New product diffusion in the presence of strategic consumers and social contagion: A mean-field game approach

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In this paper, we introduce a framework for new product dfiffusion that integrates consumer heterogeneity and strategic interactions 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, even when the word-of-mouth effect is weak, in the presence of strategic consumers, whereas it implements a cyclic penetration-skimming policy in face of myopic consumers. Also, depending on the distribution of consumers, the diffusion curve can be S-shaped, concave or convex, which shows clearly that heterogeneity matters.

, 31 pages

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