Abstract
In this article we extend the Marketing Mix Diffusion (MMD) model to inhomogenous networks (i.e. complex networks of arbitrary topology). The (Homogenous) MMD model is an innovation diffusion model, similar to the Bass model, which includes four decision variables (the 4Ps of Marketing: Product, Price, Place, Promotion). We introduce the Inhomogenous MMD (IMMD) model and we conduct two separate experiments: one based on simulation and another one relying on empirical evidence. The simulation study compares the behavior of the IMMD model with the classic Bass diffusion model. Results suggest that the classic Bass model is able to represent the IMMD curves quite well in most cases. The IMMD is more general and capable of representing extreme scenarios. The empirical study focuses on the geographic diffusion of mobile broadband technology in Japan, combining adoption data with a spatial network of municipalities. The in-sample performance of the model is comparable to the existing methods, which suggests a good explanatory power of the IMMD model.
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Notes
- 1.
The use of the hyperbolic tangent (tanh) ensures that the outputs are contained between –1 and 1, such that when combined with the ReLU function on Eqs. 3 and 4, only positive outputs will flow into the neighboring nodes. This simulates the adoption dynamic of each individual node.
References
Akamai.: State of Internet Reports (2014)
Bass, F.M.: A new product growth for model consumer durables. Manag. Sci. 50(12_Supplement), 1825–1832 (2004)
Bass, Frank M., Krishnan, Trichy V., Jain, Dipak C.: Why the Bass model fits without decision variables. Market. Sci. 13(3), 203–223 (1994)
Bertotti, M.L., Brunner, J., Modanese, G.: The Bass diffusion model on networks with correlations and inhomogeneous advertising. Chaos, Solitons Fractals 90, 55–63 (2016)
Dentsu.: Advertising Expenditures in Japan (2020)
Godes, D., Mayzlin, D.: Using online conversations to study word-of-mouth communication. Market. Sci. 23(4), 545–560 (2004)
Hamrick, B.: Discrete Calculus (2007)
Holtz, G.: An individual level diffusion model, carefully derived from the Bass-model (2004)
Kempe, D., Kleinberg, J., Tardos, É.: Maximizing the spread of influence through a social network. In: Proceedings of the Ninth ACM SIGKDD International Conference on Knowledge Discovery and Data Mining - KDD ’03, p. 137. ACM Press, New York (2003)
Kempe, D., Kleinberg, J., Tardos, É.: Maximizing the spread of influence through a social network. Theory Comput. 11(4), 105–147 (2015)
Kermack, W.O., McKendrick, A.G.: A contribution to the mathematical theory of epidemics. Proc. R. Soc. Lond. Ser. A, Contain. Papers Math. Phys. Charact. 115(772), 700–721 (1927)
Li, M., Wang, X., Gao, K., Zhang, S.: A survey on information diffusion in online social networks: models and methods. Inf. (Switzerland) 8(4) (2017)
Mesak, H.I.: Incorporating price, advertising and distribution in diffusion models of innovation: some theoretical and empirical results. Comput. Operat. Res. 23(10), 1007–1023 (1996)
Morone, F., Makse, H.A.: Influence maximization in complex networks through optimal percolation. Technical report (2015)
Morone, F., Min, B., Bo, L., Mari, R., Makse, H.A.: Collective Influence Algorithm to find influencers via optimal percolation in massively large social media. Sci, Rep (2016)
Narasimhan, R., Ghosh, S., Mendez, D.: A dynamic model of product quality and pricing decisions on sales response. Decis, Sci (1993)
Nelder, J.A., Mead, R.: A simplex method for function minimization. Comput. J. 7(4), 308–313 (1965)
Niu, S.-C.: A stochastic formulation of the Bass model of new-product diffusion. Math. Probl. Engin. 8(3), 249–263 (2002)
OECD. Mobile broadband subscriptions (2018)
Pinto, L., Cavíque, L., Santos, J.M.A.: Marketing mix and new product diffusion models. Proc. Comput, Sci (2022)
Portal Site of Official Statistics of Japan website (https://www.e-stat.go.jp/). Report on Internal Migration in Japan (2014)
Portal Site of Official Statistics of Japan website (https://www.e-stat.go.jp/). Consumer Price Index 2015 - Base Consumer Price Index, 2015
Pyo, T.-H., Gruca, T.S., Russell, G.J.: A new bass model utilizing social network data (2017)
Richardson, M., Domingos, P.: Mining knowledge-sharing sites for viral marketing, p. 61 (2002)
Everett, M.: Rogers. Free Press, Diffusion of Innovation (2003)
Site Rank Data. https://siterankdata.com/ (2021)
Wang, W., Liu, Q.H., Liang, J., Hu, Y., Zhou, T.: Coevolution spreading in complex networks. Phys. Rep. 820, 1–51 (2019)
Zonghan, W., Pan, S., Chen, F., Long, G., Zhang, C., Philip, S.Y.: A comprehensive survey on graph neural networks. IEEE Trans. Neural Netw. Learn. Syst. 32(1), 4–24 (2021)
Zhong, Y.D., Leonard, N.E.: A continuous threshold model of cascade dynamics. In: Proceedings of the IEEE Conference on Decision and Control, 2019, pp. 1704–1709 (2019)
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Pinto, L.G., Cavique, L., Gomes, O., Santos, J.M.A. (2024). Inhomogenous Marketing Mix Diffusion. In: Botta, F., Macedo, M., Barbosa, H., Menezes, R. (eds) Complex Networks XV. CompleNet-Live 2024. Springer Proceedings in Complexity. Springer, Cham. https://doi.org/10.1007/978-3-031-57515-0_3
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