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plenty of synergies to be exploited by using the two techniques together, i.e. the full
potential of each technique will not be reached until they are used in conjunction.
The remaining of this introduction outlines the structure of the chapter.
Sections 13.2, 13.3 and 13.4 are devoted to explaining in detail what we
understand by ‘computer model’, and they therefore provide the basic framework
for the rest of the chapter. In particular, Sect. 13.2 shows that a computer model
can be seen as an implementation—i.e. an explicit representation—of a certain
deterministic input–output function in a particular programming language. This
interpretation is very useful since, in particular, it will allow us to abstract from the
details of the modelling platform where the computer model has been programmed
and focus on analysing the formal model that the computer model implements.
This is clarified in Sect. 13.3, which explains that any computer model can be
re-implemented in many different formalisms (in particular, in any sophisticated
enough programming language), leading to alternative representations of the same
input–output relation.
Most computer models in the social simulation literature make use of pseudoran-
dom number generators. Section 13.4 explains that—for these cases and given our
purposes—it is useful to abstract from the details of how pseudorandom numbers
are generated and look at the computer model as an implementation of a stochastic
process. In a stochastic process, a certain input does not necessarily lead to one
certain output only; instead, there are many different paths that the process may
take with potentially different probabilities. Thus, in a stochastic process, a certain
input will generally lead to a particular probability distribution over the range of
possible outputs, rather than to a single output only. Stochastic processes are used
to formally describe how a system subjected to random events evolves through time.
Having explained our interpretation of the term ‘computer model’, Sect. 13.5
introduces and compares the two techniques to analyse formal models that are
assessed in this chapter: computer simulation and mathematical analysis. The
following two sections sketch possible ways in which each of these two techniques
can be used to obtain useful insights about the dynamics of a model. Section 13.8 is
then focused on the joint use of computer simulation and mathematical analysis. It
is shown here that the two techniques can be used together to provide a picture of the
dynamics of the model that could not be drawn by using one of the two techniques
only. Finally, our conclusions are summarised in Sect. 13.9.

13.2 Computer Models as Input–Output Functions

At the most elementary level, a computer model can be seen as an implementation—
i.e. an explicit representation—of a certain deterministic input–output function in a
particular programming language. The word ‘function’ is useful because it correctly
conveys the point that any particular input given to the computer model will lead