MARKOV CHAIN AGGREGATION FOR SIMPLE AGENT-BASED MODELS ON SYMMETRIC NETWORKS: THE VOTER MODEL

Authored by Ricardo Lima, Sven Banisch

Date Published: 2015

DOI: 10.1142/s0219525915500113

Sponsors: European Union German Federal Ministry of Education and Research (BMBF)

Platforms: No platforms listed

Model Documentation: Other Narrative Mathematical description

Model Code URLs: Model code not found

Abstract

For Agent-based models, in particular the Voter Model (VM), a general framework of aggregation is developed which exploits the symmetries of the agent network G. Depending on the symmetry group Aut(omega)(N) of the weighted agent network, certain ensembles of agent configurations can be interchanged without affecting the dynamical properties of the VM. These configurations can be aggregated into the same macro state and the dynamical process projected onto these states is, contrary to the general case, still a Markov chain. The method facilitates the analysis of the relation between microscopic processes and a their aggregation to a macroscopic level of description and informs about the complexity of a system introduced by heterogeneous interaction relations. In some cases the macro chain is solvable.
Tags
Opinion dynamics Distance