Market dimensionality and the proliferation of small-scale firms

We build an agent-based computational model to study how market structure evolution, in terms of the increasing diversity of available product options in an w-dimensional space of product attributes, affects the performance of firm strategies (i.e. being a large-scale or a small-scale firm). Our aim is to study how the degree of space heterogeneity affects firm viability when different levels of scale advantage characterize firm structure. Such an increasing heterogeneity is associated with the increasing number of dimensions in the so-called resource space. A resource space with higher number of dimensions implies a market where there is higher product diversity. We study the effect on firm performance through the realized profit/cost ratio of every time period. We build a novel approach to measure the evolution of the number of dimensions in the product space, based on the assumptions that i) not all the possibilities of a single dimension (attribute) are active at a given point of time, and ii) product attributes or characteristics in a new dimension might start to emerge when the previously established dimensions have not been fully developed yet. This motivates us to think that the number of dimensions may be a "fraction" of the Euclidean dimensions. We use the concept of "similarity dimension" in order to measure those fractional dimensions in the resource space. Market starts with only one product characteristic option (dimension = 0) and evolves until a maximum of dimension = 2. We confirm that increasing dimensionality gives a differential advantage to small-scale firms. However, this advantage comes from the "opening up" of new product characteristics mostly generated by large-scale firms. We also find that large-scale firms may also benefit from increasing dimensionality, whenever it allows only a small degree of differentiation without weakening the power of scale advantages.