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achieve any arbitrary level of accuracy in our computational approximations by
running the model sufficiently many times.
Bearing in mind the relative strengths and limitations of both approaches, this
chapter explains three different ways in which mathematical analysis and computer
simulation can be usefully combined to produce a better understanding of the
dynamics of computer models. In doing so, it becomes clear that mathematical
analysis and computer simulation should not be regarded as alternative—or even
opposed—approaches to the formal study of social systems but as complementary.
Not only can they provide fundamentally different insights on the same model, but
they can also produce hints for solutions for each other. In short, there are plenty of
synergies to be exploited by using the two techniques together, so the full potential
of each technique cannot be reached unless they are used in conjunction.

Why Read This Chapter?
This chapter is about how to better understand the dynamics of computer models
using both simulation and mathematical analysis. The starting point is a computer
model which is already implemented and ready to be run; the objective is to gain
a thorough understanding of its dynamics. Combining computer simulation with
mathematical analysis can help to provide a picture of the model dynamics that
could not be drawn by only using one of the two techniques.

13.1 Introduction

This chapter is about how to better understand the dynamics of computer models
using both simulation and mathematical analysis. Our starting point is a computer
model which is already implemented and ready to be run; our objective is to gain
a thorough understanding of its dynamics. Thus, this chapter is not about how to
design, implement, verify or validate a model; this chapter is about how to better
understand its behaviour.
Naturally, we start by clearly defining our object of study: a computer model.
The term ‘computer model’ can be understood in many different ways—i.e. seen
from many different perspectives—and not all of them are equally useful for every
possible purpose. Thus, we start by interpreting the term ‘computer model’ in a
way that will prove useful for our objective: to characterise and understand its
behaviour. Once our object of study has been clearly defined, we then describe
two techniques that are particularly useful to understand the dynamics of computer
models: mathematical analysis and computer simulation.
In particular, this chapter will show that mathematical analysis and computer
simulation should not be regarded as alternative—or even opposed—approaches to
the formal study of social systems but as complementary (Gotts et al. 2003, b). They
are both extremely useful tools to analyse formal models, and they are certainly
complementary in the sense that they can provide fundamentally different insights
on the same model. Even more importantly, this chapter will show that there are