Divisionalization and symmetric product differentiation

I consider a standard two-stage game of divisionalization in which, in the first stage, two firms choose the number of divisions and, in the second stage, divisions compete independently à la Cournot. Two important assumptions are made. The creation of a division involves a fixed cost, and all divisions sell symmetrically differentiated goods. I obtain that differentiation stimulates the creation of divisions in equilibrium. This effect is so important that prices decrease with the level of product differentiation. As far as welfare is concerned, I obtain that the equilibrium number of divisions is lower than the one that it would maximize social welfare if no intervention at the market stage is feasible.