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Supermodular mechanism design

Author

Listed:
  • , 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

  • , 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. Mariann Ollar & Antonio Penta, 2021. "A network solution to robust implementation: The case of identical but unknown distributions," Economics Working Papers 1776, Department of Economics and Business, Universitat Pompeu Fabra.
    3. Olga Gorelkina, 2018. "The expected externality mechanism in a level-k environment," International Journal of Game Theory, Springer;Game Theory Society, vol. 47(1), pages 103-131, March.
    4. Tilman Börgers & Jiangtao Li, 2019. "Strategically Simple Mechanisms," Econometrica, Econometric Society, vol. 87(6), pages 2003-2035, November.
    5. Anne-Christine Barthel & Tarun Sabarwal, 2018. "Directional monotone comparative statics," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 66(3), pages 557-591, October.
    6. Barthel, Anne-Christine & Hoffmann, Eric & Monaco, Andrew, 2019. "Coordination and learning in games with strategic substitutes and complements," Research in Economics, Elsevier, vol. 73(1), pages 53-65.
    7. Mariann Ollár & Antonio Penta, 2019. "Implementation via transfers with identical but unknown distributions," Economics Working Papers 1676, Department of Economics and Business, Universitat Pompeu Fabra.
    8. , J. & ,, 2012. "Designing stable mechanisms for economic environments," Theoretical Economics, Econometric Society, vol. 7(3), September.
    9. Kunimoto, Takashi & Yamashita, Takuro, 2020. "Order on types based on monotone comparative statics," Journal of Economic Theory, Elsevier, vol. 189(C).
    10. Mathevet, Laurent, 2014. "Beliefs and rationalizability in games with complementarities," Games and Economic Behavior, Elsevier, vol. 85(C), pages 252-271.
    11. Korpela, Ville, 2018. "Procedurally fair implementation under complete information," Journal of Mathematical Economics, Elsevier, vol. 77(C), pages 25-31.
    12. Mathevet, Laurent & Taneva, Ina, 2013. "Finite supermodular design with interdependent valuations," Games and Economic Behavior, Elsevier, vol. 82(C), pages 327-349.
    13. Korpela Ville, 2016. "Procedurally Fair Implementation: The Cost of Insisting on Symmetry," Discussion Papers 108, Aboa Centre for Economics.
    14. Javier Rivas Ruiz, 2014. "Mechanism Design and Robust Control," Department of Economics Working Papers 22/14, University of Bath, Department of Economics.
    15. Sylvain Chassang & Lucia Del Carpio & Samuel Kapon, 2022. "Using Divide and Conquer to Improve Tax Collection: Theory and Laboratory Evidence," Working Papers 299, Princeton University, Department of Economics, Center for Economic Policy Studies..
    16. Anne-Christine Barthel & Eric Hoffmann, 2019. "Rationalizability and learning in games with strategic heterogeneity," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 67(3), pages 565-587, April.
    17. Rivas, Javier, 2015. "Mechanism design and bounded rationality: The case of type misreporting," Mathematical Social Sciences, Elsevier, vol. 78(C), pages 6-13.
    18. 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..
    19. Koch, Caleb M., 2019. "Index-wise comparative statics," Mathematical Social Sciences, Elsevier, vol. 102(C), pages 35-41.

    More about this item

    Keywords

    Implementation; mechanisms; learning; strategic complementarities; supermodular games;
    All these keywords.

    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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