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Equilibrium and Efficiency in the Tug-Of-War

Listed author(s):
  • Konrad, Kai A.
  • Kovenock, Dan

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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File URL: http://www.krannert.purdue.edu/programs/phd/Working-papers-series/Year-2005/1177.pdf
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Paper provided by Purdue University, Department of Economics in its series Purdue University Economics Working Papers with number 1177.

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Length: 31 pages
Date of creation: Jul 2005
Handle: RePEc:pur:prukra:1177
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Web page: http://www.krannert.purdue.edu/programs/phd

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  7. 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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  11. Ellingsen, Tore, 1991. "Strategic Buyers and the Social Cost of Monopoly," American Economic Review, American Economic Association, vol. 81(3), pages 648-657, June.
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  17. Gavious, Arieh & Moldovanu, Benny & Sela, Aner, 2000. "Bid Costs and Endogenous Bid Caps," Sonderforschungsbereich 504 Publications 01-19, Sonderforschungsbereich 504, Universität Mannheim;Sonderforschungsbereich 504, University of Mannheim.
  18. Kai A. Konrad, 2003. "Inverse Campaigning," CESifo Working Paper Series 905, CESifo Group Munich.
  19. Kaplan, Todd R. & Luski, Israel & Wettstein, David, 2003. "Innovative activity and sunk cost," International Journal of Industrial Organization, Elsevier, vol. 21(8), pages 1111-1133, October.
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  21. Eric Maskin & Jean Tirole, 1997. "Markov Perfect Equilibrium, I: Observable Actions," Harvard Institute of Economic Research Working Papers 1799, Harvard - Institute of Economic Research.
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  23. Arbatskaya, Maria, 2003. "The exclusion principle for symmetric multi-prize all-pay auctions with endogenous valuations," Economics Letters, Elsevier, vol. 80(1), pages 73-80, July.
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