IDEAS home Printed from https://ideas.repec.org/p/mik/wpaper/05_07.html
   My bibliography  Save this paper

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

Author

Listed:
  • Kai A. Konrad
  • Wolfgang Leininger

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.

Suggested Citation

  • Kai A. Konrad & Wolfgang Leininger, 2005. "The generalized Stackelberg equilibrium of the all-pay auction with complete information," Discussion Papers in Economics 05_07, University of Dortmund, Department of Economics.
  • Handle: RePEc:mik:wpaper:05_07
    as

    Download full text from publisher

    File URL: http://www.wiso.uni-dortmund.de/mik/de/content/forschung/DPSeries/PDF/05-07.pdf
    Download Restriction: no
    ---><---

    Other versions of this item:

    References listed on IDEAS

    as
    1. Hamilton, Jonathan H. & Slutsky, Steven M., 1990. "Endogenous timing in duopoly games: Stackelberg or cournot equilibria," Games and Economic Behavior, Elsevier, vol. 2(1), pages 29-46, March.
    2. 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, July.
    3. Michael R. Baye & Dan Kovenock & Casper G. Vries, 1996. "The all-pay auction with complete information," Springer Books, in: Roger D. Congleton & Arye L. Hillman & Kai A. Konrad (ed.), 40 Years of Research on Rent Seeking 1, pages 209-223, Springer.
    4. Konrad, Kai A., 2002. "Investment in the absence of property rights; the role of incumbency advantages," European Economic Review, Elsevier, vol. 46(8), pages 1521-1537, September.
    5. Kyung H. Baik & Jason F. Shogren, 2008. "Strategic Behavior in Contests: Comment," Springer Books, in: Roger D. Congleton & Arye L. Hillman & Kai A. Konrad (ed.), 40 Years of Research on Rent Seeking 1, pages 439-442, Springer.
    6. Arye Hillman & Dov Samet, 1987. "Dissipation of contestable rents by small numbers of contenders," Public Choice, Springer, vol. 54(1), pages 63-82, January.
    7. 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.
    8. Arye L. Hillman & John G. Riley, 1989. "Politically Contestable Rents And Transfers," Economics and Politics, Wiley Blackwell, vol. 1(1), pages 17-39, March.
    9. Maskin, Eric & Tirole, Jean, 2001. "Markov Perfect Equilibrium: I. Observable Actions," Journal of Economic Theory, Elsevier, vol. 100(2), pages 191-219, October.
    10. Holger M. Müller & Karl Wärneryd, 2001. "Inside versus outside ownership: a political theory of the firm," Springer Books, in: Roger D. Congleton & Kai A. Konrad & Arye L. Hillman (ed.), 40 Years of Research on Rent Seeking 2, pages 679-693, Springer.
    11. Richard Cornes & Roger Hartley, 2005. "Asymmetric contests with general technologies," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 26(4), pages 923-946, November.
    12. Deneckere, Raymond J & Kovenock, Dan & Lee, Robert, 1992. "A Model of Price Leadership Based on Consumer Loyalty," Journal of Industrial Economics, Wiley Blackwell, vol. 40(2), pages 147-156, June.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Konrad, Kai A., 2007. "Strategy in contests: an introduction [Strategie in Turnieren – eine Einführung]," Discussion Papers, Research Unit: Market Processes and Governance SP II 2007-01, WZB Berlin Social Science Center.
    2. Ella Segev & Aner Sela, 2014. "Sequential all-pay auctions with head starts," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 43(4), pages 893-923, December.
    3. Pau Balart & Sabine Flamand & Oliver Gürtler & Orestis Troumpounis, 2018. "Sequential choice of sharing rules in collective contests," Journal of Public Economic Theory, Association for Public Economic Theory, vol. 20(5), pages 703-724, October.
    4. Johannes Münster, 2007. "Contests with investment," Managerial and Decision Economics, John Wiley & Sons, Ltd., vol. 28(8), pages 849-862.
    5. Konrad, Kai A. & Kovenock, Dan, 2005. "Equilibrium and Efficiency in the Tug-Of-War," Purdue University Economics Working Papers 1177, Purdue University, Department of Economics.
    6. Münster, Johannes, 2006. "Contests with Investment," Discussion Paper Series of SFB/TR 15 Governance and the Efficiency of Economic Systems 120, Free University of Berlin, Humboldt University of Berlin, University of Bonn, University of Mannheim, University of Munich.
    7. Münster, Johannes, 2006. "Contests with investment [Wettkämpfe mit Investitionen]," Discussion Papers, Research Unit: Market Processes and Governance SP II 2006-09, WZB Berlin Social Science Center.
    8. Ella Segev & Aner Sela, 2011. "Sequential All-Pay Auctions with Head Starts and Noisy Outputs," Working Papers 1106, Ben-Gurion University of the Negev, Department of Economics.
    9. Matthew D. Mitchell, 2019. "Uncontestable favoritism," Public Choice, Springer, vol. 181(1), pages 167-190, October.
    10. Häfner, Samuel, 2017. "A tug-of-war team contest," Games and Economic Behavior, Elsevier, vol. 104(C), pages 372-391.
    11. Subhasish M. Chowdhury & Patricia Esteve‐González & Anwesha Mukherjee, 2023. "Heterogeneity, leveling the playing field, and affirmative action in contests," Southern Economic Journal, John Wiley & Sons, vol. 89(3), pages 924-974, January.
    12. Kaplan, Todd R. & Zamir, Shmuel, 2015. "Advances in Auctions," Handbook of Game Theory with Economic Applications,, Elsevier.
    13. Karl Wärneryd, 2012. "Nine points of the law: evidentiary rules and the costs of litigation," Public Choice, Springer, vol. 153(3), pages 279-285, December.
    14. Ewerhart, Christian, 2017. "Contests with small noise and the robustness of the all-pay auction," Games and Economic Behavior, Elsevier, vol. 105(C), pages 195-211.
    15. Hirata, Daisuke, 2014. "A model of a two-stage all-pay auction," Mathematical Social Sciences, Elsevier, vol. 68(C), pages 5-13.
    16. Emmanuel Dechenaux & Dan Kovenock & Roman Sheremeta, 2015. "A survey of experimental research on contests, all-pay auctions and tournaments," Experimental Economics, Springer;Economic Science Association, vol. 18(4), pages 609-669, December.
    17. Franke, Jörg & Leininger, Wolfgang & Wasser, Cédric, 2018. "Optimal favoritism in all-pay auctions and lottery contests," European Economic Review, Elsevier, vol. 104(C), pages 22-37.
    18. Konrad, Kai A., 2004. "Bidding in hierarchies," European Economic Review, Elsevier, vol. 48(6), pages 1301-1308, December.
    19. Kai A. Konrad & Florian Morath, 2018. "To Deter Or To Moderate? Alliance Formation In Contests With Incomplete Information," Economic Inquiry, Western Economic Association International, vol. 56(3), pages 1447-1463, July.
    20. Baik, Kyung Hwan, 1998. "Difference-form contest success functions and effort levels in contests," European Journal of Political Economy, Elsevier, vol. 14(4), pages 685-701, November.

    More about this item

    JEL classification:

    • D72 - Microeconomics - - Analysis of Collective Decision-Making - - - Political Processes: Rent-seeking, Lobbying, Elections, Legislatures, and Voting Behavior
    • D74 - Microeconomics - - Analysis of Collective Decision-Making - - - Conflict; Conflict Resolution; Alliances; Revolutions

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:mik:wpaper:05_07. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Eva Borchard (email available below). General contact details of provider: https://edirc.repec.org/data/wsdorde.html .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.