Although machine learning (ML) algorithms are widely used to make decisions about individuals in various domains, concerns have arisen that (1) these algorithms are vulnerable to strategic manipulation and "gaming the algorithm"; and (2) ML decisions may exhibit bias against certain social groups. Existing works have largely examined these as two separate issues, e.g., by focusing on building ML algorithms robust to strategic manipulation, or on training a fair ML algorithm. In this study, we set out to understand the impact they each have on the other, and examine how to characterize fair policies in the presence of strategic behavior. The strategic interaction between a decision maker and individuals (as decision takers) is modeled as a two-stage (Stackelberg) game; when designing an algorithm, the former anticipates the latter may manipulate their features in order to receive more favorable decisions. We analytically characterize the equilibrium strategies of both, and examine how the algorithms and their resulting fairness properties are affected when the decision maker is strategic (anticipates manipulation), as well as the impact of fairness interventions on equilibrium strategies. In particular, we identify conditions under which anticipation of strategic behavior may mitigate/exacerbate unfairness, and conditions under which fairness interventions can serve as (dis)incentives for strategic manipulation.