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 non-buyers contribute to information diffusion while buyers are more likely to get engaged. By analyzing the structure of the underlying endogenous 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. By attracting low-valuation agents with free-offers and getting them more engaged in the spread, the firm can reach out to 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 smartphone app market, where price histories indicate frequent free-offerings. Moreover, we show that despite infinitely often drops of the price to zero, the optimal price trajectory does not get trapped near zero. We demonstrate the validity of our results in face of strategic forward-looking agents, homophily-based engagement in word of mouth, network externalities, and consumer inattention to price changes. We further unravel the key role of the product type in the drops by showing that the price fluctuations disappear after a finite time for a nondurable product.