The name is absent

Equilibrium and Efficiency in the Tug-of-War*

Kai A. Konrad^and Dan Kovenock^

July 27, 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 de-
termined 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 out-
comes.

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. Com-
pared to a single stage conflict, such structures can reduce the overall
resources that are dissipated among the group of players.

* Corresponding author: Dan Kovenock, Krannert School of Management, Purdue
University, West Lafayette, IN 47907, USA, fax: +1-765-494-9658, e-mail:
[email protected]. Comments by Daniel Krahmer and Johannes Münster are grate-
fully acknowledged. Part of this work was completed while the second author was Visiting
Professor at the Social Science Research Center Berlin (WZB). The usual caveat applies.

⅛ree University of Berlin and Social Science Research Centre Berlin (WZB).
^Krannert School of Management, Purdue University.

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