1 What is Complexity?
Firstly one has to distinguish what complexity is and what may cause it. Without an idea of the former it will be very difficult to get a clear idea of the later. In general there will be many possible cause of complexity and there well may be no overall characterisation of such causes.
Secondly, I argue that complexity is not a property usefully attributed to natural systems but only to our models of such systems. The reasons for this include:
Thirdly, the complexity is a comparative thing, frequently we want to be able to say "A is more complex than B which is, in turn, more complex than C".
Fourthly, complexity is relative to the framework you are modelling in. This includes the language of representation of your model, your general framework (what is given what you are trying to formulate) and your goals in modelling.
Finally complexity is usefully distinguished from ignorance. Ignorance can cause complexity in many ways, including the misframing of a problem, and complexity can certainly cause ignorance, for example where there are only limited problem solving resources available. However, it is easy to give examples where the two concepts diverge.
Packaging these all up into a definition we get:
"Complexity is that property of models which make it difficult to formulate its overall behaviour in a given language of representation, even when given almost complete information about its components and their inter-relations" [6]Thus I have relativised complexity to the model, the type of difficulty, the language of modelling and how one characterises "overall behaviour" and "atomic components". Many of the confusions that have abounded with the use of this word have occurred because of unshared assumptions about these relativisations. Thus you will get different kinds of complexity for different kinds of "difficulty", different modelling languages etc.
Frequently the complexity of a pattern, system or data model is taken to be the complexity of the most "suitable" model given a certain framework. The definition above does not mean that you can make complexity to mean whatever you want. When a framework has been agreed (either explicitly or, as frequently occurs in the hard sciences, implicitly), complexity can be objectively measured and attributed, just as whether the number of cows in a particular field is prime is an objective question despite the fact that "primality" refers to our (numerical) model of the cows and not the cows themselves.
Such a definition imposes some obligation to explicitly make clear the chosen relativisations but this is no bad thing. The justification of such an approach to defining complexity ultimately comes down to the extent it makes the analysis of the effects and causes of complexity clear (for more on this see [9]). We will now apply it to modelling agents which economically interact.
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