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Techniques to Understand Computer Simulations: Markov Chain Analysis

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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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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  1. Roberto Leombruni & Matteo Richiardi & Nicole J. Saam & Michele Sonnessa, 2005. "A Common Protocol for Agent-Based Social Simulation," LABORatorio R. Revelli Working Papers Series 47, LABORatorio R. Revelli, Centre for Employment Studies.
  2. M.A. Nowak & K. Sigmund, 1998. "Evolution of Indirect Reciprocity by Image Scoring/ The Dynamics of Indirect Reciprocity," Working Papers ir98040, International Institute for Applied Systems Analysis.
  3. Andreas Flache & Rainer Hegselmann, 2001. "Do Irregular Grids Make a Difference? Relaxing the Spatial Regularity Assumption in Cellular Models of Social Dynamics," Journal of Artificial Societies and Social Simulation, Journal of Artificial Societies and Social Simulation, vol. 4(4), pages 6.
  4. Leombruni, Roberto & Richiardi, Matteo, 2005. "Why are economists sceptical about agent-based simulations?," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 355(1), pages 103-109.
  5. Wolfgang Balzer & Karl R. Brendel & Solveig Hofmann, 2001. "Bad Arguments in the Comparison of Game Theory and Simulation in Social Studies," Journal of Artificial Societies and Social Simulation, Journal of Artificial Societies and Social Simulation, vol. 4(2), pages 1.
  6. Juan Carlos González-Avella & Mario G. Cosenza & Konstantin Klemm & Víctor M. Eguíluz & Maxi San Miguel, 2007. "Information Feedback and Mass Media Effects in Cultural Dynamics," Journal of Artificial Societies and Social Simulation, Journal of Artificial Societies and Social Simulation, vol. 10(3), pages 9.
  7. Andreas Flache & Rainer Hegselmann, 1998. "Understanding Complex Social Dynamics: a Plea for Cellular Automata Based Modelling," Journal of Artificial Societies and Social Simulation, Journal of Artificial Societies and Social Simulation, vol. 1(3), pages 1.
  8. Young, H Peyton, 1993. "The Evolution of Conventions," Econometrica, Econometric Society, vol. 61(1), pages 57-84, January.
  9. Epstein, Joshua M., 2006. "Remarks on the Foundations of Agent-Based Generative Social Science," Handbook of Computational Economics, in: Leigh Tesfatsion & Kenneth L. Judd (ed.), Handbook of Computational Economics, edition 1, volume 2, chapter 34, pages 1585-1604 Elsevier.
  10. Schelling, Thomas C, 1969. "Models of Segregation," American Economic Review, American Economic Association, vol. 59(2), pages 488-93, May.
  11. Klemm, Konstantin & Eguiluz, Victor M. & Toral, Raul & Miguel, Maxi San, 2005. "Globalization, polarization and cultural drift," Journal of Economic Dynamics and Control, Elsevier, vol. 29(1-2), pages 321-334, January.
  12. Vega-Redondo,Fernando, 2003. "Economics and the Theory of Games," Cambridge Books, Cambridge University Press, number 9780521772518, Junio.
  13. John H. Miller & Scott E. Page, 2007. "Complexity in Social Worlds, from Complex Adaptive Systems: An Introduction to Computational Models of Social Life," Introductory Chapters, in: Complex Adaptive Systems: An Introduction to Computational Models of Social Life Princeton University Press.
  14. Axelrod, Robert & Bennett, D. Scott, 1993. "A Landscape Theory of Aggregation," British Journal of Political Science, Cambridge University Press, vol. 23(02), pages 211-233, April.
  15. N. Emrah Aydinonat, 2007. "Models, conjectures and exploration: an analysis of Schelling's checkerboard model of residential segregation," Journal of Economic Methodology, Taylor & Francis Journals, vol. 14(4), pages 429-454.
  16. Segismundo S. Izquierdo & Luis R. Izquierdo & Nicholas M. Gotts, 2008. "Reinforcement Learning Dynamics in Social Dilemmas," Journal of Artificial Societies and Social Simulation, Journal of Artificial Societies and Social Simulation, vol. 11(2), pages 1.
  17. José Manuel Galán & Luis R. Izquierdo, 2005. "Appearances Can Be Deceiving: Lessons Learned Re-Implementing Axelrod's 'Evolutionary Approach to Norms'," Journal of Artificial Societies and Social Simulation, Journal of Artificial Societies and Social Simulation, vol. 8(3), pages 2.
  18. Robert Axelrod & Will Mitchell & Robert E. Thomas & D. Scott Bennett & Erhard Bruderer, 1995. "Coalition Formation in Standard-Setting Alliances," Management Science, INFORMS, vol. 41(9), pages 1493-1508, September.
  19. John H. Miller & Scott E. Page, 2007. "Social Science in Between, from Complex Adaptive Systems: An Introduction to Computational Models of Social Life," Introductory Chapters, in: Complex Adaptive Systems: An Introduction to Computational Models of Social Life Princeton University Press.
  20. Arthur, W Brian, 1989. "Competing Technologies, Increasing Returns, and Lock-In by Historical Events," Economic Journal, Royal Economic Society, vol. 99(394), pages 116-31, March.
  21. Glenn Ellison, 2000. "Basins of Attraction, Long-Run Stochastic Stability, and the Speed of Step-by-Step Evolution," Review of Economic Studies, Oxford University Press, vol. 67(1), pages 17-45.
  22. Joshua M. Epstein & Robert L. Axtell, 1996. "Growing Artificial Societies: Social Science from the Bottom Up," MIT Press Books, The MIT Press, edition 1, volume 1, number 0262550253, March.
  23. Felix Flentge & Daniel Polani & Thomas Uthmann, 2001. "Modelling the Emergence of Possession Norms Using Memes," Journal of Artificial Societies and Social Simulation, Journal of Artificial Societies and Social Simulation, vol. 4(4), pages 3.
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