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

• Record Nr.: UNINA9910254613503321
• Autore: Banisch Sven
• Pubbl/distr/stampa: Cham : , : Springer International Publishing : , : Imprint : Springer, , 2016
• ISBN: 3-319-24877-4
• Edizione: [1st ed. 2016.]
• Descrizione fisica: 1 online resource (XIV, 195 p. 83 illus., 18 illus. in color.)
• Collana: Understanding Complex Systems, , 1860-0832
• Disciplina: 519.233
• Soggetti: Statistical physics; System theory; Physics; Computational complexity; Applications of Nonlinear Dynamics and Chaos Theory; Complex Systems; Mathematical Methods in Physics; Complexity
• Lingua di pubblicazione: Inglese
• Formato: Materiale a stampa
• Livello bibliografico: Monografia
• Note generali: Bibliographic Level Mode of Issuance: Monograph
• Nota di contenuto: 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.
• Sommario/riassunto: 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.