Product innovation and process innovation in a dynamic Stackelberg game

Under a Stackelberg game structure, we investigate the optimal R&D portfolio of a single-product monopolist investment in product and process innovations of a South-country firm. The research is conducted using a dynamic game with knowledge accumulation. The South-country firm is a manufacturer (the Stackelberg leader) with a two-market framework, in which it supplies products for its domestic market and a North-country firm (the Stackelberg follower). Consumers in the two markets have different green preferences and price sensitivities. Two conventional results reveal that: (a) the investment decisions in product and process innovations are complementary; and (b) the optimal investment efforts positively respond to a learning rate and a knowledge accumulation rate. Specifically, we find that: (a) the optimal innovation efforts of the manufacturer are more heavily affected by the green product preferences of the Stackelberg follower than that of itself; and (b) when consumers' marginal willingness to pay for green products is sufficiently high, optimal investment efforts are higher in the profit-seeking optimum than that in social welfare seeking optimum. In addition, we demonstrate that under both the monopolist optimum and the social optimum, a unique saddle steady-state equilibrium exists.