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Markov Chain Aggregation for Agent-Based Models

  • Book
  • © 2016

Overview

Authors:
  1. Sven Banisch

    1. in the Sciences, Max Planck Institute for Mathematics in the Sciences, Leipzig, Germany

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  • Introduces and describes a new approach for modelling certain types of complex dynamical systems
  • Self-contained presentation and introductory level
  • Useful as advanced text and as self-study guide
  • Includes supplementary material: sn.pub/extras

Part of the book series: Understanding Complex Systems (UCS)

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Table of contents (10 chapters)

  1. Front Matter

    Pages i-xiv
    Download chapter PDF

  2. Introduction

    • Sven Banisch
    Pages 1-10

  3. Background and Concepts

    • Sven Banisch
    Pages 11-33

  4. Agent-Based Models as Markov Chains

    • Sven Banisch
    Pages 35-55

  5. The Voter Model with Homogeneous Mixing

    • Sven Banisch
    Pages 57-82

  6. From Network Symmetries to Markov Projections

    • Sven Banisch
    Pages 83-107

  7. Application to the Contrarian Voter Model

    • Sven Banisch
    Pages 109-126

  8. Information-Theoretic Measures for the Non-Markovian Case

    • Sven Banisch
    Pages 127-155

  9. Overlapping Versus Non-overlapping Generations

    • Sven Banisch
    Pages 157-175

  10. Aggregation and Emergence: A Synthesis

    • Sven Banisch
    Pages 177-186

  11. Conclusion

    • Sven Banisch
    Pages 187-195
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Keywords

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

Authors and Affiliations

  • in the Sciences, Max Planck Institute for Mathematics in the Sciences, Leipzig, Germany

    Sven Banisch

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