The Generalized Stackelberg Equilibrium of the All-Pay Auction with Complete Information

18 Pages Posted: 15 Dec 2005

See all articles by Kai A. Konrad

Kai A. Konrad

Max Planck Institute for Tax Law and Public Finance; Centre for Economic Policy Research (CEPR); CESifo (Center for Economic Studies and Ifo Institute for Economic Research); IZA Institute of Labor Economics

Wolfgang Leininger

University of Dortmund - Department of Economics; CESifo (Center for Economic Studies and Ifo Institute for Economic Research)

Date Written: November 2005

Abstract

We characterize the equilibrium of the all-pay auction with general convex cost of effort and sequential effort choices. We consider a set of n players who are arbitrarily partitioned into a group of players who choose their efforts 'early' and a group of players who choose 'late.' Only the player with the lowest cost of effort has a positive payoff in any equilibrium. This payoff depends on his own timing vis-a-vis the timing of others. We also show that the choice of timing can be endogenized, in which case the strongest player typically chooses 'late,' whereas all other players are indifferent with respect to their choice of timing. In the most prominent equilibrium the player with the lowest cost of effort wins the auction at zero aggregate cost.

Keywords: sequential all-pay auction, complete information, generalized cost, generalized Stackelberg game

JEL Classification: D72, D74

Suggested Citation

Konrad, Kai A. and Leininger, Wolfgang, The Generalized Stackelberg Equilibrium of the All-Pay Auction with Complete Information (November 2005). CESifo Working Paper Series No. 1609, Available at SSRN: https://ssrn.com/abstract=870400

Kai A. Konrad

Max Planck Institute for Tax Law and Public Finance ( email )

Marstallplatz 1
Munich, 80539
Germany

HOME PAGE: http://www.tax.mpg.de/en/pub/home.cfm

Centre for Economic Policy Research (CEPR)

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CESifo (Center for Economic Studies and Ifo Institute for Economic Research)

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Munich, 81679
Germany

IZA Institute of Labor Economics

P.O. Box 7240
Bonn, 53072
Germany

Wolfgang Leininger (Contact Author)

University of Dortmund - Department of Economics ( email )

D-44221 Dortmund
Germany
+49 231 755 3297 (Phone)
+49 231 755 3027 (Fax)

CESifo (Center for Economic Studies and Ifo Institute for Economic Research)

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Munich, DE-81679
Germany

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

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