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Agent Based Modeling, Mathematical Formalism for

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Encyclopedia of Complexity and Systems Science

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Definition of the Subject

Agent‐based simulations are generative or computational approachesused for analyzing “complex systems .” What is a “system?”Examples of systems include a collection of molecules in a container,the population in an urban area, and the brokers in a stockmarket. The entities or agents in these three systems would bemolecules, individuals and stock brokers, respectively. The agents insuch systems interact in the sense that molecules collide, individualscome into contact with other individuals and brokers tradeshares. Such systems, often called multiagent systems , are notnecessarily complex. The label “complex” is typically attached toa system if the number of agents is large, if the agent interactions areinvolved, or if there is a large degree of heterogeneity in agentcharacter or their interactions.

This is of course not an attempt to define a complex system.Currently there is no generally agreed upon definition of complexsystems. It is not the goal of this...

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Abbreviations

Agent‐based simulation:

An agent‐based simulation of a complexsystem is a computer model that consists of a collection ofagents/variables that can take on a typically finite collection ofstates. The state of an agent at a given point in time is determinedthrough a collection of rules that describe the agent's interactionwith other agents. These rules may be deterministic or stochastic.The agent's state depends on the agent's previous state and the stateof a collection of other agents with whom it interacts.

Mathematical framework:

A mathematical framework for agent‐basedsimulation consists of a collection of mathematical objects that areconsidered mathematical abstractions of agent‐based simulations. Thiscollection of objects should be general enough to capture the keyfeatures of most simulations, yet specific enough to allow thedevelopment of a mathematical theory with meaningful results andalgorithms.

Finite dynamical system:

A finite dynamical system isa time‐discrete dynamical system on a finite state set. That is, it isa mapping from a Cartesian product of finitely many copies of a finiteset to itself. This finite set is often considered to be a field.The dynamics is generated by iteration of the mapping.

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Author information

Authors and Affiliations

  1. Virginia Bioinformatics Institute, Virginia Polytechnic Institute and State University, Virginia, USA

    Reinhard Laubenbacher, Abdul S. Jarrah & Henning S. Mortveit

  2. Department of Computer Science, University at Albany – State University of New York, New York, USA

    S.S. Ravi

Authors
  1. Reinhard Laubenbacher
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  2. Abdul S. Jarrah
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  3. Henning S. Mortveit
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  4. S.S. Ravi
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Editors and Affiliations

  1. RAMTECH LIMITED, 122 Escalle Lane, Larkspur, CA, 94939, USA

    Robert A. Meyers Ph. D. (Editor-in-Chief) (Editor-in-Chief)

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Laubenbacher, R., Jarrah, A.S., Mortveit, H.S., Ravi, S. (2009). Agent Based Modeling, Mathematical Formalism for. In: Meyers, R. (eds) Encyclopedia of Complexity and Systems Science. Springer, New York, NY. https://doi.org/10.1007/978-0-387-30440-3_10

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