The benefits of being small: Duopolistic competition with market segmentation

Consider a duopolistic market in which consumers are not necessarily aware of the firms' existence. The market is characterized by the existence of four segments: a duopolistic segment which consists of consumers who are aware of both firms, a segment of consumers who are unaware of either firm and two captive market segments. We assume that by advertising, firms control the proportion of consumers who are aware of their existence. The relative sizes of the four segments affect the equilibrium of the duopolistic pricing game. We show that being large may be disadvantageous, and that even if gaining awareness is costless firms may wish to remain small.