Negative royalty in duopoly and definition of license fee: general demand and cost functions

We examine the relationship between the definition of license fee and a possibility of negative royalty in a duopoly with an outside innovator which has an option to enter the market and imposes a combination of a royalty per output and a fixed fee under general demand and cost functions. We consider two scenarios about determination of license fee. One is a scenario which does not assume entry of the innovator, and the other is a scenario which takes a possibility of entry of the innovator into the market. We will show that the optimal royalty rate for the innovator in the former case is smaller than that in the latter case, and the sign of the optimal royalty rate depends on whether the goods of firms are strategic substitutes or strategic complements