From Network Symmetries to Markov Projections

Abstract

In the third chapter, we have seen that an agent-based model (ABM) defines a process of change at the individual level—a micro process—by which in each time step one configuration of individuals is transformed into another configuration. For a class of models we have shown this micro process to be a Markov chain on the space of all possible agent configurations. Moreover, we have shown that the full aggregation—that is, the re-formulation of the model by mere aggregation over the individual attributes of all agents—may give rise to a new process that is again a Markov chain, however, only under the rather restrictive assumption of homogeneous mixing. Heterogeneities in the micro description, in general, destroy the Markov property of the macro process obtained by such a full aggregation.