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Asymmetric Auctions with Discretely Distributed Valuations

Author

Listed:
  • Muhammed Ceesay
  • Nicola Doni
  • Domenico Menicucci

Abstract

We examine a two-bidder auction setting in which the distributions for the bidders’ valuations are asymmetric over a support consisting of three elements. For the first price auction we derive the unique Bayes Nash Equilibrium in closed form, which allows to obtain more precise results with respect to the classical results in the literature on how asymmetries affect equilibrium bidding. Then we compare the revenue in the first price auction with the revenue in the second price auction. The latter is often superior to the former and we determine precisely, given a distribution for the value of the weak bidder, when a distribution for the value of the strong bidder exists such that the first price auction is superior to the second auction. For two particular asymmetries, shift and stretch, we show that in our setting the results are quite different from the results which are well-known in the literature.

Suggested Citation

  • Muhammed Ceesay & Nicola Doni & Domenico Menicucci, 2024. "Asymmetric Auctions with Discretely Distributed Valuations," Working Papers - Economics wp2024_20.rdf, Universita' degli Studi di Firenze, Dipartimento di Scienze per l'Economia e l'Impresa.
    • Handle: RePEc:frz:wpaper:wp2024_20.rdf
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    More about this item

    Keywords

    Asymmetric auctions; First price auction; Second price auction; Revenue ranking;
    All these keywords.

    JEL classification:

    • D44 - Microeconomics - - Market Structure, Pricing, and Design - - - Auctions
    • D82 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Asymmetric and Private Information; Mechanism Design

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