Cellular automata modelling of direct selling multilevel marketing dynamics

<div> This paper deals with the development of a new cellular automatabased model to describe the dynamics of direct selling, multilevel marketing companies. While many cellular automata models have been developed in the field of theoretical marketing, direct selling with multilevel marketing has not been addressed up to now. This specific marketing technique requires to account for both spatial spreading and the internal dynamics of each cell, in which six types of individuals are defined. The associated populations in each cell evolve using a new proposed aggregated-level model made of discrete time equations based on a mix of classical social contagion models and Boltzmann-inspired relaxationreaction models. The proposed model is able to account for spatial spreading via weak social ties on a Moore neighbourhood, along with internal dynamics (growth, decay and equilibrium) of the six interacting populations in each cell. The model incorporates user-defined parameters that allow to model the dynamics of a given company via parameter fitting. </div>