Animals that live in cooperative societies form hierarchies in which dominant individuals reap disproportionate benefits from group cooperation. The stability of these societies requires subordinates to accept their inferior status rather than engage in escalated conflict with dominants over rank. Applying the logic of animal contests to these cases predicts that escalated conflict is more likely where subordinates are reproductively suppressed, where group productivity is high, relatedness is low, and where subordinates are relatively strong. We tested these four predictions in the field on co-foundress associations of the paper wasp Polistes dominulus by inducing contests over dominance rank experimentally. Subordinates with lower levels of ovarian development, and those in larger, more productive groups, were more likely to escalate in conflict with their dominant, as predicted. Neither genetic relatedness nor relative body size had significant effects on the probability of escalation. The original dominant emerged as the winner in all except one escalated contest. The results provide the first evidence that reproductive suppression of subordinates increases the threat of escalated conflict, and hence that reproductive sharing can promote stability of the dominant–subordinate relationship.