, 2022. "Mechanism design with level-k types: Theory and an application to bilateral trade," Journal of Economic Theory, Elsevier, vol. 201(C).

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    More about this item

    Keywords

    Prevention; Mechanism design; Bilateral trading; Level-k thinking; Behavioral game theory; Economic Theory; Applied Economics;
    All these keywords.

    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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