Equilibrium and Efficiency in the Tug-of-War

35 Pages Posted: 10 Nov 2005

See all articles by Kai A. Konrad

Kai A. Konrad

Max Planck Institute for Tax Law and Public Finance; Centre for Economic Policy Research (CEPR); CESifo (Center for Economic Studies and Ifo Institute for Economic Research); IZA Institute of Labor Economics

Dan Kovenock

Chapman University - Economic Science Institute; CESifo (Center for Economic Studies and Ifo Institute)

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Date Written: October 2005

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.

Keywords: winner-take-all, all-pay auction, tipping, multi-stage contest, dynamic game

JEL Classification: D72, D74

Suggested Citation

Konrad, Kai A. and Kovenock, Daniel, Equilibrium and Efficiency in the Tug-of-War (October 2005). CESifo Working Paper Series No. 1564, Available at SSRN: https://ssrn.com/abstract=844644

Kai A. Konrad (Contact Author)

Max Planck Institute for Tax Law and Public Finance ( email )

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Germany

HOME PAGE: http://www.tax.mpg.de/en/pub/home.cfm

Centre for Economic Policy Research (CEPR)

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CESifo (Center for Economic Studies and Ifo Institute for Economic Research)

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Germany

IZA Institute of Labor Economics

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Bonn, 53072
Germany

Daniel Kovenock

Chapman University - Economic Science Institute ( email )

One University Dr.
Orange, CA 92866
United States

CESifo (Center for Economic Studies and Ifo Institute)

Poschinger Str. 5
Munich, DE-81679
Germany

HOME PAGE: http://www.CESifo.de

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