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Abstract types and distributions in independent private value auctions

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  • Paulo Monteiro

Abstract

In this note, in an independent private values auction framework, I discuss the relationship between the set of types and the distribution of types. I show that any set of types, finite dimensional or not, can be extended to a larger set of types preserving incentive compatibility constraints, expected revenue and bidder’s expected utilities. Thus for example we may convexify a set of types making our model amenable to the large body of theory in economics and mathematics that relies on convexity assumptions. An interesting application of this extension procedure is to show that although revenue equivalence is not valid in general if the set of types is not convex these mechanism have underlying distinct allocation mechanism in the extension. Thus we recover in these situations the revenue equivalence.
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Suggested Citation

  • Paulo Monteiro, 2009. "Abstract types and distributions in independent private value auctions," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 40(3), pages 497-507, September.
    • Handle: RePEc:spr:joecth:v:40:y:2009:i:3:p:497-507
    DOI: 10.1007/s00199-008-0386-0
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    Cited by:

    1. Siddharth Prasad & Maria-Florina Balcan & Tuomas Sandholm, 2025. "Revenue-Optimal Efficient Mechanism Design with General Type Spaces," Papers 2505.13687, arXiv.org.
    2. Monteiro, Paulo Klinger & Page, Frank H. & Svaiter, Benar fux, 2013. "Optimal auctions with multidimensional types and the desirability of exclusion," Journal of Mathematical Economics, Elsevier, vol. 49(1), pages 106-110.
    3. Carrasco, Vinicius & Farinha Luz, Vitor & Kos, Nenad & Messner, Matthias & Monteiro, Paulo & Moreira, Humberto, 2018. "Optimal selling mechanisms under moment conditions," Journal of Economic Theory, Elsevier, vol. 177(C), pages 245-279.

    More about this item

    Keywords

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    JEL classification:

    • D44 - Microeconomics - - Market Structure, Pricing, and Design - - - Auctions

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