A standard form of citation of this article is:
Izquierdo, Luis R., Izquierdo, Segismundo S., Galán, José Manuel and Santos, José Ignacio (2009). 'Techniques to Understand Computer Simulations: Markov Chain Analysis'. Journal of Artificial Societies and Social Simulation 12(1)6 <https://www.jasss.org/12/1/6.html>.
The following can be copied and pasted into a Bibtex bibliography file, for use with the LaTeX text processor:
@article{izquierdo,
title = {Techniques to Understand Computer Simulations: Markov Chain Analysis},
author = {Izquierdo, Luis R. and Izquierdo, Segismundo S. and Gal\'{a}n, Jos\'{e} Manuel and Santos, Jos\'{e} Ignacio},
journal = {Journal of Artificial Societies and Social Simulation},
ISSN = {1460-7425},
volume = {12},
number = {1},
pages = {6},
year = {2009},
URL = {https://www.jasss.org/12/1/6.html},
keywords = {Computer Modelling, Simulation, Markov, Stochastic Processes, Analysis, Re-Implementation},
abstract = {The aim of this paper is to assist researchers in understanding the dynamics of simulation models that have been implemented and can be run in a computer, i.e. computer models. To do that, we start by explaining (a) that computer models are just input-output functions, (b) that every computer model can be re-implemented in many different formalisms (in particular in most programming languages), leading to alternative representations of the same input-output relation, and (c) that many computer models in the social simulation literature can be usefully represented as time-homogeneous Markov chains. Then we argue that analysing a computer model as a Markov chain can make apparent many features of the model that were not so evident before conducting such analysis. To prove this point, we present the main concepts needed to conduct a formal analysis of any time-homogeneous Markov chain, and we illustrate the usefulness of these concepts by analysing 10 well-known models in the social simulation literature as Markov chains. These models are:
• Schelling's (1971) model of spatial segregation
• Epstein and Axtell's (1996) Sugarscape
• Miller and Page's (2004) standing ovation model
• Arthur's (1989) model of competing technologies
• Axelrod's (1986) metanorms models
• Takahashi's (2000) model of generalized exchange
• Axelrod's (1997) model of dissemination of culture
• Kinnaird's (1946) truels
• Axelrod and Bennett's (1993) model of competing bimodal coalitions
• Joyce et al.'s (2006) model of conditional association
In particular, we explain how to characterise the transient and the asymptotic dynamics of these computer models and, where appropriate, how to assess the stochastic stability of their absorbing states. In all cases, the analysis conducted using the theory of Markov chains has yielded useful insights about the dynamics of the computer model under study.},
}The following can be copied and pasted into a text file, which can then be imported into a reference database that supports imports using the RIS format, such as Reference Manager and EndNote.
TY - JOUR
TI - Techniques to Understand Computer Simulations: Markov Chain Analysis
AU - Izquierdo, Luis R.
AU - Izquierdo, Segismundo S.
AU - Galán, José Manuel
AU - Santos, José Ignacio
Y1 - 2009
JO - Journal of Artificial Societies and Social Simulation
SN - 1460-7425
VL - 12
IS - 1
SP - 6
UR - https://www.jasss.org/12/1/6.html
KW - Computer Modelling
KW - Simulation
KW - Markov
KW - Stochastic Processes
KW - Analysis
KW - Re-Implementation
N2 - The aim of this paper is to assist researchers in understanding the dynamics of simulation models that have been implemented and can be run in a computer, i.e. computer models. To do that, we start by explaining (a) that computer models are just input-output functions, (b) that every computer model can be re-implemented in many different formalisms (in particular in most programming languages), leading to alternative representations of the same input-output relation, and (c) that many computer models in the social simulation literature can be usefully represented as time-homogeneous Markov chains. Then we argue that analysing a computer model as a Markov chain can make apparent many features of the model that were not so evident before conducting such analysis. To prove this point, we present the main concepts needed to conduct a formal analysis of any time-homogeneous Markov chain, and we illustrate the usefulness of these concepts by analysing 10 well-known models in the social simulation literature as Markov chains. These models are: • Schelling's (1971) model of spatial segregation • Epstein and Axtell's (1996) Sugarscape • Miller and Page's (2004) standing ovation model • Arthur's (1989) model of competing technologies • Axelrod's (1986) metanorms models • Takahashi's (2000) model of generalized exchange • Axelrod's (1997) model of dissemination of culture • Kinnaird's (1946) truels • Axelrod and Bennett's (1993) model of competing bimodal coalitions • Joyce et al.'s (2006) model of conditional association In particular, we explain how to characterise the transient and the asymptotic dynamics of these computer models and, where appropriate, how to assess the stochastic stability of their absorbing states. In all cases, the analysis conducted using the theory of Markov chains has yielded useful insights about the dynamics of the computer model under study.
ER -