This paper scrutinizes the effects of the European Directive on Copyright in the Digital Single Market on platform competition in media markets. Platforms that are Online Content-Sharing Service Providers must have a license agreement with collective management organizations that control the content platform users may (or must not) upload to the platform. The paper shows that the new directive may imply market concentration and an aggregate welfare loss. The reason is that only users of the large platform will be allowed to upload content if the content asset controlled by a collective management organization is sufficiently valuable and if network effects are strong.