By Sven Banisch
This self-contained textual content develops a Markov chain procedure that makes the rigorous research of a category of microscopic types that designate the dynamics of complicated structures on the person point attainable. It offers a basic framework of aggregation in agent-based and similar computational versions, one that uses lumpability and data thought with a view to hyperlink the micro and macro degrees of remark. the place to begin is a microscopic Markov chain description of the dynamical strategy in entire correspondence with the dynamical habit of the agent-based version (ABM), that's acquired via contemplating the set of all attainable agent configurations because the country house of an immense Markov chain. An specific formal illustration of a ensuing “micro-chain” together with microscopic transition charges is derived for a category of versions by utilizing the random mapping illustration of a Markov technique. the kind of likelihood distribution used to enforce the stochastic a part of the version, which defines the updating rule and governs the dynamics at a Markovian point, performs a vital half within the research of “voter-like” types utilized in inhabitants genetics, evolutionary video game idea and social dynamics. The publication demonstrates that the matter of aggregation in ABMs - and the lumpability stipulations particularly - could be embedded right into a extra common framework that employs details concept to be able to determine various degrees and proper scales in advanced dynamical systems
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Synthese, 151(3), 445–475. Wolfram, S. (1983). Statistical mechanics of cellular automata. Reviews of Modern Physics, 55(3), 601–644. Wolfram, S. (2002). A new kind of science. Champaign, IL: Wolfram Media Inc. Wright, S. (1932). The roles of mutation, inbreeding, crossbreeding, and selection in evolution. In Proceedings of the Sixth International Congress on Genetics. Chapter 3 Agent-Based Models as Markov Chains This chapter spells out the most important theoretical ideas developed in this book.
Simon, H. , & Ando, A. (1961). Aggregation of variables in dynamic systems. Econometrica: Journal of The Econometric Society, 29, 111–138. , & Lavicka, H. (2003). Analytical results for the Sznajd model of opinion formation. The European Physical Journal B - Condensed Matter and Complex Systems, 35(2), 279–288. Slatkin, M. (1981). Fixation probabilities and fixation times in a subdivided population. Evolution, 35(3), 477–488. Smith, J. M. (1982). Evolution and the theory of games. Cambridge: Cambridge University Press.
ACM Siggraph Computer Graphics 21(4), 25–34. Roca, C. , Cuesta, J. , & Sánchez, A. (2009). Evolutionary game theory: Temporal and spatial effects beyond replicator dynamics. Physics of Life Reviews, 6(4), 208–249. Rogers, L. C. , & Pitman, J. W. (1981). Markov functions. The Annals of Probability, 9(4), 573–582. Rosenblatt, M. (1959). Functions of a Markov process that are Markovian. Journal of Mathematics and Mechanics, 8(4), 134–145. , & Sericola, B. (1989). On weak lumpability in Markov chains.