Optimal licensing of a cost reducing innovation in a linear symmetric model

I compare here fixed fee and royalty licensing in a linear model where a duopoly is located symmetrically. One of the firms, called the patent holder, owns a patented cost-reducing innovation and will decide, according to its total revenue, to share or not its new technology with the non innovative firm. The difference with other papers in the literature is that here firms are not located at the end points of the city but are symmetric. Results show that royalty licensing is better than fixed fee licensing for a non drastic innovation while a fixed fee is better than a royalty when the innovation is very high. I also find that non licensing is always better than fixed fee licensing independently of the size of the innovation. Finally, when innovation is non drastic, the patent holder license its patent under a royalty and do not license when innovation is drastic.
JEL codes: C21, L24, O31, O32