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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.

Suggested Citation

  • Konrad, Kai A. & Kovenock, Dan, 2005. "Equilibrium and Efficiency in the Tug-of-War," CEPR Discussion Papers 5205, C.E.P.R. Discussion Papers.
  • Handle: RePEc:cpr:ceprdp:5205
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    References listed on IDEAS

    as
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    Citations

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    Cited by:

    1. Häfner, Samuel, 2012. "Clausewitz on Auctions," Working papers 2012/12, Faculty of Business and Economics - University of Basel.
    2. Konrad, Kai A. & Kovenock, Dan, 2009. "Multi-battle contests," Games and Economic Behavior, Elsevier, vol. 66(1), pages 256-274, May.
    3. Johannes Hörner & Nicolas Sahuguet, 2011. "A war of attrition with endogenous effort levels," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 47(1), pages 1-27, May.
    4. Derek J. Clark & Kai A. Konrad, 2007. "Contests with Multi-tasking," Scandinavian Journal of Economics, Wiley Blackwell, vol. 109(2), pages 303-319, June.
    5. 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.
    6. Aner Sela, 2012. "Sequential two-prize contests," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 51(2), pages 383-395, October.
    7. Gelder, Alan & Kovenock, Dan, 2017. "Dynamic behavior and player types in majoritarian multi-battle contests," Games and Economic Behavior, Elsevier, vol. 104(C), pages 444-455.
    8. Friedel Bolle & Jonathan H. W. Tan & Daniel John Zizzo, 2014. "Vendettas," American Economic Journal: Microeconomics, American Economic Association, vol. 6(2), pages 93-130, May.
    9. Dan Kovenock & Brian Roberson, 2009. "Is the 50-State Strategy Optimal?," Journal of Theoretical Politics, , vol. 21(2), pages 213-236, April.
    10. Erik O. Kimbrough & Kevin Laughren & Roman Sheremeta, 2017. "War and Conflict in Economics: Theories, Applications, and Recent Trends," Discussion Papers dp17-10, Department of Economics, Simon Fraser University.
    11. 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).
    12. 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, Social Science Research Center Berlin (WZB).
    13. Konrad, Kai A. & Kovenock, Dan, 2006. "Multi-Stage Contests with Stochastic Ability," CEPR Discussion Papers 5844, C.E.P.R. Discussion Papers.
    14. Kai A. Konrad & Dan Kovenock, 2010. "Contests With Stochastic Abilities," Economic Inquiry, Western Economic Association International, vol. 48(1), pages 89-103, January.
    15. Mattias Polborn & Zaruhi Sahakyan, 2007. "Dynamic Lobbying Conflicts," Economics of Governance, Springer, vol. 8(3), pages 263-279, May.
    16. repec:eee:gamebe:v:104:y:2017:i:c:p:372-391 is not listed on IDEAS
    17. Gelder, Alan, 2014. "From Custer to Thermopylae: Last stand behavior in multi-stage contests," Games and Economic Behavior, Elsevier, vol. 87(C), pages 442-466.
    18. Häfner, Samuel, 2017. "A tug-of-war team contest," Games and Economic Behavior, Elsevier, vol. 104(C), pages 372-391.
    19. Sela, Aner, 2009. "Best-of-Three All-Pay Auctions," CEPR Discussion Papers 7224, C.E.P.R. Discussion Papers.
    20. Samuel Häfner & Kai A. Konrad, 2016. "Eternal Peace in the Tug-of-War?," Working Papers tax-mpg-rps-2016-09, Max Planck Institute for Tax Law and Public Finance.
    21. Romain Gauriot & Lionel Page, 2014. "Does success breed success? A quasi-experiment on strategic momentum in dynamic contests," QuBE Working Papers 028, QUT Business School.
    22. Amegashie, J. Atsu & Runkel, Marco, 2008. "The Desire for Revenge and the Dynamics of Conflicts," MPRA Paper 6746, University Library of Munich, Germany.
    23. Deck, Cary & Sheremeta, Roman, 2015. "Tug-of-War in the Laboratory," MPRA Paper 67521, University Library of Munich, Germany.
    24. 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.

    More about this item

    Keywords

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

    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

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