Elimination contests with collusive team players

We consider a standard two-stage elimination (Tullock) contest where multiple (team) players can perfectly and publicly collude with each other throughout. We analyze and compare equilibrium outcomes under various seedings where the collusive players meet or are separated in the group stage. We identify the impact of collusion on the contest organizer and non-collusive players, as well as the organizer's optimal seeding. We find that collusion, while always undermining fairness of the competition, can hurt or benefit the organizer, depending on the discriminatory powers of the two stages. We also discuss issues such as sequential group-stage competitions, comparison between the elimination contest and the corresponding one-shot contest, secret collusion, and large discriminatory powers.