Group contests with private information and the “Weakest Link”

We study weakest-link group contests with private information. We characterize all pure-strategy Bayes-Nash equilibria: various degrees of coordination are possible, from every cost type choosing a distinct effort level to all cost types coordinating on a single 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 asymmetries regard multiple dimensions, no clear-cut conclusions are evident. As an additional avenue for cooperation, we investigate cheap-talk sharing of private information among teammates, who then coordinate on the effort level most preferred by the player with the largest announced cost. A single group sharing information does better. But, with respect to the equilibrium in which all types choose a distinct effort, when players of both groups cooperate in this fashion all within-group gains are lost to increased competition between groups.