Studies on parochial altruism have insofar focused on the causes leading individuals to attack any out-group on the behalf of one’s group. Yet, we have no clue to understand why parochial altruists target specific groups, such as big firms in some contexts and refugees in other contexts. The present paper introduces an experiment to analyse the conditions under which individuals costly attack strong versus weak out-groups. In our study, 300 participants played a repeated Inter-group Prisonner Dilemma (IPD) involving multiple groups and inter-group differences in resources. The results show that individuals have a basic preference for targeting strong out-groups, but that attacks decrease when the inequality in destructive capacity between groups is high. Besides, individuals target weak out-groups when they are threatening their in-group status. Decisions in the game correlate with participants’ political ideology and social dominance orientation. Overall, the results give clues to understand historical variations in the targets of political violence.