Group Contests with Private Information and the 'Weakest Link'

We study group competition with a single public good prize, perfectly discriminating contest success function, and the weakest-link effort technology, in which the marginal cost of effort for each player is private information. We focus on pure strategy Bayes-Nash equilibria and show that teammates always employ symmetric strategies. Various degrees of coordination are possible, ranging from all cost types coordinating on a single effort level to every cost type choosing a distinct effort level. Such coordination may not enhance welfare. If groups are symmetric except for group size, players in the smaller group bid more aggressively than those in the larger group, but when the asymmetries are along multiple dimensions, no clear-cut conclusions can be made with respect to the effects of group sizes and valuations. As an additional avenue for cooperation, we investigate incentives to share private information via cheap talk among teammates, who then coordinate on the effort level most preferred by the player with the largest cost. A single group sharing information does better. But when players within-group cooperate in this fashion, all within-group gains are lost to increased competition between groups.