License and entry strategies for an outside innovator in Stackelberg duopoly with royalty and fixed fee under vertical differentiation**

Abstract We examine a choice of options for an outside innovating firm in Stackelberg duopoly under vertical differentiation. The options for an innovating firm are to enter the market with or without licensing its technology for producing a higher‐quality good by a combination of royalty and fixed license fee, and to license its technology without entry. When the innovating firm licenses its technology to the incumbent firm without entry, its optimal royalty rate is zero. When the innovating firm enters the market with a license to the incumbent firm, and the cost function is strictly concave, its optimal royalty rate is one such that the incumbent firm drops out of the market with a negative fixed license fee. If the cost function is strictly convex, there is an internal solution of the positive optimal royalty rate with positive or negative fixed license fee. Without entry cost, if the cost function is strictly concave, the entry without license and entry with license strategies are optimal, and if it is strictly convex, the entry with license strategy is optimal.