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 in attempting to understand and mitigate the sources of discrimination in these tools. However, previous work has largely assumed that discrimination is the result of some initial 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. Recent work on relational equality have suggested that there are other sources of discrimination that are non-distributional, namely inequality in social relationships. Here, we demonstrate how 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 discriminatory outcomes, yet there was no initial unequal distribution of resources across groups of candidates or firms. We provide the range of possible expected payoffs to the firms and candidates at equilibrium, including asymmetric payoffs where some candidates receive less. This is the result of asymmetric strategies where firms successfully take advantage of those candidates, resulting in discrimination. Thus, we show that we must look beyond the distribution of resources to understand sources of discrimination in machine learning.