Characterization of incentive compatible single-parameter mechanisms revisited

We reexamine the characterization of incentive compatible single-parameter mechanisms introduced in Archer & Tardos (2001). We argue that the claimed uniqueness result, called 'Myerson's Lemma' was not well established. We provide an elementary proof of uniqueness that unifies the...

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Bibliographic Details
Published inJournal of mechanism and institution design (Online) Vol. 7; no. 1; pp. 113 - 129
Main Authors Apt, Krzysztof R., Heering, Jan
Format Journal Article
LanguageEnglish
Published Society for the Promotion of Mechanism and Institution Design 03.12.2022
Subjects
auctions
incentive compatibility
myerson's lemma
revenue equivalence
single-parameter mechanisms
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Summary:We reexamine the characterization of incentive compatible single-parameter mechanisms introduced in Archer & Tardos (2001). We argue that the claimed uniqueness result, called 'Myerson's Lemma' was not well established. We provide an elementary proof of uniqueness that unifies the presentation for two classes of allocation functions used in the literature and show that the general case is a consequence of a little known result from the theory of real functions. We also clarify that our proof of uniqueness is more elementary than the previous one. Finally, by generalizing our characterization result to more dimensions, we provide alternative proofs of revenue equivalence results for multiunit auctions and combinatorial auctions.
ISSN:2399-844X
2399-8458
DOI:10.22574/jmid.2022.12.004