Abstract types and distributions in independent private value auctions
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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- Svaiter, Benar Fux & Monteiro, P. K., 2008.
"Optimal auction with a general distribution: virtual valuation without densities,"
Economics Working Papers (Ensaios Economicos da EPGE)
681, FGV/EPGE Escola Brasileira de Economia e Finanças, Getulio Vargas Foundation (Brazil).
- Monteiro, Paulo Klinger & Svaiter, Benar Fux, 2010. "Optimal auction with a general distribution: Virtual valuation without densities," Journal of Mathematical Economics, Elsevier, vol. 46(1), pages 21-31, January.
- Skreta, Vasiliki, 2006. "Mechanism design for arbitrary type spaces," Economics Letters, Elsevier, vol. 91(2), pages 293-299, May.
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