Eternal peace in the tug-of-war?

The tug-of-war between single players is known to have a non-cooperative Markov-perfect equilibrium in which both players expend zero efforts and neither player drives the Markov process to one of the terminal states. We show that these peaceful outcomes vanish if the single players are replaced by teams with team members permanently assigned to the different Markov states and interacting pairwise in an all-pay auction. The reason for this phenomenon is that the members of the teams can externalize future effort costs while the single players cannot. Our analysis also highlights the impact of the discount factor on the expected trajectory of the tug-of-war, the dynamics of the expected efforts, and the degree of rent dissipation.