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The generalized Stackelberg equilibrium of the all-pay auction with complete information

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Kai A. Konrad
Wolfgang Leininger

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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.

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Paper provided by University of Dortmund, Department of Economics in its series Discussion Papers in Economics with number 05_07.

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Length: 14 pages
Date of creation: Sep 2005
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Handle: RePEc:mik:wpaper:05_07

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  1. Kaplan, Todd R. & Luski, Israel & Wettstein, David, 2003. "Innovative activity and sunk cost," International Journal of Industrial Organization, Elsevier, vol. 21(8), pages 1111-1133, October. [Downloadable!] (restricted)
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  2. Richard Cornes & Roger Hartley, 2002. "Asymmetric Contests with General Technologies," Keele Economics Research Papers KERP 2002/22, Centre for Economic Research, Keele University. [Downloadable!]
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  3. Michael R. Baye & Dan Kovenock & Casper G. Vries, 2005. "Comparative Analysis of Litigation Systems: An Auction-Theoretic Approach," Economic Journal, Royal Economic Society, vol. 115(505), pages 583-601, 07. [Downloadable!] (restricted)
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  4. Kai A. Konrad & Wolfgang Leininger, 2005. "The Generalized Stackelberg Equilibrium of the All-Pay Auction with Complete Information," CESifo Working Paper Series CESifo Working Paper No. , CESifo Group Munich. [Downloadable!]
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  5. Arye L. Hillman & John G. Riley, 1987. "Politically Contestable Rents and Transfers," UCLA Economics Working Papers 452, UCLA Department of Economics. [Downloadable!]
  6. Dan Kovenock & Michael R. Baye & Casper G. de Vries, 1996. "The all-pay auction with complete information (*)," Economic Theory, Springer, vol. 8(2), pages 291-305.
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  7. Deneckere, Raymond J & Kovenock, Dan & Lee, Robert, 1992. "A Model of Price Leadership Based on Consumer Loyalty," Journal of Industrial Economics, Blackwell Publishing, vol. 40(2), pages 147-56, June. [Downloadable!] (restricted)
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  8. Baik, Kyung H & Shogren, Jason F, 1992. "Strategic Behavior in Contests: Comment," American Economic Review, American Economic Association, vol. 82(1), pages 359-62, March. [Downloadable!] (restricted)
  9. Kai Konrad, 2002. "Investment in the Absence of Property Rights: The Role of Incumbency Advantages," CESifo Working Paper Series CESifo Working Paper No. , CESifo Group Munich. [Downloadable!]
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  10. Muller, Holger M & Warneryd, Karl, 2001. "Inside versus Outside Ownership: A Political Theory of the Firm," RAND Journal of Economics, The RAND Corporation, vol. 32(3), pages 527-41, Autumn.
  11. Maskin, Eric & Tirole, Jean, 2001. "Markov Perfect Equilibrium: I. Observable Actions," Journal of Economic Theory, Elsevier, vol. 100(2), pages 191-219, October. [Downloadable!] (restricted)
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  1. Kai A. Konrad & Wolfgang Leininger, 2006. "The generalized Stackelberg equilibrium of the all-pay auction with complete information," Discussion Papers in Economics 06_01, University of Dortmund, Department of Economics. [Downloadable!]
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  2. Oliver Gürtler, 2006. "Contractual Incentive Provision and Commitment in Rent-Seeking Contests," Discussion Papers 100, SFB/TR 15 Governance and the Efficiency of Economic Systems, Free University of Berlin, Humboldt University of Berlin, University of Bonn, University of Mannheim, University of Munich. [Downloadable!]
  3. Konrad, Kai A & Leininger, Wolfgang, 2007. "Self-enforcing Norms and the Efficient Non-cooperative Organization of Clans," CEPR Discussion Papers 6333, C.E.P.R. Discussion Papers. [Downloadable!] (restricted)
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