Eur. Phys. J. Spec. Top. (2022) 231: 2335-2352
https://doi.org/10.1140/epjs/s11734-022-00482-0

Regular Article

Marketing consumer durables on random networks with dynamic advertising rate and individual consciousness

¹ School of Mathematics, Southeast University, 210096, Nanjing, China
² School of Mathematics and Physics, China University of Geosciences, 430074, Wuhan, China
³ Department of Mathematics and Statistics, University of Victoria, V8W 3R4, Victoria, BC, Canada
⁴ Yonsei Frontier Lab, Yonsei University, 03722, Seoul, South Korea

^a wangyi-mail@163.com
^d jdcao@seu.edu.cn

Received: 13 October 2021
Accepted: 16 February 2022
Published online: 25 February 2022

Abstract

In this paper, we consider network models for marketing consumer durables based on the classical Bass model, derived using the degree-based mean field theory. For the annealed network setting, we establish its equilibria, stability, and positivity properties. For the quenched network setting, we first review a model using the edge-based compartmental modeling approach, which agrees well with the ensemble means of the stochastic marketing process. Then, we extend the model to include dynamic advertising rate, which accounts for the fact that advertising may become less efficient and have less impact on people’s choice with the reduction of potential buyers, and individual consciousness, allowing nodes to become alerted to the fact individuals are purchasing the product in the population and therefore reinforce their aspiration. Finally, we perform extensive numerical simulations to explore the effect of dynamic advertising rate and individual consciousness on the marketing durables. Numerical results show that there may exist a trade-off in maximizing the fraction of adopters in the population and minimizing the cost associated with advertising in practical applications.