The working paper studies the approaches of the digital economy leaders (the US, the EU and China) to data governance and approaches they promote in international institutions. Data can generate not only profits for tech giants, but also social value. However, the market forces by themselves will not create data-based public goods. Government actions are needed at the county level and inter-state and multilateral institutions cooperation at the international level. The study is highly relevant, since to date despite numerous initiatives to establish coordination mechanisms and data regulation, cooperation on data governance is highly fragmented and gridlocked due to contradictions and tough competition between key players. One of the key disagreements is related to the regulation of cross-border data flows. The working paper aims to explore contradictions between the regulatory practices of the key actors in digital economy, the US, EU and China in the first place, and approaches they promote in international institutions (the WTO, G20, G7, OECD). In particular, the author looks into the G20 agenda on data governance and the Initiative on free data flow with trust, its challenges, and risks of cooperation stagnation. The working paper presents possible scenarios of future cooperation on data governance, their risks and perspectives, including the establishment of the Digital Economy and Data Governance Board by the G20, G7 initiative on shaping global digital order, deepening of cooperation on data governance within the G7 and the OECD, and the UNCTAD proposal on building a multilevel distributed polycentric data-governance model with the UN central role. The author concludes with a proposal on BRICS cooperation aimed at shaping inclusive multilateral data governance.