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Taking into Account the Variations of Neighbourhood Sizes in the Mean-Field Approximation of the Threshold Model on a Random Network

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Abstract

We compare the individual-based 'threshold model' of innovation diffusion in the version which has been studied by Young (1998), with an aggregate model we derived from it. This model allows us to formalise and test hypotheses on the influence of individual characteristics upon global evolution. The classical threshold model supposes that an individual adopts a behaviour according to a trade-off between a social pressure and a personal interest. Our study considers only the case where all have the same threshold. We present an aggregated model, which takes into account variations of the neighbourhood sizes, whereas previous work assumed this size fixed (Edwards et al. 2003a). The comparison between the aggregated models (the first one assuming a neighbourhood size and the second one, a variable one) points out an improvement of the approximation in most of the value of parameter space. This proves that the average degree of connectivity (first aggregated model) is not sufficient for characterising the evolution, and that the node degree variability has an impact on the diffusion dynamics. Remaining differences between both models give us some clues about the specific ability of individual-based model to maintain a minority behaviour which becomes a majority by an addition of stochastic effects.

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  • Sylvie Huet & Margaret Edwards & Guillaume Deffuant, 2007. "Taking into Account the Variations of Neighbourhood Sizes in the Mean-Field Approximation of the Threshold Model on a Random Network," Journal of Artificial Societies and Social Simulation, Journal of Artificial Societies and Social Simulation, vol. 10(1), pages 1-10.
    • Handle: RePEc:jas:jasssj:2006-52-2
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    1. Matthew Oremland & Reinhard Laubenbacher, 2014. "Using difference equations to find optimal tax structures on the SugarScape," Journal of Economic Interaction and Coordination, Springer;Society for Economic Science with Heterogeneous Interacting Agents, vol. 9(2), pages 233-253, October.
    2. Sylvie Huet & Floriana Gargiulo & Felicia Pratto, 2020. "Can gender inequality be created without inter-group discrimination?," PLOS ONE, Public Library of Science, vol. 15(8), pages 1-25, August.
    3. José Manuel Galán & Luis R. Izquierdo & Segismundo S. Izquierdo & José Ignacio Santos & Ricardo del Olmo & Adolfo López-Paredes & Bruce Edmonds, 2009. "Errors and Artefacts in Agent-Based Modelling," Journal of Artificial Societies and Social Simulation, Journal of Artificial Societies and Social Simulation, vol. 12(1), pages 1-1.
    4. Segismundo S. Izquierdo & Luis R. Izquierdo & Nicholas M. Gotts, 2008. "Reinforcement Learning Dynamics in Social Dilemmas," Journal of Artificial Societies and Social Simulation, Journal of Artificial Societies and Social Simulation, vol. 11(2), pages 1-1.

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