Techno-economic studies are investigating procurement costs of hydrogen and related derivatives across various international trade routes. However, the strategic behavior of exporters is rarely considered in this context, despite similar behavior frequently observed in the fossil fuel world and market characteristics indicating some potential. This work introduces a novel techno-economic model of oligopolistic trade tailored around the value chain of potential future global hydrogen markets. It is formulated as a mixed complementarity problem with a convex reformulation, allowing to solve both competitive and oligopolistic equilibria much beyond the capabilities of traditional complementarity models. Illustrative results show that assuming perfectly competitive price formation in early phases of future global hydrogen markets may lead to overly optimistic hydrogen price projections. This is especially the case within Europe, Japan, and South Korea. In contrast, strategically withholding quantities in export may decrease prices for some domestic markets.