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that a particular input (together with the set of rules that define the model) is
sufficient to generate the output that is observed during the simulation. This first part
of the computer simulation approach is therefore, in a way, very ‘mathematical’:
outputs obtained follow with logical necessity from applying to the inputs the
algorithmic rules that define the model.
In contrast, the second part of the computer simulation approach, i.e. inferring
general patterns from particular instances of input–output pairs, can only lead
8
to probable—rather than necessarily true—conclusions. The following section
explains how to rigorously assess the confidence we can place on the conclusions
obtained using computer simulation, but the simple truth is irrefutable: inferences
obtained using generalisation by induction can potentially fail when applied to
instances that were not used to infer the general pattern. This is the domain of
statistical extrapolation.
So why bother with computer simulation at all? The answer is clear: computer
simulation enables us to study formal systems in ways that go beyond mathematical
tractability. This role should not be underestimated: most models in the social
simulation literature are mathematically intractable, and in such cases computer
simulation is our only chance to move things forward. As a matter of fact, the
formal models that many computer programs implement are often so complicated
and cumbersome that the computer code itself is not that far from being one of the
best descriptions of the formal model that can be provided.
Computer simulation can be very useful even when dealing with formal models
that are mathematically tractable. Valuable uses of computer simulation in these
cases include conducting insightful initial explorations of the model and presenting
dynamic illustrations of its results.
And there is yet another important use of computer simulation. Note that
understanding a formal model in depth requires identifying the parts of the model
(i.e. the subset of rules) that are responsible for generating particular (sub)sets of
results or properties of results. Investigating this in detail often involves changing
certain subsets of rules in the model, so one can pinpoint which subsets of
rules are necessary or sufficient to produce certain results. Importantly, changing
subsets of rules can make the original model mathematically intractable, and
in such (common) cases, computer simulation is, again, our only hope. In this
context, computer simulation can be very useful to produce counterexamples. This
approach is very common in the literature of, e.g. evolutionary game theory, where
several authors (see, e.g. Hauert and Doebeli 2004; Imhof et al. 2005; Izquierdo
and Izquierdo 2006; Lieberman et al. 2009; Nowak and May 1992; Nowak and
Sigmund 1992; Nowak and Sigmund 1993; Santos et al. 2006; Traulsen et al. 2006)
resort to computer simulations to assess the implications of assumptions made in
mathematically tractable models (e.g. the assumptions of ‘infinite populations’ and
‘random encounters’).

8 Unless, of course, all possible particular instances are explored.