Bültmann & Gerriets
Markov Chain Aggregation for Agent-Based Models
von Sven Banisch
Verlag: Springer International Publishing
Reihe: Understanding Complex Systems
Gebundene Ausgabe
ISBN: 978-3-319-24875-2
Auflage: 1st ed. 2016
Erschienen am 05.01.2016
Sprache: Englisch
Format: 241 mm [H] x 160 mm [B] x 18 mm [T]
Gewicht: 489 Gramm
Umfang: 212 Seiten

Preis: 80,24 €
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Klappentext
Inhaltsverzeichnis

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



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.


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