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

Madhuparna Karmokar () and Souvik Roy ()
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Madhuparna Karmokar: Indian Statistical Institute
Souvik Roy: Applied Statistics Unit, Indian Statistical Institute

Economic Theory, 2023, vol. 76, issue 1, No 4, 152 pages

Abstract: 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.

Keywords: Random Bayesian rules; Random social choice functions; (Local) ordinal Bayesian incentive compatibility; (Local) dominant strategy incentive compatibility (search for similar items in EconPapers)
JEL-codes: D71 D82 (search for similar items in EconPapers)
Date: 2023
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Citations: View citations in EconPapers (1)

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DOI: 10.1007/s00199-022-01449-x

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