  Firms in the U.S. spend over 200 billion dollars each year advertising their
products to consumers, around one percent of the country's gross domestic
product. It is of great interest to understand how that aggregate expenditure
affects prices, market efficiency, and overall welfare. Here, we present a
mathematical model for the dynamics of competition through advertising and find
a surprising prediction: when advertising is relatively cheap compared to the
maximum benefit advertising offers, rational firms split into two groups, one
with significantly less advertising (a "generic" group) and one with
significantly more advertising (a "name brand" group). Our model predicts that
this segmentation will also be reflected in price distributions; we use large
consumer data sets to test this prediction and find good qualitative agreement.
