Markov Chain Aggregation for Agent-Based Models

Sven Banisch (Autor)

Buch | Softcover

XIV, 195 Seiten

2018 | 1. Softcover reprint of the original 1st ed. 2016
Springer International Publishing (Verlag)
978-3-319-79691-8 (ISBN)

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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.

Erscheinungsdatum	18.06.2018
Reihe/Serie	Understanding Complex Systems
Zusatzinfo	XIV, 195 p. 83 illus., 18 illus. in color.
Verlagsort	Cham
Sprache	englisch
Maße	155 x 235 mm
Gewicht	332 g
Themenwelt	Mathematik / Informatik ► Informatik ► Theorie / Studium
	Mathematik / Informatik ► Mathematik ► Angewandte Mathematik
	Naturwissenschaften ► Physik / Astronomie ► Optik
	Naturwissenschaften ► Physik / Astronomie ► Theoretische Physik
Schlagworte	agent-based modelling • Complexity • 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
ISBN-10	3-319-79691-7 / 3319796917
ISBN-13	978-3-319-79691-8 / 9783319796918
Zustand	Neuware