Drastic innovation reduces firms’ incentives to create divisions

I study a game in which two firms create independent divisions, then they choose whether to do R&D so as to reduce their divisions’ marginal costs, and then the divisions compete in the market. I provide necessary and sufficient conditions under which the game has an equilibrium in pure strategies, and I show that the game has an equilibrium only if each firm threatens that if the rival creates more divisions it will use R&D to foreclose the market. The case we find in the literature, in which firms flood the market with their divisions, should happen only in industries with low returns to R&D.