In the principal-agent literature, a collective tournament, i.e. a tournament between teams, has been proposed as a solution to the free-rider problem. Competition between the teams is said to foster within-team cooperation and, hence, to mitigate free-riding. In this paper, we analyse the impact of an agent's liability on the tournament outcome. In the more realistic case of limited liability, a collective tournament is found to perform very poorly. Free-riding is, in this case, even intensified when applying a collective tournament.