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The dynamics of innovation diffusion: A survey of Bass-type models

Nicolas Langrené, Rui Liu, Xiangqin Wu, Tianhao Zhi

Abstract

This paper synthesises the existing research on the dynamics of innovation diffusion, with a focus on Bass-type models and their extensions. The theoretical foundation of innovation diffusion proposed by Rogers (1962) and the seminal work of Bass (1969) serve as a starting point for the analysis. We identify and examine various generalizations and stochastic extensions of the Bass model, including counting processes, diffusion processes, and uncertain processes, as well as parameter estimation techniques, from classical statistical techniques to more advanced techniques such as Bayesian filtering and metaheuristic optimisation. We finally explore alternative models of innovation diffusion, with a particular focus on agent-based models. This overview of the evolution of Bass-type models illustrates the progress made in innovation diffusion research over the past decades.

The dynamics of innovation diffusion: A survey of Bass-type models

Abstract

This paper synthesises the existing research on the dynamics of innovation diffusion, with a focus on Bass-type models and their extensions. The theoretical foundation of innovation diffusion proposed by Rogers (1962) and the seminal work of Bass (1969) serve as a starting point for the analysis. We identify and examine various generalizations and stochastic extensions of the Bass model, including counting processes, diffusion processes, and uncertain processes, as well as parameter estimation techniques, from classical statistical techniques to more advanced techniques such as Bayesian filtering and metaheuristic optimisation. We finally explore alternative models of innovation diffusion, with a particular focus on agent-based models. This overview of the evolution of Bass-type models illustrates the progress made in innovation diffusion research over the past decades.
Paper Structure (27 sections, 34 equations, 3 figures)

This paper contains 27 sections, 34 equations, 3 figures.

Table of Contents

  1. Introduction
  2. Theory of innovation diffusion
  3. The Bass model
  4. Aims of the paper
  5. The Bass model
  6. Bass model variations
  7. Stochastic Bass model
  8. Integration with stochastic jump processes
  9. Modelling with stochastic diffusion processes
  10. Uncertain theory approach
  11. Estimation of Bass model parameters
  12. Statistical methods
  13. Ordinary least squares
  14. Nonlinear least squares
  15. Maximum likelihood estimation
  16. ...and 12 more sections

Figures (3)

  • Figure 1: Evolution of adopter fraction under varying innovation $p$ and imitation $q$.
  • Figure 2: Evolution of sales under varying innovation $p$ and imitation $q$, with a market potential of $m=1$ million.
  • Figure 3: Difference between the two strategies