Dynamic pricing and advertising in the presence of strategic consumers and social contagion: A mean-field game approach

In this paper, we introduce a framework for new product diffusion that integrates consumer heterogeneity and strategic social influences at individual level. Forward-looking consumers belong to two mutually exclusive segments: individualists, whose adoption decision is influenced by the price and reputation of the innovation, and conformists, whose adoption decision depends on social influences exerted by other consumers and on the price. We use a mean-field game approach to translate consumer strategic interactions into aggregate social influences that affect conformists' adoption decision. The game is played à la Stackelberg, with the firm acting as leader and consumers as followers. The firm determines its pricing and advertising strategies to maximize its profit over a finite planning horizon. We provide the conditions for existence and uniqueness of equilibrium and a numerical scheme to compute it. We conduct a series of numerical simulations to analyze firm's strategy and diffusion processes for different parameter constellations. Our results suggest that the firm adopts a penetration pricing strategy in the presence of strategic consumers, whereas it decreases the price first and then increases it in face of myopic consumers. Moreover, our model asserts that diffusion of innovations is considerably shaped by the consumer heterogeneity. Indeed, our results show that as the fraction of one segment increases in the market, the consumers in the other segment have less tendency towards adoption.