Licensing of a product innovation by an outside innovator to a Stackelberg duopoly

We examine the optimal strategy of an outside innovator owning a quality-improved product when licensing it to a Stackelberg duopoly. We show that only a single licence is granted, regardless of whether there is quantity or price competition in the marketplace. However, both the licensee and contractual terms in each context differ. Under quantity competition, the licence is granted to the market-leading firm by means of a non-distorting contract, whereas under price competition the licence is granted to the market-following firm by means of a distorting two-part tariff contract with per-unit royalty. From a welfare perspective, exclusive licensing is beneficial in both contexts compared to the pre-licensing scenario, although under price competition, consumers can be harmed if the innovation is small. Finally, licensing leads price competition to yield a less efficient outcome than quantity competition due to greater market collusion. Licensing by means of three-part tariff contracts is also discussed, as well as licensing when potential licensees operate as a mixed duopoly.