Optimal licensing of uncertain patents in a differentiated Stackelberg duopolistic competition market

Abstract

This study investigates the strategy implications of patent licensing between two firms in a differentiated Stackelberg framework, when the innovator faces an uncertain research and development (R&D) outcome. We establish a three-stage duopoly game (with an R&D stage, a licensing stage and an output stage), in order to analyze the effects of product differentiation and technology spillover on the optimal licensing strategy for a stochastic R&D firm. Our results demonstrate that, in cases where the R&D outcome is uncertain, (i) whether the innovator chooses fixed-fee licensing or royalty licensing depends on the degree of product differentiation and technology spillover; (ii) when the technology spillover is lower than a critical value, regardless of the degree of product differentiation, two-part tariff licensing is superior to fixed-fee licensing and royalty licensing, and (iii) the optimal royalty rate is dependent upon the technology spillover, with the value possibly being higher than the cost reduction.