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:
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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