Second-Price Auctions with Power-Related Distributions

30 Pages Posted: 14 Mar 2001

See all articles by Luke M. Froeb

Luke M. Froeb

Vanderbilt University - Owen Graduate School of Management

Steven Tschantz

Vanderbilt University - Department of Mathematics

Philip Crooke

Vanderbilt University - Department of Mathematics

Date Written: February 21, 2001

Abstract

We analyze a class of parametric second-price auction models where asymmetry is modeled by allowing bidders to take different numbers of draws from the same distribution. We compute the closed-form distribution of price and construct likelihood and method-of-moments estimators to recover the underlying value distribution from observed prices. We derive a Herfindahl-like formula that predicts merger effects and find that merger effects depend on the shares of the merging bidders, the variance, and the "shape" of the distribution. We generalize the model by allowing bidders to mix over power-related distributions. The dominant strategy equilibrium implies that an auction among bidders who mix over distributions can be expressed as a mixture of auctions. This implies that an auction among bidders with potentially correlated values can be expressed as a mixture over independent power-related auctions.

Keywords: Second-price, private-values auctions, merger, antitrust

JEL Classification: D44, C50, L41

Suggested Citation

Froeb, Luke M. and Tschantz, Steven T. and Crooke, Philip, Second-Price Auctions with Power-Related Distributions (February 21, 2001). Available at SSRN: https://ssrn.com/abstract=261064 or http://dx.doi.org/10.2139/ssrn.261064

Luke M. Froeb (Contact Author)

Vanderbilt University - Owen Graduate School of Management ( email )

401 21st Avenue South
Nashville, TN 37203
United States
615-322-9057 (Phone)
615-343-7177 (Fax)

Steven T. Tschantz

Vanderbilt University - Department of Mathematics ( email )

Nashville, TN 37240
United States

Philip Crooke

Vanderbilt University - Department of Mathematics ( email )

Nashville, TN 37240
United States
615-322-6671 (Phone)
615-322-0215 (Fax)

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