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The structure of (local) ordinal Bayesian incentive compatible random rules

Author

Listed:
  • Madhuparna Karmokar

    (Indian Statistical Institute)

  • Souvik Roy

    (Applied Statistics Unit, Indian Statistical Institute)

Abstract

We explore the structure of locally ordinal Bayesian incentive compatible (LOBIC) random Bayesian rules (RBRs). We show that under lower contour monotonicity, for almost all prior profiles (with full Lebesgue measure), a LOBIC RBR is locally dominant strategy incentive compatible (LDSIC). We further show that for almost all prior profiles, a unanimous and LOBIC RBR on the unrestricted domain is random dictatorial, and thereby extend the result in Gibbard (Econometrica 45:665–681, 1977) for Bayesian rules. Next, we provide a sufficient condition on a domain so that for almost all prior profiles, unanimous RBRs on it are tops-only. Finally, we provide a wide range of applications of our results on single-peaked (on arbitrary graphs), hybrid, multiple single-peaked, single-dipped, single-crossing, multi-dimensional separable domains, and domains under partitioning. Since OBIC implies LOBIC by definition, all our results hold for OBIC RBRs.

Suggested Citation

  • Madhuparna Karmokar & Souvik Roy, 2023. "The structure of (local) ordinal Bayesian incentive compatible random rules," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 76(1), pages 111-152, July.
    • Handle: RePEc:spr:joecth:v:76:y:2023:i:1:d:10.1007_s00199-022-01449-x
    DOI: 10.1007/s00199-022-01449-x
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    More about this item

    Keywords

    Random Bayesian rules; Random social choice functions; (Local) ordinal Bayesian incentive compatibility; (Local) dominant strategy incentive compatibility;
    All these keywords.

    JEL classification:

    • D71 - Microeconomics - - Analysis of Collective Decision-Making - - - Social Choice; Clubs; Committees; Associations
    • D82 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Asymmetric and Private Information; Mechanism Design

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