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Equilibrium and Efficiency in the Tug-of-War

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Author Info
Kai A. Konrad ()
Dan Kovenock ()

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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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Paper provided by CESifo GmbH in its series CESifo Working Paper Series with number CESifo Working Paper No. 1564.

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Date of creation: 2005
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Handle: RePEc:ces:ceswps:_1564

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

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Find related papers by JEL classification:
D72 - Microeconomics - - Analysis of Collective Decision-Making - - - Models of Political Processes: Rent-seeking, Elections, Legislatures, and Voting Behavior
D74 - Microeconomics - - Analysis of Collective Decision-Making - - - Conflict; Conflict Resolution; Alliances

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References listed on IDEAS
Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:
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  3. Amann, Erwin & Leininger, Wolfgang, 1996. "Asymmetric All-Pay Auctions with Incomplete Information: The Two-Player Case," Games and Economic Behavior, Elsevier, vol. 14(1), pages 1-18, May. [Downloadable!] (restricted)
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  7. Arieh Gavious & Benny Moldovanu & Aner Sela, 2002. "Bid Costs and Endogenous Bid Caps," RAND Journal of Economics, The RAND Corporation, vol. 33(4), pages 709-722, Winter.
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  10. 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, 07. [Downloadable!] (restricted)
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  11. Harris, Christopher & Vickers, John, 1987. "Racing with Uncertainty," Review of Economic Studies, Blackwell Publishing, vol. 54(1), pages 1-21, January. [Downloadable!] (restricted)
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  14. Krishna, Vijay & Morgan, John, 1997. "An Analysis of the War of Attrition and the All-Pay Auction," Journal of Economic Theory, Elsevier, vol. 72(2), pages 343-362, February. [Downloadable!] (restricted)
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  15. Baye, M.R. & Kovenock, D. & De Vries, C.G., 1992. "Rigging the Lobbying Process: An Application of the All- Pay Auction," Papers 9-92-2, Pennsylvania State - Department of Economics.
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  20. Baik, Kyung Hwan & Kim, In-Gyu & Na, Sunghyun, 2001. "Bidding for a group-specific public-good prize," Journal of Public Economics, Elsevier, vol. 82(3), pages 415-429, December. [Downloadable!] (restricted)
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Cited by:
(explanations, Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.)

  1. Konrad, Kai A & Kovenock, Dan, 2006. "Multi-Stage Contests with Stochastic Ability," CEPR Discussion Papers 5844, C.E.P.R. Discussion Papers. [Downloadable!] (restricted)
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  2. Kai A. Konrad & Dan Kovenock, 2006. "Multi-battle contests," Discussion Papers 122, SFB/TR 15 Governance and the Efficiency of Economic Systems, Free University of Berlin, Humboldt University of Berlin, University of Bonn, University of Mannheim, University of Munich. [Downloadable!]
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  3. Mattias Polborn & Zaruhi Sahakyan, 2007. "Dynamic Lobbying Conflicts," Economics of Governance, Springer, vol. 8(3), pages 263-279, May. [Downloadable!] (restricted)
  4. Amegashie, J. Atsu & Runkel, Marco, 2008. "The Paradoxes of Revenge in Conflicts," MPRA Paper 7687, University Library of Munich, Germany. [Downloadable!]
  5. Amegashie, J. Atsu & Runkel, Marco, 2008. "The Desire for Revenge and the Dynamics of Conflicts," MPRA Paper 6746, University Library of Munich, Germany, revised 16 Jan 2008. [Downloadable!]
  6. Derek J. Clark & Kai A. Konrad, 2005. "Contests with multi-tasking," Discussion Papers 125, SFB/TR 15 Governance and the Efficiency of Economic Systems, Free University of Berlin, Humboldt University of Berlin, University of Bonn, University of Mannheim, University of Munich, revised May 2006. [Downloadable!]
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