Some remarks about notation

Abstract

The formal representation of the history-friendly models presented some notable issues, first of all because of the huge amount of variables and parameters defining the models: some of these elements were common or at least analogous across the models, while others referred to completely different domains. In order to reduce the number of the main symbols to a manageable size, we adapted from computer programming languages the idea of overloading notation: a main symbol can have slightly different meanings according to the presence or absence of further details, such as superscripts and subscripts. For example, the symbol T indicates the total number of periods of a simulation, Tk indicates the period of introduction of technology k, and TI the minimum number of periods a firm has to stay integrated after its decision to switch to internal production of components. In general, we use as subscripts the indices for elements (products, firms, markets, technologies) that take different values, without changing the meaning of the main symbol. Instead, we use as superscripts further identifiers of the main symbols that are not instances of a general category: for example, PT is the symbol of patents and E is the symbol of exit. In a very limited number of cases an identifier can be used both as a subscript identifier (TR and MP in most of the cases are used as instances of component technology k) and as a superscript identifier (TR and MP are used as superscripts of the main symbol α, as they refer to different parts of the same equation).