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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.

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File URL: http://jasss.soc.surrey.ac.uk/12/1/6/6.pdf
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Bibliographic Info

Article provided by Journal of Artificial Societies and Social Simulation in its journal Journal of Artificial Societies and Social Simulation.

Volume (Year): 12 (2009)
Issue (Month): 1 ()
Pages: 6

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Handle: RePEc:jas:jasssj:2008-19-2

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Keywords: Computer Modelling; Simulation; Markov; Stochastic Processes; Analysis; Re-Implementation;

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Cited by:
  1. Grazzini, Jakob & Richiardi, Matteo, 2013. "Consistent Estimation of Agent-Based Models by Simulated Minimum Distance," Department of Economics and Statistics Cognetti de Martiis. Working Papers 201335, University of Turin.
  2. Edoardo Gaffeo & Mauro Gallegati & Umberto Gostoli, 2012. "An agent-based "proof of principle" for Walrasian macroeconomic theory," CEEL Working Papers 1202, Cognitive and Experimental Economics Laboratory, Department of Economics, University of Trento, Italia.
  3. Sven Banischa & Ricardo Lima & Tanya Araújo, 2012. "Agent based models and opinion dynamics as markov chains," Working Papers Department of Economics 2012/10, ISEG - School of Economics and Management, Department of Economics, University of Lisbon.
  4. 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.

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