Dynamic Pricing in Social Networks: The Word-of-Mouth Effect

We study the problem of optimal dynamic pricing for a monopolist selling a product to consumers in a social network. In the proposed model, the only means of spread of information about the product is via word-of-mouth communication; consumers' knowledge of the product is only through friends who already know about the product's existence. Both buyers and nonbuyers contribute to information diffusion, while buyers are more likely to spread the news about the product. By analyzing the structure of the underlying endogenous dynamic process, we show that the optimal dynamic pricing policy for durable products with zero or negligible marginal cost drops the price to zero infinitely often. The firm uses free offers to attract low-valuation agents and to get them more engaged in the spread. As a result, the firm can reach potential high-valuation consumers in parts of the network that would otherwise remain untouched without the price drops. We provide evidence for this behavior from the smartphone app market, where price histories indicate frequent zero-price sales. Moreover, we show that despite dropping the price to zero infinitely often, the optimal price trajectory does not get trapped near zero. We demonstrate the validity of our results in the face of forward-looking consumers and homophily in word-of-mouth engagement. We further unravel the key role of the product type in the optimality of zero-price sales by showing that the price fluctuations disappear after a finite time for a nondurable product.