Emission taxation, green innovations and inverted-U aggregate R&D efforts in a linear state differential game

We revisit a well known differential Cournot game with polluting emissions, to propose a version of the model in which environmental taxation is levied on emissions rather than the environmental damage. This allows to attain strong time consistency under open-loop information, and yields two main results which can be summarized as follows: (i) to attain a fully green technology in steady state, the regulator may equivalently adopt an appropriate tax rate (for any given number of firms) or regulate market access (for any given tax rate); (ii) if the environmental damage depends on emissions only (i.e., not on industry output) then the aggregate green R&D effort takes an inverted-U shape, and the industry structure maximising aggregate green innovation also minimises individual and aggregate emissions. This calls for a coordination of environmental and merger regulation so as to create the industry structure most favourable to green innovation.