The Attack‐and‐defense Group Contests: Best Shot Versus Weakest Link

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 (IF). We fully characterize the Nash and coalition‐proof equilibria and show that with symmetric valuation the coalition‐proof 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 the attacker group free‐ride completely on a group member 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 the Nash and coalition‐proof equilibria for the case in which one group follows either a best shot or a weakest link but the other group follows an additive IF. ( JEL C72, D70, D72, D74, H41)