Licensing in a Differentiated Product Duopoly With Price and Quantity Contracts

Abstract

In this paper, we extend the differentiated product duopoly model of Singh and Vives (1984) to a setting where the firms are asymmetric in terms of their marginal costs, and the more efficient firm has the option to license its technology to its rival before they engage in price competition, quantity competition, or mixed competition. Our numerical computations reveal that the unique subgame perfect Nash equilibrium of the duopolistic competition game with licensing involves price competition when the products are complements. However, when the products are substitutes, either price or quantity competition can emerge in an equilibrium, depending on the level of cost asymmetry and the degree of substitution. Furthermore, when the products are complements, consumers and the firms benefit from licensing. In contrast, when the products are substitutes, licensing can benefit both consumers and the firms only if the degree of substitution and cost asymmetry are sufficiently low. Our results complement the earlier findings in Niu (2008), where the timing of licensing and contract decisions differs from ours.