Optimal patent licensing: from three to two part tariffs

We study the licensing of a cost-reducing innovation in a Cournot oligopoly where an outside innovator uses three part tariffs that are combinations of upfront fees, per unit royalties and ad valorem royalties. Under general demand, the maximum possible licensing revenue under three part tariffs can be always attained by a policy that uses at most two of the three components. For relatively significant innovations, there exists an optimal policy consisting of a per unit royalty and upfront fee and a continuum of other optimal policies that are three part tariffs whose all components are positive. Completely characterizing optimal policies under linear demand, we show that for oligopolies with four or more firms: (i) pure upfront fees are optimal for insignificant innovations; (ii) for intermediate and significant innovations: (a) there is a continuum of optimal policies which always includes a two part tariff with unit royalty and upfront fee and (b) a two part tariff with an ad valorem royalty and fee or a two part royalty can be optimal for some, but not all parametric configurations.