Contests between groups are plagued by intra-group externalities (freeriding). Yet, costless incentive schemes that entirely avoid free-riding within a group might not be desirable, neither individually nor socially. In contests among two groups, a relatively weak (i.e., small or unproductive) group will optimally not implement them because they compound strength differences between groups. If both groups rein in their intra-group externalities, they are both worse off, compared to a situation with free-riding, if they are relatively similar. If they are sufficiently heterogenous, the weak group loses at the expense of the relatively strong group.