International investor-state arbitration (IAI) and administrative contracts raise complex and interesting questions in the field of international law and administrative law.
The investment agreements will usually contain provisions meant to streamline this.
As a general rule, courts will decide based on the rules for its own jurisdiction (including international treaties that apply to its jurisdiction, in the way they apply there, from a local perspective), which law applies. That said, it is possible that courts in different jurisdictions come to deviating conclusions about the applicable law.