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Fig. 13.3 In general terms, mathematical analysis tends to examine the rules that define the formal
model directly. In contrast, computer simulation tries to infer general properties of such rules by
looking at the outputs they produce when applied to particular instances of the input space

the mathematics employed). The aim when using mathematical analysis is usually
to ‘solve’ the formal system (or, most often, certain aspects of it) by producing
general closed-form solutions that can be applied to any instance of the whole
input set (or, at least, to large portions of the input set). Since the inferences
obtained with mathematical analysis pertain to the rules themselves, such inferences
can be safely particularised to any specific parameterisation of the model, even
if such a parameterisation was never explicitly contemplated when analysing the
model mathematically. This greatly facilitates conducting sensitivity analyses and
assessing the robustness of the model.
Computer simulation is a rather different approach to the characterisation of the
formal model (Epstein 2006;Axelrod 1997a). When using computer simulation, one
often treats the formal model as a black box, i.e. a somewhat obscure abstract entity
that returns certain outputs when provided with inputs. Thus, the path to understand
the behaviour of the model consists in obtaining many input–output pairs and—
using generalisation by induction—inferring general patterns about how the rules
transform the inputs into the outputs (i.e. how the formal model works).
Importantly, the execution of a simulation run, i.e. the logical process that trans-
forms any (potentially stochastic) given input into its corresponding (potentially
stochastic) output, is pure deduction (i.e. strict application of the formal rules that
define the model). Thus, running the model in a computer provides a formal proof