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Agent-Based Models as Markov Chains

  • Sven Banisch
Chapter
Part of the Understanding Complex Systems book series (UCS)

Abstract

This chapter spells out the most important theoretical ideas developed in this book. However, it begins with an illustrative introductory description of agent-based models (ABMs) in order to provide an intuition for what follows. It then shows for a class of ABMs that, at the micro level, they give rise to random walks on regular graphs (Sect. 3.2). The transition from the micro to the macro level is formulated in Sect. 3.3. When a model is observed in terms of a certain system property, this effectively partitions the state space of the micro chains such that micro configurations with the same observable value are projected into the same macro state. The conditions for the projected process to be again a Markov chain are given which relates the symmetry structure of the micro chains to the partition induced by macroscopic observables. We close with a simple example that will be discussed further in the next chapter.

Keywords

Markov Chain Cellular Automaton Regular Graph Functional Graph Interaction Rule 
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Copyright information

© Springer International Publishing Switzerland 2016

Authors and Affiliations

  • Sven Banisch
    • 1
  1. 1.Max Planck Institute for Mathematics in the SciencesLeipzigGermany

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