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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 behavior 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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Bibliographic Info

Paper provided by Free University of Berlin, Humboldt University of Berlin, University of Bonn, University of Mannheim, University of Munich in its series Discussion Paper Series of SFB/TR 15 Governance and the Efficiency of Economic Systems with number 121.

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Date of creation: May 2006
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Handle: RePEc:trf:wpaper:121

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

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References

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  1. Moldovanu, Benny & Sela, Aner, 1999. "The Optimal Allocation of Prizes in Contests," Sonderforschungsbereich 504 Publications 99-75, Sonderforschungsbereich 504, Universität Mannheim & Sonderforschungsbereich 504, University of Mannheim.
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Citations

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Cited by:
  1. Sela, Aner, 2009. "Best-of-Three All-Pay Auctions," CEPR Discussion Papers 7224, C.E.P.R. Discussion Papers.
  2. J. Atsu Amegashie & Marco Runkel, 2012. "The Paradox of Revenge in Conflicts," Journal of Conflict Resolution, Peace Science Society (International), vol. 56(2), pages 313-330, April.
  3. Konrad, Kai A. & Kovenock, Dan, 2006. "Multi-battle contests," Purdue University Economics Working Papers 1187, Purdue University, Department of Economics.
  4. Derek J. Clark & Kai A. Konrad, 2007. "Contests with Multi-tasking," Scandinavian Journal of Economics, Wiley Blackwell, vol. 109(2), pages 303-319, 06.
  5. Amegashie, J. Atsu & Runkel, Marco, 2008. "The Desire for Revenge and the Dynamics of Conflicts," MPRA Paper 6746, University Library of Munich, Germany.
  6. Samuel Haefner, 2012. "Clausewitz on Auctions," Working papers 2012/12, Faculty of Business and Economics - University of Basel.
  7. Dan Kovenock & Brian Roberson, 2008. "Is the 50-State Strategy Optimal?," Purdue University Economics Working Papers 1211, Purdue University, Department of Economics.
  8. 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).
  9. Konrad, Kia A. & Kovenock, Dan, 2006. "Multi-Stage Contests with Stochastic Ability," Purdue University Economics Working Papers 1192, Purdue University, Department of Economics.
  10. 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).
  11. Johannes Hörner & Nicolas Sahuguet, 2011. "A war of attrition with endogenous effort levels," Economic Theory, Springer, vol. 47(1), pages 1-27, May.
  12. 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.
  13. Mattias Polborn & Zaruhi Sahakyan, 2007. "Dynamic Lobbying Conflicts," Economics of Governance, Springer, vol. 8(3), pages 263-279, May.

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