Markov Chain Aggregation for Agent-Based Models / by Sven Banisch.

Format:

Book

Author/Creator:

Banisch, Sven., Author.

Series:

Understanding Complex Systems, 1860-0832

Language:

English

Subjects (All):

Statistical physics.

System theory.

Physics.

Computational complexity.

Applications of Nonlinear Dynamics and Chaos Theory.

Complex Systems.

Mathematical Methods in Physics.

Complexity.

Local Subjects:

Applications of Nonlinear Dynamics and Chaos Theory.

Complex Systems.

Mathematical Methods in Physics.

Complexity.

Physical Description:

1 online resource (XIV, 195 p. 83 illus., 18 illus. in color.)

Edition:

1st ed. 2016.

Place of Publication:

Cham : Springer International Publishing : Imprint: Springer, 2016.

Language Note:

English

Summary:

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.

Contents:

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.

Notes:

Bibliographic Level Mode of Issuance: Monograph

Description based on publisher supplied metadata and other sources.

ISBN:

3-319-24877-4

OCLC:

1066177239