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A stochastic two-stage innovation diffusion model on a lattice

Published online by Cambridge University Press:  09 December 2016

Cristian F. Coletti
Affiliation:
Universidade Federal do ABC
Karina B. E. de Oliveira
Affiliation:
Universidade de São Paulo
Pablo M. Rodriguez
Affiliation:
Universidade de São Paulo

Abstract

We propose a stochastic model describing a process of awareness, evaluation, and decision making by agents on the d-dimensional integer lattice. Each agent may be in any of the three states belonging to the set {0, 1, 2. In this model 0 stands for ignorants, 1 for aware, and 2 for adopters. Aware and adopters inform its nearest ignorant neighbors about a new product innovation at rate λ. At rate α an agent in aware state becomes an adopter due to the influence of adopters' neighbors. Finally, aware and adopters forget the information about the new product, thus becoming ignorant, at rate 1. Our purpose is to analyze the influence of the parameters on the qualitative behavior of the process. We obtain sufficient conditions under which the innovation diffusion (and adoption) either becomes extinct or propagates through the population with positive probability.

Type
Research Papers
Copyright
Copyright © Applied Probability Trust 2016 

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