The Interaction of Agents in a Heterogeneous Firm

Stephen Maher

MATH345 Mathematics Advanced Project

Spring 2006


The aim of this project was to research the distribution of firm sizes and the growth of firms. The initial focus was on the distribution of firm sizes, and the research that has been carried out by Robert Axtell (2006). This paper dealt with the statistics surrounding the distribution of firm sizes. There was also a hypothesis suggesting that it could be possible to predict the distribution with mathematical techniques. However, the statistical nature of this research made it very difficult to put together a worthwhile project. This was mainly due to the limitations of my skills in statistics. The decision was then made to look into some of the earlier work that had been done in this area.

This step lead to the reading of Robert Axtell's, CSED Working Paper No. 3 (Axtell, 1999), which developed a computational model looking at the growth of firms. While this project does not focus on the growth of firms, the ideas that were developed in that particular paper have been taken and studied.

The main focus of this project is to look at the interaction of workers in a firm consisting of three workers. This interaction is restricted by a range of constraints, which leads to interesting behaviour. While Axtell looked briefly at homogeneous firms, this projects extends this and looks at the interaction of heterogeneous workers.

This paper looks at the different work that has been studied over the course of this project. Section 2 gives a quick look at the work that Robert Axtell has done in the distribution of firm sizes. Section 3 looks at the hypothesised work by Axtell on Stirling number of the second kind which appears in his paper (Axtell, 2006). Section 4 describes what an agent based model is, and gives a brief explanation as to why it is necessary in this research. Section 5 is a summary of (Axtell, 1999), looking at the main parts that have been used in my research and presents my findings. Section 6 is the analysis of the heterogeneous firm, which looks at my research and presents my findings. Finally, section 7 gives a couple of ideas that could be followed in further research of this particular model.


Axtell, R. (1999). The Emergence of Firms in a Population of Agents: Local Increasing Returns, Unstable Nash Equilibria, and Power law Size Distribution. CSED Working Paper No. 3.
Axtell, R. (2006). Firm Sizes: Facts, Formulae, Fables and Fantasies. CSED Working Paper No. 44.

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