Kinetic theory for the emergence of complex behavior in social and economic systems

Firm Dynamics Driven by Job-to-Job Flows (of Workers)

Robert Axtell

George Mason University


The emergence and evolution of firms within a population of agents are investigated from the 'kinetic' perspective of individual workers. I will first review the micro-data on the universe of U.S. firms, data that are turning out to be similar to the rest of the industrialized world as other countries make their data on businesses available. In summary, firm sizes (by many measures) are Pareto-distributed with exponent (shape parameter) near unity, firm ages are Weibull-distributed, log growth rates are approximately Laplace-distributed, and growth rate variance declines with size at a rate less than one would expect from the central limit theorem. I will then motivate the analysis with a simple computational model capable of reproducing most of these empirical regularities. In the model agents who search for new jobs occasionally find them and change jobs, or start up new firms with some small probability. Mathematically I first formulate this as Becker-Doring dynamics in which 'monomers' bind with 'polymers' of various sizes and occasionally disassociate. This simple kinetic scheme is useful for building up intuition about the character of the solution space. I then move on to a more general master equation specification of aggregation-fregmentation dynamics. Knowing what the firm size distribution has to look like I 'back-calculate' what the coefficient terms have to be to make this system of equations relevant empirically. I will highlight open problems with this research program and speculate on what my research group perceives as the most fertile directions. Overall, having the agent-level in a social science model operate away from static (Nash) equilibrium is heretical, and I will conclude with a brief discussion of the difficulties most economists have with 'kinetic' approaches. Fortunately, social scientists working with multi-agent systems typically have the experience of the agent-level behaving dynamically while the aggregate (social) level may reach a steady-state, making kinetic descriptions natural.