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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

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 CESifo Group Munich in its series CESifo Working Paper Series with number 1609.

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Date of creation: 2005
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Handle: RePEc:ces:ceswps:_1609

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

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References

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  1. Kai A. Konrad, 2002. "Investment in the Absence of Property Rights: The Role of Incumbency Advantages," CESifo Working Paper Series 698, CESifo Group Munich.
  2. Arye L. Hillman & John G. Riley, 1987. "Politically Contestable Rents and Transfers," UCLA Economics Working Papers 452, UCLA Department of Economics.
  3. Baye, M.R. & Kovenock D. & De Vries, C.G., 2000. "Comparative Analysis of Litigation Systems: an Auction-Theoretic Approach," Purdue University Economics Working Papers 1137, Purdue University, Department of Economics.
  4. Richard Cornes & Roger Hartley, 2002. "Asymmetric Contests with General Technologies," Keele Economics Research Papers KERP 2002/22, Centre for Economic Research, Keele University.
  5. 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.
  6. Baye, M.R. & Kovenock, D. & De Vries, C.G., 1991. "The All-Pay Auction With Complete Information," Purdue University Economics Working Papers 1007, Purdue University, Department of Economics.
  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. 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.
  9. Eric Maskin & Jean Tirole, 1997. "Markov Perfect Equilibrium, I: Observable Actions," Harvard Institute of Economic Research Working Papers 1799, Harvard - Institute of Economic Research.
  10. Deneckere, R. & Kovenock, D. & Lee, R.E., 1988. "A Model of Price Leadership Based on Consumer Loyalty," Purdue University Economics Working Papers 947, Purdue University, Department of Economics.
  11. Arye Hillman & Dov Samet, 1987. "Dissipation of contestable rents by small numbers of contenders," Public Choice, Springer, vol. 54(1), pages 63-82, January.
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Cited by:
  1. Aner Sela & Ella Segev, 2012. "Multi-Stage Sequential All-Pay Auctions," Working Papers 1211, Ben-Gurion University of the Negev, Department of Economics.
  2. Grégoire Rota-Graziosi & Magnus Hoffmann, 2011. "Endogenous Timing in General Rent‐Seeking and Conflict Models," Working Papers halshs-00553119, HAL.
  3. Chiappinelli, Olga, 2014. "An elimination contest with non-sunk bids," MPRA Paper 56140, University Library of Munich, Germany.
  4. Kai A. Konrad & Wolfgang Leininger, 2007. "Self-enforcing Norms and the Efficient Non-cooperative Organization of Clans," Ruhr Economic Papers 0016, Rheinisch-Westfälisches Institut für Wirtschaftsforschung, Ruhr-Universität Bochum, Universität Dortmund, Universität Duisburg-Essen.
  5. Baumann, Florian & Denter, Philipp & Friehe, Tim, 2013. "Hide or show? Endogenous observability of private precautions against crime when property value is private information," DICE Discussion Papers 115, Heinrich‐Heine‐Universität Düsseldorf, Düsseldorf Institute for Competition Economics (DICE).
  6. Florian Baumann & Tim Friehe, 2013. "A note on the timing of investments in litigation contests," European Journal of Law and Economics, Springer, vol. 35(3), pages 313-326, June.
  7. 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.
  8. Konrad, Kai A., 2010. "Dynamic contests," Discussion Papers, Research Professorship & Project "The Future of Fiscal Federalism" SP II 2010-10, Social Science Research Center Berlin (WZB).
  9. Segev, Ella & Sela, Aner, 2011. "Sequential All-Pay Auctions with Head Starts," CEPR Discussion Papers 8183, C.E.P.R. Discussion Papers.
  10. Hirata, Daisuke, 2014. "A model of a two-stage all-pay auction," Mathematical Social Sciences, Elsevier, vol. 68(C), pages 5-13.
  11. Francoise Forges & Frédéric Koessler, 2006. "Long Persuasion Games," CESifo Working Paper Series 1669, CESifo Group Munich.
  12. Kai Konrad & Wolfgang Leininger, 2011. "Self-enforcing norms and efficient non-cooperative collective action in the provision of public goods," Public Choice, Springer, vol. 146(3), pages 501-520, March.
  13. Gürtler, Oliver, 2006. "Contractual Incentive Provision and Commitment in Rent-Seeking Contests," Discussion Paper Series of SFB/TR 15 Governance and the Efficiency of Economic Systems 100, Free University of Berlin, Humboldt University of Berlin, University of Bonn, University of Mannheim, University of Munich.
  14. Denter, Philipp & Morgan, John & Sisak, Dana, 2011. ""Where Ignorance is Bliss, 'tis Folly to be Wise": Transparency in Contests," Economics Working Paper Series 1128, University of St. Gallen, School of Economics and Political Science.
  15. Brennan C. Platt & Joseph Price & Henry Tappen, 2010. "Pay-to-Bid Auctions," NBER Working Papers 15695, National Bureau of Economic Research, Inc.

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