Autonomous and advertising-dependent ‘word of mouth’ under costly dynamic pricing

• We study dynamic pricing and advertising policies in a sales model for a monopolist firm.
• Both autonomous and advertising-dependent word of mouth are considered.
• Optimal limit cycles alternating building and leveraging of the price advantage are found.
• Multiple equilibria separated by Skiba curves are numerically ascertained.

Autonomous ‘word of mouth’, as a channel of social influence that is out of firms’ direct control, has acquired particular importance with the development of the Internet. Depending on whether a given product or service is a good or a bad deal, this can significantly contribute to commercial success or failure. Yet the existing dynamic models of sales in marketing still assume that the influence of word of mouth on sales is at best advertising-dependent. This omission can produce ineffective management and therefore misleading marketing policies. This paper seeks to bridge the gap by introducing a contagion sales model of a monopolist firm's product where sales are affected by advertising-dependent as well as autonomous word of mouth. We assume that the firm's attraction rate of new customers is determined by the degree at which the current sales price is advantageous or not compared with the current customers’ reservation price. A primary goal of the paper is to determine the optimal sales price and advertising effort. We show that, despite costly price adjustments, the interactions between sales price, advertising-dependent and autonomous word of mouth can result in complex dynamic pricing policies involving history-dependence or limit cycling consisting of alternating attraction of new customers and attrition of current customers.