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Comparing an Individual-Based Model of Behaviour Diffusion with Its Mean Field Aggregate Approximation

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Abstract

In this paper we compare a version of the individual-based “threshold model†of innovation diffusion (Valente 95) with an aggregate deterministic model that we constructed from it. The classical threshold model supposes that an individual adopts a behaviour according to a trade-off between a social pressure (the number of his neighbours adopting the behaviour) and a personal interest or resistance to change (the threshold). The aggregate model makes approximations in order to estimate the evolution of groups of individuals with the same number of neighbours of similar behaviour. We compare both models at different points of the parameter space. We find that the aggregate model gives a good approximation of the individual in some cases ; however in other cases the behaviour of the aggregate approximation differs. Using theoretical interpretation of this difference based on a study of the attractors of the aggregate model, we hypothesise that the two models have the same behaviour when the aggregate model has only one attractor and that differences can occur when it has two.

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  • Margaret Edwards & Sylvie Huet & François Goreaud & Guillaume Deffuant, 2003. "Comparing an Individual-Based Model of Behaviour Diffusion with Its Mean Field Aggregate Approximation," Journal of Artificial Societies and Social Simulation, Journal of Artificial Societies and Social Simulation, vol. 6(4), pages 1-9.
    • Handle: RePEc:jas:jasssj:2003-30-1
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    Citations

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    Cited by:

    1. Uri Wilensky & William Rand, 2007. "Making Models Match: Replicating an Agent-Based Model," Journal of Artificial Societies and Social Simulation, Journal of Artificial Societies and Social Simulation, vol. 10(4), pages 1-2.
    2. 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.
    3. 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.
    4. Mario Paolucci & Francisco Grimaldo, 2014. "Mechanism change in a simulation of peer review: from junk support to elitism," Scientometrics, Springer;Akadémiai Kiadó, vol. 99(3), pages 663-688, June.
    5. Hazhir Rahmandad & John Sterman, 2008. "Heterogeneity and Network Structure in the Dynamics of Diffusion: Comparing Agent-Based and Differential Equation Models," Management Science, INFORMS, vol. 54(5), pages 998-1014, May.
    6. Sylvie Huet & Guillaume Deffuant, 2008. "Differential Equation Models Derived from an Individual-Based Model Can Help to Understand Emergent Effects," Journal of Artificial Societies and Social Simulation, Journal of Artificial Societies and Social Simulation, vol. 11(2), pages 1-10.
    7. 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.
    8. 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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