A Tug-of-War Team Contest

Abstract

This paper analyzes a tug-of-war contest between two teams. In each round of the tug-of-war, a pair of agents from the opposing teams competes in a private value all-pay auction with asymmetric value distributions and effort effectiveness. Whichever team arrives first at a given lead in terms of battle victories over the opponent wins the tug-of-war. There exists a unique Markov-perfect equilibrium in bidding strategies which depend on the respective player's valuation and the current state of the tug-of-war. We derive rich comparative statics for this equilibrium by using the fact that the state of the tug-of-war evolves according to a time-homogeneous absorbing Markov chain.