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 consider a simultaneous move game between two durable-good firms in a quantity-setting. The outside innovator chooses from fix fee, royalty or their combination maximizing his profits without triggering patent litigation. We also relate the optimal licensing contract and the innovator´s licensing revenue to the patent´s strength. We show that, for relatively weak patents, it´s optimal for the innovator to charge the royalty rate as high as possible in exchange for a negative fix fee. But for relatively strong patents, contract involving the combination of a medium level royalty rate and a positive fix fee is optimal. Moreover, the social value of a patent of strength θ is nonnegative.