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Techniques to Understand Computer Simulations: Markov Chain Analysis

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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.

Suggested Citation

  • Luis R. Izquierdo & Segismundo S. Izquierdo & José Manuel Galán & José Ignacio Santos, 2009. "Techniques to Understand Computer Simulations: Markov Chain Analysis," Journal of Artificial Societies and Social Simulation, Journal of Artificial Societies and Social Simulation, vol. 12(1), pages 1-6.
  • Handle: RePEc:jas:jasssj:2008-19-2
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    File URL: http://jasss.soc.surrey.ac.uk/12/1/6/6.pdf
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    References listed on IDEAS

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    Citations

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    Cited by:

    1. Sven Banischa & Ricardo Lima & Tanya Araújo, 2012. "Agent based models and opinion dynamics as markov chains," Working Papers Department of Economics 2012/10, ISEG - Lisbon School of Economics and Management, Department of Economics, Universidade de Lisboa.
    2. repec:eee:jeborg:v:140:y:2017:i:c:p:70-90 is not listed on IDEAS
    3. Pfau, Jens & Kirley, Michael & Kashima, Yoshihisa, 2013. "The co-evolution of cultures, social network communities, and agent locations in an extension of Axelrod’s model of cultural dissemination," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 392(2), pages 381-391.
    4. José Manuel Galán & Luis R. Izquierdo & Segismundo S. Izquierdo & José Ignacio Santos & Ricardo del Olmo & Adolfo López-Paredes & Bruce Edmonds, 2009. "Errors and Artefacts in Agent-Based Modelling," Journal of Artificial Societies and Social Simulation, Journal of Artificial Societies and Social Simulation, vol. 12(1), pages 1-1.
    5. Grazzini, Jakob & Richiardi, Matteo, 2015. "Estimation of ergodic agent-based models by simulated minimum distance," Journal of Economic Dynamics and Control, Elsevier, vol. 51(C), pages 148-165.
    6. Jakob Grazzini & Matteo G. Richiardi, 2013. "Consistent Estimation of Agent-Based Models by Simulated Minimum Distance," LABORatorio R. Revelli Working Papers Series 130, LABORatorio R. Revelli, Centre for Employment Studies.
    7. Michele Catalano & Corrado Di Guilmi, 2016. "Uncertainty, rationality and complexity in a multi sectoral dynamic model: the Dynamic Stochastic Generalized Aggregation approach," CAMA Working Papers 2016-16, Centre for Applied Macroeconomic Analysis, Crawford School of Public Policy, The Australian National University.
    8. Giovanna Devetag & Hykel Hosni & Giacomo Sillari, 2012. "You Better Play 7: Mutual versus Common Knowledge of Advice in a Weak-link Experiment," LEM Papers Series 2012/01, Laboratory of Economics and Management (LEM), Sant'Anna School of Advanced Studies, Pisa, Italy.

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