Techniques to Understand Computer Simulations

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 inputoutput 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.