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Supermodular mechanism design

Author

Listed:
  • Mathevet, Laurent A.

    () (Department of Economics, University of Texas, Austin)

Abstract

This paper introduces a mechanism design approach that allows dealing with the multiple equilibrium problem, using mechanisms that are robust to bounded rationality. This approach is a tool for constructing supermodular mechanisms, i.e. mechanisms that induce games with strategic complementarities. In quasilinear environments, I prove that if a social choice function can be implemented by a mechanism that generates bounded strategic substitutes - as opposed to strategic complementarities - then this mechanism can be converted into a supermodular mechanism that implements the social choice function. If the social choice function also satisfies some efficiency criterion, then it admits a supermodular mechanism that balances the budget. Building on these results, I address the multiple equilibrium problem. I provide sufficient conditions for a social choice function to be implementable with a supermodular mechanism whose equilibria are contained in the smallest interval among all supermodular mechanisms. This is followed by conditions for supermodular implementability in unique equilibrium. Finally, I provide a revelation principle for supermodular implementation in environments with general preferences.

Suggested Citation

  • Mathevet, Laurent A., 2010. "Supermodular mechanism design," Theoretical Economics, Econometric Society, vol. 5(3), September.
  • Handle: RePEc:the:publsh:604
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    Citations

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    Cited by:

    1. Bierbrauer, Felix & Netzer, Nick, 2016. "Mechanism design and intentions," Journal of Economic Theory, Elsevier, vol. 163(C), pages 557-603.
    2. Mathevet, Laurent, 2014. "Beliefs and rationalizability in games with complementarities," Games and Economic Behavior, Elsevier, vol. 85(C), pages 252-271.
    3. Olga Gorelkina, 2015. "The Expected Externality Mechanism in a Level-k Environment," Discussion Paper Series of the Max Planck Institute for Research on Collective Goods 2015_03, Max Planck Institute for Research on Collective Goods.
    4. Mathevet, Laurent & Taneva, Ina, 2013. "Finite supermodular design with interdependent valuations," Games and Economic Behavior, Elsevier, vol. 82(C), pages 327-349.
    5. Korpela Ville, 2016. "Procedurally Fair Implementation: The Cost of Insisting on Symmetry," Discussion Papers 108, Aboa Centre for Economics.
    6. Anne-Christine Barthel & Tarun Sabarwal, 2016. "Directional Monotone Comparative Statics," WORKING PAPERS SERIES IN THEORETICAL AND APPLIED ECONOMICS 201601, University of Kansas, Department of Economics.
    7. Rivas, Javier, 2015. "Mechanism design and bounded rationality: The case of type misreporting," Mathematical Social Sciences, Elsevier, vol. 78(C), pages 6-13.
    8. repec:spr:jogath:v:47:y:2018:i:1:d:10.1007_s00182-017-0579-5 is not listed on IDEAS
    9. Healy, Paul J. & Mathevet, Laurent, 2012. "Designing stable mechanisms for economic environments," Theoretical Economics, Econometric Society, vol. 7(3), September.

    More about this item

    Keywords

    Implementation; mechanisms; learning; strategic complementarities; supermodular games;

    JEL classification:

    • C72 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Noncooperative Games
    • D78 - Microeconomics - - Analysis of Collective Decision-Making - - - Positive Analysis of Policy Formulation and Implementation
    • D83 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Search; Learning; Information and Knowledge; Communication; Belief; Unawareness

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