First-Price Auctions When the Ranking of Valuations is Common Knowledge

18 Pages Posted: 10 Feb 1997 Last revised: 31 Oct 2017

See all articles by Michael Landsberger

Michael Landsberger

University of Haifa - Department of Economics

Reuven Rubinstein

Technion-Israel Institute of Technology - The William Davidson Faculty of Industrial Engineering & Management

Elmar Wolfstetter

Humboldt University of Berlin - Faculty of Economics; Korea University - College of Economics and Commerce; CESifo (Center for Economic Studies and Ifo Institute)

Shmuel Zamir

Hebrew University - Center for the Study of Rationality

Date Written: August 1, 1996

Abstract

We consider an augmented version of the symmetric private value auction model with independent types. The augmentation, intended to illustrate reality, concerns information bidders have about their opponents. To the standard assumption that every bidder knows his type and the distribution of types is common knowledge we add the assumption that the ranking of bidders' valuations is common knowledge.

This set-up induces a particular asymmetric auction model that raises serious technical difficulties. We prove existence and uniqueness of equilibrium in pure strategies in the two bidder case. We also show that the model generally has no analytic solution. If the distribution of valuations is uniform, both bidders bid pointwise more aggressively relative to the standard symmetric case. However, this property does not apply to all distributions of valuations. Finally, we also provide a numerical solution of equilibrium bid functions for the uniform distribution case.

JEL Classification: D44, D82, H57, C72

Suggested Citation

Landsberger, Michael and Rubinstein, Reuven and Wolfstetter, Elmar G. and Zamir, Shmuel, First-Price Auctions When the Ranking of Valuations is Common Knowledge (August 1, 1996). Review of Economic Design, Vol. 6, 2001, Available at SSRN: https://ssrn.com/abstract=2188 or http://dx.doi.org/10.2139/ssrn.2188

Michael Landsberger

University of Haifa - Department of Economics ( email )

Haifa 31905
Israel
972-4-8240023 (Phone)
972-4-8240059 (Fax)

Reuven Rubinstein

Technion-Israel Institute of Technology - The William Davidson Faculty of Industrial Engineering & Management ( email )

Haifa 32000
Israel
972-4-8294458 (Phone)
972-4-8235194 (Fax)

Elmar G. Wolfstetter (Contact Author)

Humboldt University of Berlin - Faculty of Economics ( email )

Institut für Wirtschaftstheorie I
Spandauer Strasse 1
Berlin
Germany
+49 30 2093 5652/3 (Phone)
+49 30 2093 5619 (Fax)

HOME PAGE: http://www2.hu-berlin.de/wt1wo/staff/wolfstetter/index.html

Korea University - College of Economics and Commerce ( email )

Anam-dong, Sungbuk-Ku
Seoul, 136-701
Korea

CESifo (Center for Economic Studies and Ifo Institute)

Poschinger Str. 5
Munich, DE-81679
Germany

HOME PAGE: http://www.CESifo.de

Shmuel Zamir

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

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

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