This article proposes an evolutionary game theoretical model in which individuals negotiate to reach a compromise settlement on who takes the dominant role in a dominant-subordinate relationship. The negotiation process is formalized by bargaining theory in economics, which makes our model different from alternative models on the formation of dominant-subordinate relationships based on detailed biological mechanisms. We find that evolution leads to a “cooperative” (“selfish”) behavior when an individual takes the dominant (subordinate) role. For example, consider two Polistes wasps in a nest-building pair who try to determine the role assignment of the queen and the subordinate cofoundress. After the roles are assigned, the queen chooses between either sharing or monopolizing reproduction, and the subordinate chooses between exerting either a high or a low effort in rearing or foraging activities. According to our model’s prediction, the queen’s behavior (sharing reproduction) increases the collective fitness of the colony but potentially hurts her reproductive interest, while the subordinate’s behavior (exerting a low effort) decreases the productivity of the colony but helps her to save energy. Such a behavior pair is evolutionarily stable because it guarantees an individual to have the comparative advantage in taking the dominant role against any other individuals via negotiation. This result may shed new light on understanding the formation of dominant-subordinate relationships. In addition, agnostic of detailed biological mechanisms, our mathematical formulation of dominant-subordinate relationships might also have wide applications in animal behavior and beyond, as its empirical support is found in article wasps and humans.