Diffusion of Innovations in Middle Eastern versus Western Markets: A Mathematical Computation Cellular Automata Simulati
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Diffusion of Innovations in Middle Eastern versus Western Markets: A Mathematical Computation Cellular Automata Simulation Model Konstantinos Petridis1 · Nikolaos E. Petridis1 Received: 19 April 2020 / Revised: 22 July 2020 / Accepted: 25 August 2020 © Springer-Verlag GmbH Germany, part of Springer Nature 2020
Abstract Simulation modelling has gained ground over the years since it can provide various scenarios applied to any scientific area. In this study, a stochastic cellular automata model is proposed, in which agents fall into three distinct categories (adopters, non-adopters and denials). Based on Hofstede’s cultural dimension individualism, we characterize three major international markets, as perfectly clustered (collective) to perfectly random (individualistic). We investigate innovation diffusion speed, in each network topology. At each time step, the decision of non-adopters to purchase innovative products, is affected by their immediate neighborhood (von Neumman). The speed of diffusion is evaluated using time at which sales reach 50% of market. Effects of simulation parameters on speed of diffusion, are assessed using a lognormal accelerated failure time model. Results demonstrate that diffusion of innovative products accelerates when innovators of a virtual economic system are placed according to a random network and when amount of innovators and imitators in the economic system increases. Slower innovative products’ diffusion process is a result of a large amount of denials and of how imitators are placed in the in the virtual economic system. Diffusion in small-world virtual economic systems lead to small time inflexion points very close to those of a random networked market. Keywords Cellular Automata models · Diffusion of innovative products · Smallworld network · Innovators and denials · Survival analysis · Computational mathematics
* Konstantinos Petridis [email protected] 1
Department of Applied Informatics, University of Macedonia, 156 Egnatia Street, Thessaloniki, Greece
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K. Petridis, N. E. Petridis
1 Introduction Sayama (2015) defines an automaton as a technical term used in computer science and mathematics for a theoretical machine that changes its internal state based on inputs and its previous state. Cellular Automata (CA) are a set of such structures, usually placed along a regular spatial grid, whose cell transit states and this procedure is conducted simultaneously for all cells, according to a function which takes into consideration their neighborhood (Von Neumann 1951; Toffoli and Margolus 1987; Stephen and John 1995). This simulation technique, which belongs to computational mathematics scientific field, has been applied in various research areas such as Biology, Chemistry, Civil Engineering and Marketing among many others. They are widely used, because of their simple application and due to the fact that they can provide useful insights when real data are not easy to collect. In the most of the cases in relative literature, CA models evolve at
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