Licensing under Cournot vs Bertrand competition

In this paper we consider, on one hand, a differentiated Cournot model, and, on the other hand, a differentiated Bertrand model, when one of the firms engages in an R&D process that gives an endogenous cost-reducing innovation. The aim of the present paper is two-fold. The first is to study the licensing of the cost-reduction by a per-unit royalty and a fixed-fee in these Cournot and Bertrand models. The second is to do a direct comparison between Cournot model and Bertrand model. We analyse the implications of these types of licensing contracts over the R&D effort, the profits of the firms, the consumer surplus and the social welfare. We show that some previous results for two-part tariff licensing are not robust, in the sense that they can be not true for just either a per-unit royalty contract or a fixed-fee contract. Furthermore, by using comparative static analysis, we conclude that the degree of the differentiation of the goods assumes a great importance in the results. We also discuss the optimal licensing, meaning that which licensing method is preferred, in each of the duopoly models considered.