Comparing individual-based model of behaviour diffusion with its mean field aggregated approximation

By:  Margaret Edwards, Sylvie Huet, François Goreaud, Guillaume Deffuant (Cemagref, France)
Date: 31st March/1st April 2003
CPM Report No.: CPM-03-113

Presented at the "Model to Model" workshop, 31st March/1st April 2003, Marseille

We compare the individual-based “threshold model” of innovation diffusion (Valente 95), in the version which has been studied by P. Young, and an aggregate deterministic model 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 in different points of the parameter space. We find that the aggregate model gives a good approximation of the individual when the individual based model is very stochastic. When the individual based model is less stochastic, the behaviour of the aggregate approximation differs ; it is attracted by local equilibrium points which are not the most probable state (dominant equilibrium point) of the individual-based model. Our theoretical interpretation of this difference is  based on a study of the attractors of both dynamics.

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