The Attack-and-Defence Group Contests

This study analyzes a group contest in which one group (defenders) follows a weakest link whereas the other group (attackers) follows a best-shot impact function. We fully characterize the equilibria and show that with symmetric valuation the equilibrium is unique up to the permutation of the identity of the active player in the attacker group. With asymmetric valuation it is always an equilibrium for one of the highest valuation players to be active; it may also be the case that the highest valuation players in group 1 free-ride completely on a player with a lower valuation. However, in any equilibrium, only one player in the attacker group is active, whereas all the players in the defender group are active and exert the same effort. We also characterize equilibria for the case in which one group follows either a best-shot or a weakestlink but the other group follows a perfectly substitute impact function.