Machine learning has grown in popularity to help assign resources and make decisions about users, which can result in discrimination. This includes hiring markets, where employers have increasingly been interested in using automated tools to help hire candidates. In response, there has been significant effort to understand and mitigate the sources of discrimination in these tools. However, previous work has largely assumed that discrimination, in any area of ML, is the result of some initial \textit{unequal distribution of resources} across groups: One group is on average less qualified, there is less training data for one group, or the classifier is less accurate on one group, etc. However, in this work, we find that resource-symmetric agents with equal merit still experience discrimination at equilibrium. Recent work on relational equality have suggested that there are other sources of discrimination, such as inequality in social relationships, that are notably non-distributional. So, first, we show equal-merit discrimination can arise from a non-distributional source: We provide subgame perfect equilibria in a simple sequential model of a hiring market with Rubinstein-style bargaining between firms and candidates that exhibits asymmetric outcomes resulting from agents' ability to make threats during bargaining. Second, we show how equal-merit discrimination can arise endogenously to the learning process via convergence of a learning algorithm to asymmetric equilibria. Ultimately, this work motivates the further study of endogenous, possibly non-distributional, mechanisms of inequality in ML.