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.