Asymmetric First-Price Auctions With Uniform Distributions: Analytic Solutions to the General Case

43 Pages Posted: 17 Sep 2006 Last revised: 27 Dec 2007

See all articles by Todd R. Kaplan

Todd R. Kaplan

University of Exeter Business School - Department of Economics; University of Haifa - Department of Economics

Shmuel Zamir

Hebrew University - Center for the Study of Rationality

Date Written: December 25, 2007

Abstract

While auction research, including asymmetric auctions, has grown significantly in recent years, there is still little analytical solutions of first-price auctions outside the symmetric case. Even in the uniform case, Griesmer et al. (1967) and Plum (1992) find solutions only to the case where the lower bounds of the two distributions are the same. We present the general analytical solutions to asymmetric auctions in the uniform case for two bidders, both with and without a minimum bid. We show that our solution is consistent with the previously known solutions of auctions with uniform distributions. Several interesting examples are presented including a class where the two bid functions are linear. We hope this result improves our understanding of auctions and provides a useful tool for future research in auctions.

Keywords: asymmetric auctions

JEL Classification: D44, D82, H57, C72

Suggested Citation

Kaplan, Todd R. and Zamir, Shmuel, Asymmetric First-Price Auctions With Uniform Distributions: Analytic Solutions to the General Case (December 25, 2007). Available at SSRN: https://ssrn.com/abstract=930518 or http://dx.doi.org/10.2139/ssrn.930518

Todd R. Kaplan (Contact Author)

University of Exeter Business School - Department of Economics ( email )

Streatham Court
Exeter, EX4 4RJ
United Kingdom
+44 13 9226 3237 (Phone)

University of Haifa - Department of Economics

Haifa 31905
Israel

Shmuel Zamir

Hebrew University - Center for the Study of Rationality ( email )

Hebrew University
Jerusalem 91904
Israel
+972 2-6586486 (Phone)

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