Game on cooperative innovation with both technology spillover and product substitution

A system consisting of duopoly was proposed to explore how the asymmetric technology spillover and product substitution impact the cooperation in innovation and production stages. The mathematical and computational results show that technology spillover induces innovation investment and production. However, product substitution has a negative on the optimal innovation and production decisions. For a company maximizing his profits, only when both technology spillover and product substitution are high enough can the company have motivation to cooperate. It is always more beneficial for the system in full-collusion with cooperation in both innovation and production than in semi-collusion with only cooperation in innovation, which suggests that a well-designed revenue-allocation mechanism can motivate the duopoly to carry on full-collusion.