Influence of space and time dimensions in multi-agent models of the free-riding collective phenomenon

This report discusses how considering spatial and temporal dimensions at the modelling stage may have an influence on the outcome of the study in collective phenomena. We compared different models built on the same initial individual behaviour hypothesis of one collective phenomenon known as ''free-riding'' (that can be observed in peer-to-peer file sharing networks). % This can be present in peer-to-peer file sharing networks. Those models are conceived to answer questions related to the convergence and stabilization of the sharing behaviour of the users in those networks, where the non-cooperative behaviour of a subset of users may lead to the collapse of the entire network. Building up from this same individual behaviour, we study one global analytical model and four multi-agent models, the latter ones adding space and time dimensions, which are rarely seen in the literature discussing aggregated models of the collective phenomenon in question. After discussing the \textit{a priori} and the experimental conditions under which the models are equivalent, we show that the same individual decision algorithm can lead to contradictory information and results