Mergers Among Asymmetric Bidders: A Logit Second-Price Auction Model

17 Pages Posted: 22 Mar 1998

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 27, 1998

Abstract

In this paper, we derive estimators of, and closed-form (non-integral) expressions for, the distribution of bids in an extreme value, asymmetric, second-price, private-values auction. In equilibrium, prices (winning bids) and shares (winning probabilities) have a simple monotonic relationship--higher-value firms win more frequently and at better prices than lower-value firms. Since the extreme value distribution is closed under the maximum function, the value of the merged coalition also has an extreme value distribution and thus lies on the same price/share curve. Consequently, merger price effects can be computed as a movement along the price/share curve, from the average pre-merger share to the post-merger aggregate share. The parameter determining how much winning prices change is the standard deviation of the extreme value component. Merger efficiency claims can be benchmarked against the marginal cost reductions necessary to offset merger price effects.

JEL Classification: C25, D44, L41

Suggested Citation

Froeb, Luke M. and Tschantz, Steven T. and Crooke, Philip, Mergers Among Asymmetric Bidders: A Logit Second-Price Auction Model (February 27, 1998). Available at SSRN: https://ssrn.com/abstract=69415 or http://dx.doi.org/10.2139/ssrn.69415

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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