The max-min group contest: Weakest-link (group) all-pay auction

We investigate a group all-pay auction in which each group's effort is represented by the minimum among the effort levels exerted by the group members and the prize is a group-specific public good. We fully characterize the symmetric equilibria for two groups. There are four types of equilibria: the pure strategy equilibria in which all (active) players exert the same effort; the semi-pure strategy equilibria in which the players in a group play the same pure strategy whereas those in the other group play the same mixed strategy; the nondegenerate mixed strategy equilibria with continuous support; and the nondegenerate mixed strategy equilibria with discontinuous support. We then analyze a general contest with n groups.