License or entry decision for innovator in international duopoly with convex cost functions

We consider a choice of options for a foreign innovating firm to license its new cost-reducing technology to a domestic incumbent firm or to enter the domestic market with or without license under convex cost functions. With convex cost functions the domestic market and the foreign market are not separated, and the results depend on the relative size of those markets. In a specific case with linear demand and quadratic cost, entry without license strategy is never the optimal strategy for the innovating firm; if the ratio of the size of the foreign market relatively to the domestic market is small, license with entry strategy is optimal; and if the ratio of the size of the foreign market relatively to the domestic market is not small, license without entry strategy is optimal.