A Model of Intra-group Tug-of-War

Abstract

In a standard tug-of-war model, two players engage in a component battle each period
and a player wins the contest if her number of battle victories exceeds the other contestant’s by
a certain number. In this paper, we introduce a multi-player model of intra-group tug-of-war
played by two groups of two players, where a player wins the contest if she wins a certain
number of battles more than the other player from her group before either player from the other
group achieves the same against one another. We characterize the unique subgame perfect Nash
equilibrium of the model and further analyze an asymmetric case with different number of
players in the competing groups. Our results indicate an extreme discouragement effect for the
laggards and a strong momentum effect for the winner of the first battle.