Patent strength and optimal two-part tariff licensing with a potential rival

•We identify the optimal two part tariff licensing for an incumbent innovator.•The incumbent and the entrant compete in a differentiated Cournot duopoly.•Patent strength, market parameter and substitution coefficient are considered.•A pure royalty licensing emerges under a weak patent.•The optimal contract always involves a positive royalty in a competitive market.

We investigate a two-part tariff licensing contract that enables an incumbent innovator to license the technology for a new product to a potential rival, who may alternatively develop a compatible technology for an imperfectly substitutable product. We identify the optimal two-part tariff licensing contract based on the development cost incurred by the rival, the market parameter, and the substitution coefficient.