As the number of globally mobile students has expanded, governments are assumed to be consistently and intentionally competing for talent, in what has been called a "great brain race". While the notion of competition has become dominant, there is little evidence on long-term policy dynamics in this field, not only across jurisdictions but also over time. We seek to address this gap in this paper through a longitudinal analysis of the politics and public policies impacting international students in four major recruiting countries--Australia, Canada, England and the USA. Through this comparative analysis of the period 2000 to 2016, we demonstrate that international student numbers across the jurisdictions have grown steadily but that this appears to be decoupled from political and policy changes. We also discuss how "internationalization" initiatives provide an insufficient policy umbrella for policy action on the recruitment and retention of international students. Public policy impacting international students spans multiple government agencies or ministries, encompassing different policy fields. This requires greater policy coordination, which remains elusive for the most part.