Existence Advertising, Price Competition and Asymmetric Market Structure

We examine a two-stage duopoly game in which firms advertise their existence to consumers in stage 1 and compete in prices in stage 2. Whenever the advertising technology generates positive overlap in customer bases, the equilibrium for the stage-1 game is asymmetric in that one firm chooses to remain small in comparison to its competitor. For a specific random advertising technology, we show that one firm will always be half as large as the other. No pure-strategy price equilibrium exists in the stage-2 game, and as long as there is some overlap in customer bases, the mixed-strategy price equilibrium does not converge to the Bertrand equilibrium.