Two experiments utilized a new experimental paradigm—the Intergroup Prisoner’s Dilemma— Maximizing Difference (IPD-MD) game—to study how relative deprivation at the group level affects intergroup competition. The IPD-MD game enables group members to make a costly contribution to either a within-group pool that benefits fellow ingroup members, or a between-group pool, which, in addition, harms outgroup members. We found that when group members were put in a disadvantaged position, either by previous actions of the outgroup (Experiment 1) or by random misfortune (Experiment 2), they contributed substantially more to the competitive between-group pool. This destructive behavior both minimized inequality between the groups and reduced collective efficiency. Our results underscore the conditions that lead group members to care about relative (rather than absolute) group outcomes and highlight the need to differentiate between the motivation to get ahead and the motivation not to fall behind: the latter, it appears, is what motivates individual participation in destructive intergroup competition.