Markov chain aggregation for agent-based models [electronic resource] / Sven Banisch.

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Markov chain aggregation for agent-based models [electronic resource] / Sven Banisch.

9783319248776 (electronic book)
3319248774 (electronic book)
9783319248752

Cham : Springer, 2016.

English

1 online resource (xiv, 195 pages) : illustrations.

10.1007/978-3-319-24877-6 doi

QA274.7

519.2/33

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 ℓ́ℓmicro-chainℓ́ℓ 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 ℓ́ℓvoter-likeℓ́ℓ 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.

Includes bibliographical references.

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Online resource; title from PDF title page (SpringerLink, viewed January 7, 2016).

Understanding complex systems.
Springer complexity.

Print version: 9783319248752

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