Kamien, M.I., Tauman, Y. (1986). Fees Versus Royalties and the Private Value of a Patent. Quarterly Journal of Economics, 101, 471-491. [PDF in utexas]
We compare how much profit an owner of a patented cost-reducing invention can realize by licensing it to an oligopolistic industry producing a homogeneous product, by means of a fixed fee or a per unit royalty. Our analysis is conducted in terms of a noncooperative game involving n + 1 players: the inventor and the n firms. In this game the inventor acts as a Stackelberg leader, and it has a unique subgame perfect equilibrium in pure strategies. It is shown that licensing by means of a fixed fee is superior to licensing by means of a royalty for both the inventor and consumers. Only a “drastic” innovation is licensed to a single producer.