Time-varying targeted marketing in networks based on competitive opinion dynamics
Ningning Lang, Quanbo Zha, Lin Wang
Abstract
Opinions reflect people's preferences and guide their decisions or behaviors. With the network science model of opinion dynamics, we develop an integrated game-theoretical framework for the targeted allocation of marketing resources over networks under different constraints. In the framework, firms attempt to steer people's opinions by competitive expenditure to maximize their finite-time cumulative profits. The dynamics of opinions in networks are driven by the simultaneous exposure to exogenous marketing campaigns and endogenous word-of-mouth communication. Based on such dynamics, we derive closed-loop equilibrium strategies for time-varying targeted marketing from the framework and highlight their dependence on individual attributes and network structure. Our theoretical results arrive at some properties of the expected gross profit concerning budget and cost, revealing an optimal budget and the importance of cost reduction. Additionally, we provide an extended analysis on the infinite-horizon marketing competition, and determine the convergence of people's opinions and the structure of resulting opinions. By simulations, three examples and a baseline case are presented to illustrate our theoretical results and the bias effect of network structure is finally discussed. Despite the mathematical characterization, our paper provides some insights into marketing management.