Probabilistic Patents

We model a homogeneous product environment where identical e-retailers endogenously engage in both brand advertising (to create loyal customers) and price advertising (to attract 'shoppers'). Our analysis allows for 'cross-channel' effects; indeed, we show that price advertising is a substitute for brand advertising. In contrast to models where loyalty is exogenous, these crosschannel effects lead to a continuum of symmetric equilibria; however, the set of equilibria converges to a unique equilibrium as the number of potential e-retailers grows arbitrarily large. Price dispersion is a key feature of all of these equilibria, including the limit equilibrium. While each firm finds it optimal to advertise its brand in an attempt to 'grow' its base of loyal customers, in equilibrium, branding (1) reduces firm profits, (2) increases prices paid by loyals and shoppers, and (3) adversely affects gatekeepers operating price comparison sites. Branding also tightens the range of prices and reduces the value of the price information provided by a comparison site. Using data from a price comparison site, we test several predictions of the model.