Strategic advertising and pricing in e-commerce

We develop a model of pricing and advertising for e-commerce. N identical sellers, selling an homogeneous product, each choose a price and a web-based advertising policy. Buyers have usual demand functions and search optimally on the Internet. A Symmetric Nash Equilibrium (SNE) is derived and characterized. If the marginal cost of advertising exceeds a critical level, then the monopoly price with zero advertising is the unique SNE; otherwise, there is a mixed-strategy SNE which can be expressed as a price distribution and an advertising policy conditional on price. Remarkably, as the number of sellers increases without limit, the SNE converges to the monopoly price and advertising per seller vanishes. On the other hand, the mean price at which sales occur is less than the monopoly price. Still for some advertising technologies, total social welfare is declining in the number of sellers. This results cast doubt on the consumer benefits of e-commerce.