Markov Chain Aggregation for Agent-Based Models

  • Sven Banisch

Part of the Understanding Complex Systems book series (UCS)

Table of contents

  1. Front Matter
    Pages i-xiv
  2. Sven Banisch
    Pages 1-10
  3. Sven Banisch
    Pages 11-33
  4. Sven Banisch
    Pages 35-55
  5. Sven Banisch
    Pages 57-82
  6. Sven Banisch
    Pages 109-126
  7. Sven Banisch
    Pages 177-186
  8. Sven Banisch
    Pages 187-195

About this book


This self-contained text develops a Markov chain approach that makes the rigorous analysis of a class of microscopic models that specify the dynamics of complex systems at the individual level possible. It presents a general framework of aggregation in agent-based and related computational models, one which makes use of lumpability and information theory in order to link the micro and macro levels of observation. The starting point is a microscopic Markov chain description of the dynamical process in complete correspondence with the dynamical behavior of the agent-based model (ABM), which is obtained by considering the set of all possible agent configurations as the state space of a huge Markov chain. An explicit formal representation of a resulting “micro-chain” including microscopic transition rates is derived for a class of models by using the random mapping representation of a Markov process. The type of probability distribution used to implement the stochastic part of the model, which defines the updating rule and governs the dynamics at a Markovian level, plays a crucial part in the analysis of “voter-like” models used in population genetics, evolutionary game theory and social dynamics. The book demonstrates that the problem of aggregation in ABMs - and the lumpability conditions in particular - can be embedded into a more general framework that employs information theory in order to identify different levels and relevant scales in complex dynamical systems


Agent-based Modelling Contrarian Voter Model Dynamics of Complex Systems Lumpability and State-space Reduction Markov Processes Microscopic Markov Chains Scaling of Complex Dynamical Systems Voter-like Models

Authors and affiliations

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

Bibliographic information