We use tools from evolutionary game theory to examine how power might influence the cultural evolution of inequitable norms between discernible groups (such as gender or racial groups) in a population of otherwise identical individuals. Similar extant models always assume that power is homogeneous across a social group. As such, these models fail to capture situations where individuals who are not themselves disempowered nonetheless end up disadvantaged in bargaining scenarios by dint of their social group membership. Thus, we assume that there is heterogeneity in the groups in that some individuals are more powerful than others. Our model shows that even when most individuals in two discernible sub-groups are relevantly identical, powerful individuals can affect the social outcomes for their entire group; this results in power by association for their in-group and a bargaining disadvantage for their out-group. In addition, we observe scenarios like those described where individuals who are more powerful will get less in a bargaining scenario because a convention has emerged disadvantaging their social group.