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.
%0 Journal Article
%1 Izquierdo:2009:jasss
%A Izquierdo, Luis R.
%A Izquierdo, Segismundo S.
%A Galán, José Manuel
%A Santos, José Ignacio
%D 2009
%J J. of Artif. Societies and Social Sim.
%K imported thesis
%N 1
%T Techniques to Understand Computer Simulations: Markov Chain Analysis
%U http://jasss.soc.surrey.ac.uk/12/1/6.html
%V 12
%X 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.
@article{Izquierdo:2009:jasss,
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.},
added-at = {2017-03-16T11:50:55.000+0100},
author = {Izquierdo, Luis R. and Izquierdo, Segismundo S. and Gal\'an, Jos\'e Manuel and Santos, Jos\'e Ignacio},
biburl = {https://www.bibsonomy.org/bibtex/20e72381ec9d2e7013711c0a2fe6528f6/krevelen},
interhash = {1c67fe657d65ce0b3f5ba4d98910a8c8},
intrahash = {0e72381ec9d2e7013711c0a2fe6528f6},
journal = {J. of Artif. Societies and Social Sim.},
keywords = {imported thesis},
number = 1,
owner = {Rick},
timestamp = {2017-03-16T11:54:14.000+0100},
title = {Techniques to Understand Computer Simulations: Markov Chain Analysis},
url = {http://jasss.soc.surrey.ac.uk/12/1/6.html},
volume = 12,
year = 2009
}