Second Chance Offers in Auctions

Posted: 19 Jan 2013 Last revised: 2 May 2014

See all articles by Aniruddha Bagchi

Aniruddha Bagchi

Kennesaw State University- Michael J. Coles College of Business

Brett Katzman

University of Miami - School of Business Administration - Department of Economics

Timothy Mathews

Kennesaw State University - Michael J. Coles College of Business

Date Written: January 18, 2013

Abstract

This paper examines situations in which a seller might make a second chance (take-it-or-leave-it) offer to a non-winning bidder at a price equal to their bid at auction. This study is motivated by the take-it-or-leave-it second chance offer rules used by eBay and a number of state procurement agencies. Equilibrium bidder behavior is determined for IPV sealed bid first price, second price, English, and Vickrey auctions when a second chance offer will be made with an exogenous probability p. In all but the Vickrey auction (which elicits the dominant strategy of bidding one's value) equilibrium bids are lower than if there were no possibility of a second chance offer and higher than if a second chance offer will be made for certain. Further, the possibility of a second chance offer erodes the strategic equivalence between second price bids and English auction drop out levels. If bidders are risk averse (with CRRA preferences), this difference leads to expected revenue dominance of the second price over the English auction, both of which dominate the Vickrey auction. The first price auction is also shown to revenue dominate the Vickrey auction, and moreover, numerical results and intuition from existing literature suggest that the first price auction revenue dominates the second price auction.

Keywords: Auctions, Second Chance Offer, Internet

JEL Classification: D44, C70

Suggested Citation

Bagchi, Aniruddha and Katzman, Brett Eric and Mathews, Timothy, Second Chance Offers in Auctions (January 18, 2013). Journal of Economics (2014), 112(1), 1-29., Available at SSRN: https://ssrn.com/abstract=2203166

Aniruddha Bagchi (Contact Author)

Kennesaw State University- Michael J. Coles College of Business ( email )

United States

Brett Eric Katzman

University of Miami - School of Business Administration - Department of Economics ( email )

P.O. Box 248126
Coral Gables, FL 33124-6550
United States
305-284-1654 (Phone)

HOME PAGE: http://www.bus.miami.edu/~eco/aaa/faculty/List/katzman.htm

Timothy Mathews

Kennesaw State University - Michael J. Coles College of Business ( email )

1000 Chastain Road
Kennesaw, GA 30144
United States

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