Advertisement

Aggregation and Emergence in Agent-Based Models: A Markov Chain Approach

  • Sven Banisch
  • Ricardo Lima
  • Tanya Araújo
Part of the Springer Proceedings in Complexity book series (SPCOM)

Abstract

We analyze the dynamics of agent-based models (ABMs) from a Markovian perspective and derive explicit statements about the possibility of linking a microscopic agent model to the dynamical processes of macroscopic observables that are useful for a precise understanding of the model dynamics. In this way the dynamics of collective variables may be studied, and a description of macro dynamics as emergent properties of micro dynamics, in particular during transient times, is possible.

References

  1. 1.
    Axelrod R (1997) The dissemination of culture: a model with local convergence and global polarization. J Confl Resolut 41(2):203–226 CrossRefGoogle Scholar
  2. 2.
    Banisch S, Lima R, Araújo T (2012) Agent based models and opinion dynamics as Markov chains. Soc Netw. doi: 10.1016/j.socnet.2012.06.001 Google Scholar
  3. 3.
    Banisch S, Lima R (2012, forthcoming) Markov projections of the Voter model. arXiv:1209.3902 [physics.soc-ph]
  4. 4.
    Castellano C, Fortunato S, Loreto V (2009) Statistical physics of social dynamics. Rev Mod Phys 81(2):591–646 ADSCrossRefGoogle Scholar
  5. 5.
    Chazottes J-R, Ugalde E (2003) Projection of Markov measures may be Gibbsian. J Stat Phys 111(5–6). doi: 10.1023/A:1023056317067
  6. 6.
    Epstein JM, Axtell R (1996) Growing artificial societies: social science from the bottom up. The Brookings Institution, Washington Google Scholar
  7. 7.
    Izquierdo LR, Izquierdo SS, Galán JM, Santos JI (2009) Techniques to understand computer simulations: Markov chain analysis. J Artif Soc Soc Simul 12(1):6 Google Scholar
  8. 8.
    Kemeny JG, Snell JL (1976) Finite Markov chains. Springer, Berlin zbMATHGoogle Scholar
  9. 9.
    Kimura M, Weiss GH (1964) The stepping stone model of population structure and the decrease of genetic correlation with distance. Genetics 49:561–576 Google Scholar
  10. 10.
    Levin DA, Peres Y, Wilmer EL (2009) Markov chains and mixing times. AMS, Providence zbMATHGoogle Scholar
  11. 11.
    Schelling T (1971) Dynamic models of segregation. J Math Sociol 1(2):143–186 CrossRefGoogle Scholar

Copyright information

© Springer International Publishing Switzerland 2013

Authors and Affiliations

  • Sven Banisch
    • 1
  • Ricardo Lima
    • 2
  • Tanya Araújo
    • 3
    • 4
  1. 1.Mathematical PhysicsBielefeld UniversityBielefeldGermany
  2. 2.Dream & Science FactoryMarseillesFrance
  3. 3.ISEG—Technical University of Lisbon (TULisbon)LisbonPortugal
  4. 4.Research Unit on Complexity in Economics (UECE)LisbonPortugal

Personalised recommendations