Cultural evolutionary models of bargaining can elucidate issues related to fairness and justice, and especially how fair and unfair conventions and norms might arise in human societies. One line of this research shows how the presence of social categories in such models creates inequitable equilibria that are not possible in models without social categories. This is taken to help explain why in human groups with social categories, inequity is the rule rather than the exception. But in previous models, it is typically assumed that these categories are rigid – in the sense that they cannot be altered, and easily observable – in the sense that all agents can identify each others’ category membership. In reality, social categories are not always so tidy. We introduce evolutionary models where the tags connected with social categories can be flexible, variable, or difficult to observe, i.e. where these tags can carry different amounts of information about group membership. We show how alterations to these tags can undermine the stability of unfair conventions. We argue that these results can inform projects intended to ameliorate inequity, especially projects that seek to alter the properties of tags by promoting experimentation, imitation, and play with identity markers.