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Markov chain aggregation for agent-b...

Banisch, Sven.

Markov chain aggregation for agent-based models

Record Type:	Electronic resources : Monograph/item
Title/Author:	Markov chain aggregation for agent-based modelsby Sven Banisch.
Author:	Banisch, Sven.
Published:	Cham :Springer International Publishing :2016.
Description:	xiv, 195 p. :ill., digital ;24 cm.
Contained By:	Springer eBooks
Subject:	Markov processes.
Online resource:	http://dx.doi.org/10.1007/978-3-319-24877-6
ISBN:	9783319248776$q(electronic bk.)

Markov chain aggregation for agent-based models
Banisch, Sven.

Markov chain aggregation for agent-based models[electronic resource] /by Sven Banisch. - Cham :Springer International Publishing :2016. - xiv, 195 p. :ill., digital ;24 cm. - Understanding complex systems,1860-0832. - Understanding complex systems..

Introduction -- Background and Concepts -- Agent-based Models as Markov Chains -- The Voter Model with Homogeneous Mixing -- From Network Symmetries to Markov Projections -- Application to the Contrarian Voter Model -- Information-Theoretic Measures for the Non-Markovian Case -- Overlapping Versus Non-Overlapping Generations -- Aggretion and Emergence: A Synthesis -- Conclusion.

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.

ISBN: 9783319248776$q(electronic bk.)

Standard No.: 10.1007/978-3-319-24877-6doiSubjects--Topical Terms:

181910
Markov processes.

LC Class. No.: QA274.7

Dewey Class. No.: 519.233

Markov chain aggregation for agent-based models
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245 1 0 $a Markov chain aggregation for agent-based models $h [electronic resource] / $c by Sven Banisch.
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490 1 $a Understanding complex systems, $x 1860-0832
505 0 $a Introduction -- Background and Concepts -- Agent-based Models as Markov Chains -- The Voter Model with Homogeneous Mixing -- From Network Symmetries to Markov Projections -- Application to the Contrarian Voter Model -- Information-Theoretic Measures for the Non-Markovian Case -- Overlapping Versus Non-Overlapping Generations -- Aggretion and Emergence: A Synthesis -- Conclusion.
520 $a 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.
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