Licensing to a durable-good duopoly in patent litigation

Incorporating patent litigation into a durable-good duopoly model, we revisit the optimal licensing contract on a cost-reducing innovation. We find that both the optimal licensing contract and the innovator's licensing revenue are closely related to the patent's strength, i.e., the probability it would be found valid if tested in court. It is shown that, for a relatively weak patent (patent's strength is low), it's optimal for the innovator to charge the royalty rate as high as possible coupled with a negative fixed fee. But for a relatively strong patent (patent's strength is high), contract involving the combination of a medium level royalty rate and a positive fixed fee is optimal. We also discuss how the patent's strength affects the social welfare of a patent. Finally we present two policy suggestions that may alleviate the social welfare loss raised by the licensing of weak patents.