New Product Diffusion with Two Interacting Segments or Products

We study the diffusion of a product in two customer segments where the acceptance level in one segment affects the diffusion rate not only in that same segment, but also in the other. The inter-segment influence can be positive or negative, i.e., the acceptance level of the product in one segment can reinforce or impede its diffusion in the other. The model set-up also applies to the diffusion of two products, with independent market potential, in a single population. Since the diffusion system we study does not have a closed-form solution, we use phase plane analysis to identify the equilibrium points of the joint diffusion process and to characterize their stability properties. Further, we provide a means to identify the regions with different convergence behavior, i.e., to identify boundaries for regions within which all trajectories converge to a particular equilibrium point. For the cases of asymmetric influence (+/-) and mutually impeding influence (-/-), we also provide conditions under which both products can achieve full market potential in equilibrium. Finally, we provide managerial insights into the effectiveness of two strategies in the context of asymmetric (+/-) interaction between two customer segments: (1) “seeding,” i.e., using free samples to support the launch of a product in one segment being harmed by the adoption in the other, and (2) “demand control,” i.e., purposely limiting market potential for the customer segment harming product diffusion in the other segment.