Endowing agents that prefer co-operative outcomes with asymmetric power substantially increases the chances that both co-operative agents survive and that co-operative worlds evolve across a variety of structural settings of conflict and co-operation present in international relations; particularly when agents are endowed with the ability to selectively interact with other agents. These results are consistent with the general finding that non-compulsory play consistently helps co-operators. The question addressed in this analysis is whether or not asymmetric power also helps exploitive agents in the same structural settings; a question heretofore not analysed. Contrary to expectations, the simulation results reported here suggest that exploitive agents benefit from asymmetric power only in very restricted circumstances – circumstances relatively unlikely to occur in international relations. In effect, there is an asymmetry in the benefits of asymmetric power.