Optimal licensing of cost-reducing innovation

Abstract

We analyze licensing of a cost reducing innovation to an oligopolistic industry, and extend previous work by Kamien and Tauman (1986) and Katz and Shapiro (1986) in two directions. First, our analysis applies to a wider class of demand functions than linear ones. Second, we derive a simple optimal licensing mechanism for the patentee. We also examine three licensing mechanisms commonly discussed in the literature and observed in practice. Auctioning of a fixed number of licenses is compared to a fixed license fee and to a per unit royalty in terms of the patentee's profit, licensees' profit, industry structure, and the product's price. The analysis is conducted in terms of a non-cooperative game involving the patentee and n identical firms. In this game the patentee acts as a Stackelberg leader selecting a licensing strategy by taking into account the reaction and competitive interaction of the firms. The competitive interaction among the firms is modeled explicitly, both as a quantity (Cournot) and a price (Bertrand) subgame in a market for a homogeneous product. We examine the implications of the three licensing strategies and how they depend on the relative magnitude of the innovation, the number of firms, and the price elasticity of demand. Licensing by means of a royalty is inferior to the other modes, both for consumers and the patentee. The firms' profit decline underboth the auction and the fixed fee policies relative to their pre-innovation profits. Finally, it is shown that auctioning licenses is the patentee's optimal strategy when the magnitude of innovation is not too small. However, this does not hold for an arbitrary innovation.