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model as a Markov chain, i.e. looking at the formal model implemented in a
computer model through Markov’s glasses, can make apparent various features of
the computer model that may not be so evident without such glasses. In particular,
as we will show later, Markov theory can be used to find out whether the initial
conditions of a model determine its asymptotic dynamics or whether they are
actually irrelevant in the long term. Also, the theory can reveal whether the model
will sooner or later be trapped in an absorbing state.

13.4 ‘Stochastic’ Computer Models as Stochastic Processes

Most computer models in the social simulation literature contain stochastic com-
ponents. This section argues that, for these cases and given our purposes, it is
convenient to revise our interpretation of computer models as deterministic input–
output relations, abstract from the (deterministic) details of how pseudorandom
numbers are generated, and reinterpret the term ‘computer model’ as an implemen-
tation of a stochastic process. This interpretation will prove useful in most cases
and, importantly, does not imply any loss of generality: even if the computer model
to be analysed does not contain any stochastic components, our interpretation will
still be valid.
In the general case, the computer model to be analysed will make use of (what
are meant to be) random numbers, i.e. the model will be stochastic. The word
‘stochastic’ requires some clarification. Strictly speaking, there does not exist a
truly stochastic computer model, but one can approximate randomness to a very
satisfactory extent by using pseudorandom number generators. The pseudorandom
number generator is a deterministic algorithm that takes as input a value called the
random seed and generates a sequence of numbers that approximates the properties
of random numbers. The sequence is not truly random in that it is completely
determined by the value used to initialise the algorithm, i.e. the random seed.
Therefore, if given the same random seed, the pseudorandom number generator will
produce exactly the same sequence of (pseudorandom) numbers. (This fact is what
made us define a computer model as an implementation of a certain deterministic
input–output function in Sect. 13.2.)
Fortunately, the sequences of numbers provided by current off-the-shelf pseu-
dorandom number generators approximate randomness remarkably well. This
basically means that, for most intents and purposes in this discipline, it seems safe to
assume that the pseudorandom numbers generated in one simulation run will follow
the intended probability distributions to a satisfactory degree. The only problem we
might encounter appears when running several simulations which we would like
to be statistically independent. As mentioned above, if we used the same random
seed for every run, we would obtain the same sequence of pseudorandom numbers,
i.e. we would obtain exactly the same results. How can we truly randomly select a
random seed? Fortunately, for most applications in this discipline, the state of the
computer system at the time of starting a new run can be considered a truly random