Exclusivity of Groups in Contests

Two group leaders each have access to a Tullock contest. They can both decide whether they allow a third player to join their group and whether this group membership must be exclusive. If the prize is mostly private, group leaders do not offer membership in equilibrium. If the prize is mostly public or the elasticity of marginal effort cost high, they offer exclusive membership. In the latter case, the potential member can ‘enforce’ non-exclusivity by committing to join non-exclusive groups. If group leaders can charge a membership fee, they offer non-exclusive membership if groups are less effective than singletons and extract the member’s surplus. This mitigates conflict and beneï¬ ts group leaders. Otherwise, group leaders compete for the member by offering potentially negative fees for exclusive membership. This harms them. A contest designer interested in maximising effort would like to prohibit non-exclusive membership and allow exclusive membership only if groups are more effective than singletons.