Sharing the Effort Costs in Group Contests

This paper addresses conflicts between two groups when trying to win a group-specific public good prize. We analyze how these contests are affected when groups are led by an organizer with the capacity to impose transfers to share the costs of individual efforts within the group. The technology of conflict that we use is the Tullock Contest Success Function with a perfect substitute impact function. We first describe centralized levels of group effort - those that organizers wish to attain - and compare with efforts when individuals act non-cooperatively. In the model a group underperforms when effort exerted by individuals in the non-cooperative setting is smaller than the centralized group effort. Otherwise, the group outperforms. We show that the larger group always underperforms, while the smaller one only does so if its size is sufficiently close to the larger group. Second, we characterize cost sharing schemes that implement group centralized levels of effort. These schemes consist of sharing costs in an egalitarian way. And third, we examine the game in which organizers compete strategically in setting the cost-sharing scheme of their group. We show that while the cost-sharing scheme is the same for the larger group as in the implementation case, it is different for the smaller group.