A dynamic model of oligopoly with R&D externalities along networks. Part I

This paper formulates and analyzes a two‐stage oligopoly game where firms can invest in cost‐reducing R&D activity with the possibility of sharing R&D results with partner firms as well as gaining knowledge for free through spillovers. Firms are arranged within networks (or districts) inside which they can cooperate by bilateral agreements for sharing knowledge and compete in the market. An adaptive dynamic mechanism is proposed to describe how firms in a two‐networks system repeatedly decide their R&D efforts over time. This adaptive adjustment may converge to a Nash equilibrium in the long run, or exhibit more complex dynamic behaviors. Analytical results about stability of equilibrium points are given, as well as numerical simulations to show global dynamical properties, including coexistence of attractors and complicated structures of their basins. In a second paper (Part II) some analytical results will be given for some relevant benchmark cases, together with numerical experiments that stress the role of the level of connectivity (i.e. the collaboration attitude) inside networks, as well as the effects of involuntary knowledge spillovers inside each network and among different competing networks.