In digital markets, antitrust law and special regulations aim to ensure that markets remain competitive despite the dominating role that digital platforms play today in everyone's life. Unlike traditional markets, market participant behavior is easily observable in these markets. We present a series of empirical investigations into the extent to which Amazon engages in practices that are typically described as self-preferencing. We discuss how the computer science tools used in this paper can be used in a regulatory environment that is based on algorithmic auditing and requires regulating digital markets at scale.