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Equilibrium and Efficiency in the Tug-of-War

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  • Konrad, Kai A
  • Kovenock, Dan

Abstract

We characterize the unique Markov perfect equilibrium of a tug-of-war without exogenous noise, in which players have the opportunity to engage in a sequence of battles in an attempt to win the war. Each battle is an all-pay auction in which the player expending the greater resources wins. In equilibrium, contest effort concentrates on at most two adjacent states of the game, the 'tipping states', which are determined by the contestants’ relative strengths, their distances to final victory, and the discount factor. In these states battle outcomes are stochastic due to endogenous randomization. Both relative strength and closeness to victory increase the probability of winning the battle at hand. Patience reduces the role of distance in determining outcomes. Applications range from politics, economics and sports, to biology, where the equilibrium behaviour finds empirical support: many species have developed mechanisms such as hierarchies or other organizational structures by which the allocation of prizes are governed by possibly repeated conflict. Our results contribute to an explanation why. Compared to a single stage conflict, such structures can reduce the overall resources that are dissipated among the group of players.

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Paper provided by C.E.P.R. Discussion Papers in its series CEPR Discussion Papers with number 5205.

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Date of creation: Aug 2005
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Handle: RePEc:cpr:ceprdp:5205

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Keywords: all-pay auction; conflict; dominance; dynamic game; multi-stage contest; preemption; tipping; winner-take-all;

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References

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Citations

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Cited by:
  1. Clark, Derek J. & Konrad, Kai A., 2006. "Contests with multi-tasking," Discussion Paper Series of SFB/TR 15 Governance and the Efficiency of Economic Systems 125, Free University of Berlin, Humboldt University of Berlin, University of Bonn, University of Mannheim, University of Munich.
  2. Mattias Polborn & Zaruhi Sahakyan, 2007. "Dynamic Lobbying Conflicts," Economics of Governance, Springer, vol. 8(3), pages 263-279, May.
  3. Konrad, Kai A. & Kovenock, Dan, 2006. "Multi-battle contests," Discussion Paper Series of SFB/TR 15 Governance and the Efficiency of Economic Systems 122, Free University of Berlin, Humboldt University of Berlin, University of Bonn, University of Mannheim, University of Munich.
  4. Dan Kovenock & Brian Roberson, 2008. "Is the 50-State Strategy Optimal?," Purdue University Economics Working Papers 1211, Purdue University, Department of Economics.
  5. Konrad, Kia A. & Kovenock, Dan, 2006. "Multi-Stage Contests with Stochastic Ability," Purdue University Economics Working Papers 1192, Purdue University, Department of Economics.
  6. Samuel Haefner, 2012. "Clausewitz on Auctions," Working papers 2012/12, Faculty of Business and Economics - University of Basel.
  7. J. Atsu Amegashie & Marco Runkel, 2008. "The Paradoxes of Revenge in Conflicts," Working Papers 0805, University of Guelph, Department of Economics and Finance.
  8. Amegashie, J. Atsu & Runkel, Marco, 2008. "The Desire for Revenge and the Dynamics of Conflicts," MPRA Paper 6746, University Library of Munich, Germany.
  9. 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).
  10. Sela, Aner, 2009. "Best-of-Three All-Pay Auctions," CEPR Discussion Papers 7224, C.E.P.R. Discussion Papers.
  11. Klumpp, Tilman & Polborn, Mattias K., 2006. "Primaries and the New Hampshire Effect," Journal of Public Economics, Elsevier, vol. 90(6-7), pages 1073-1114, August.
  12. Konrad, Kai A., 2007. "Strategy in contests: an introduction," Discussion Papers, Research Unit: Market Processes and Governance SP II 2007-01, Social Science Research Center Berlin (WZB).
  13. Johannes Hörner & Nicolas Sahuguet, 2011. "A war of attrition with endogenous effort levels," Economic Theory, Springer, vol. 47(1), pages 1-27, May.

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