We develop a model in which vaccine‐producing firms from different developed countries supply vaccines to the developing world during a pandemic. Exporting countries experience a negative externality from incomplete global vaccination, which they try to mitigate by exporting vaccines to developing countries. A cooperative export policy is compared to the alternative regimes of non‐cooperation and non‐intervention. When the negative externality is low, cooperation among exporting countries is worse for global welfare than non‐intervention. However, at high externality levels, export policy cooperation is globally superior to non‐cooperative export subsidization. It then even has the potential to maximize global welfare.