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Continuous implementation with direct revelation mechanisms

Author

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  • Chen, Yi-Chun
  • Mueller-Frank, Manuel
  • Pai, Mallesh M.

Abstract

We investigate how a principal's knowledge of agents' higher-order beliefs impacts their ability to robustly implement a given social choice function. We adapt a formulation of Oury and Tercieux (2012): a social choice function is continuously implementable if it is partially implementable for types in an initial model and “nearby” types. We characterize when a social choice function is truthfully continuously implementable, i.e., using game forms corresponding to direct revelation mechanisms for the initial model. Our characterization hinges on how our formalization of the notion of nearby preserves agents' higher order beliefs. If nearby types have similar higher order beliefs, truthful continuous implementation is roughly equivalent to requiring that the social choice function is implementable in strict equilibrium in the initial model, a very permissive solution concept. If they do not, then our notion is equivalent to requiring that the social choice function is implementable in unique rationalizable strategies in the initial model. Truthful continuous implementation is thus very demanding without non-trivial knowledge of agents' higher order beliefs.

Suggested Citation

  • Chen, Yi-Chun & Mueller-Frank, Manuel & Pai, Mallesh M., 2022. "Continuous implementation with direct revelation mechanisms," Journal of Economic Theory, Elsevier, vol. 201(C).
    • Handle: RePEc:eee:jetheo:v:201:y:2022:i:c:s0022053122000126
    DOI: 10.1016/j.jet.2022.105422
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    Cited by:

    1. de Clippel, Geoffroy & Saran, Rene & Serrano, Roberto, 2023. "Continuous level-k mechanism design," Games and Economic Behavior, Elsevier, vol. 140(C), pages 481-501.
    2. Chen, Yi-Chun & Kunimoto, Takashi & Sun, Yifei, 2023. "Continuous implementation with payoff knowledge," Journal of Economic Theory, Elsevier, vol. 209(C).

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    More about this item

    Keywords

    Continuous implementation; Robust implementation; Contagion; Higher-order beliefs;
    All these keywords.

    JEL classification:

    • D82 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Asymmetric and Private Information; Mechanism Design
    • D83 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Search; Learning; Information and Knowledge; Communication; Belief; Unawareness

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