On the competitive effects of divisionalization

In this paper, we assume that firms can create independent divisions which compete in quantities in a homogeneous good market. Assuming complete information, identical firms and constant returns to scale, we prove the following: 1) Subgame Perfect Nash Equilibrium (SPNE) implies Perfect Competition if the number of firms is beyond some critical Level 2) This Level is small (sometimes one) under reasonable circumstances. Assuming a fixed cost per firm, SPNE implies that even if this cost is arbitrarily small and the number of potential firms is arbitrary Large, 3) the number of active firms is small (sometimes a monopoly) and 4) the total number of divisions is bounded above. This implies that the market under consideration is a Natural Oligopoly. Next we study a model in which there is both a fixed cost and an upper bound on the maximum number of divisions which can be created. We show that 5) when this upper bound tends to infinity and the fixed cost tends to zero, SPNE may imply either Perfect Competition or a Natural Oligopoly. Finally 6) it is shown that the above results hold under incomplete information.