Agent-Based Models as Markov Chains

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


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.


Markov Chain Cellular Automaton Regular Graph Functional Graph Interaction Rule 
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  1. Banisch, S., Lima, R., & Araújo, T. (2012). Agent based models and opinion dynamics as Markov chains. Social Networks, 34, 549–561.CrossRefGoogle Scholar
  2. Chazottes, J.-R., & Ugalde, E. (2003). Projection of Markov measures may be Gibbsian. Journal of Statistical Physics, 111(5/6), 1245–1272.MathSciNetCrossRefzbMATHGoogle Scholar
  3. Epstein, J. M. (2006). Remarks on the foundations of agent-based generative social science. In L. Tesfatsion & K. L. Judd (Eds.), Handbook of computational economics: Agent-based computational economics (Vol. 2, pp. 1585–1604). New York: Elsevier.Google Scholar
  4. Epstein, J. M., & Axtell, R. (1996). Growing artificial societies: Social science from the bottom up. Washington, DC: The Brookings Institution.Google Scholar
  5. Flajolet, P., & Odlyzko, A. M. (1990). Random mapping statistics. In Advances in cryptology (pp. 329–354). Heidelberg: Springer.Google Scholar
  6. Humphreys, P. (2008). Synchronic and diachronic emergence. Minds and Machines, 18(4), 431–442.CrossRefGoogle Scholar
  7. Izquierdo, L. R., Izquierdo, S. S., Galán, J. M., & Santos, J. I. (2009). Techniques to understand computer simulations: Markov chain analysis. Journal of Artificial Societies and Social Simulation, 12(1), 6.Google Scholar
  8. Kemeny, J. G., & Snell, J. L. (1976). Finite Markov chains. Berlin: Springer.zbMATHGoogle Scholar
  9. Levin, D. A., Peres, Y., & Wilmer, E. L. (2009). Markov chains and mixing times. Providence, R.I.: American Mathematical Society.zbMATHGoogle Scholar
  10. Macy, M. W., & Willer, R. (2002). From factors to actors: Computational sociology and agent-based modeling. Annual Review of Sociology, 28(1), 143–166.CrossRefGoogle Scholar
  11. Moran, P. A. P. (1958). Random processes in genetics. Proceedings of the Cambridge Philosophical Society, 54, 60–71Google Scholar
  12. Squazzoni, F. (2008). The micro-macro link in social simulation. Sociologica, 2(1).Google Scholar

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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