The Simple Algebra of Surplus in Open, Private Values Auctions: A Nested Logit Merger Model

9 Pages Posted: 21 Aug 2017 Last revised: 2 Oct 2018

See all articles by Luke M. Froeb

Luke M. Froeb

Vanderbilt University - Owen Graduate School of Management

Vlad Mares

INSEAD

Charles Taragin

University of Michigan at Ann Arbor

Steven Tschantz

Vanderbilt University - Department of Mathematics

Date Written: July 5, 2017

Abstract

In a private values, open auction, we show that bidder surplus can be expressed as a simple difference between unconditional moments of order statistics. The strength of the result is its simplicity and generality, as we dispense with the typical assumptions of independence and/or symmetry. We show how to use the expression to derive closed-form expressions for the effects of a merger among bidders for any joint value distribution, and illustrate its use by simulating the effects of the 2016 proposed Anthem-Cigna merger using a nested logit specification.

Keywords: Auctions; Merger; Antitrust; Horizontal Anticompetitive Practices, Nested Logit

JEL Classification: D44, L41, G34

Suggested Citation

Froeb, Luke M. and Mares, Vladimir and Taragin, Charles and Tschantz, Steven T., The Simple Algebra of Surplus in Open, Private Values Auctions: A Nested Logit Merger Model (July 5, 2017). Vanderbilt Owen Graduate School of Management Research Paper No. 3020255. Available at SSRN: https://ssrn.com/abstract=3020255 or http://dx.doi.org/10.2139/ssrn.3020255

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)

Vladimir Mares

INSEAD ( email )

Boulevard de Constance
77305 Fontainebleau Cedex
France

Charles Taragin

University of Michigan at Ann Arbor ( email )

500 S. State Street
Ann Arbor, MI 48109
United States

Steven T. Tschantz

Vanderbilt University - Department of Mathematics ( email )

Nashville, TN 37240
United States

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