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Equilibrium and Efficiency in the Tug-of-War

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Author Info
Konrad, Kai A
Kovenock, Dan

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

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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
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    Other versions:
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(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. Amegashie, A. & Runkel, M., 2008. "The Paradoxes of Revenge in Conflicts," Working Papers 2008-5, University of Guelph, Department of Economics. [Downloadable!]
    Other versions:
  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!]
    Other versions:
  3. Konrad, Kai A & Kovenock, Dan, 2006. "Multi-Stage Contests with Stochastic Ability," CEPR Discussion Papers 5844, C.E.P.R. Discussion Papers. [Downloadable!] (restricted)
    Other versions:
  4. 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!]
    Other versions:
  5. Mattias Polborn & Zaruhi Sahakyan, 2007. "Dynamic Lobbying Conflicts," Economics of Governance, Springer, vol. 8(3), pages 263-279, May. [Downloadable!] (restricted)
  6. 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!]
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