Complex Systems Paper of the Day...

And today's winner is...

"The Emergence of Firms in a Population of Agents: Local Increasing Returns, Unstable Nash Equilibria, And Power Law Size Distributions"

The paper is long and demanding, but lays out an early (circa 1999) complex systems theory of the firm.  The author relates the complex systems approach to the classical literature on the theory of the firm, outlines his agent-based computational model in detail, and then discusses whether or not the model's predictions concerning various aggregate distributions of firm size, firm growth rates, etc are born out empirically (they are!)

A nice summary paragraph taken from the intro:

"Firms form in the model due to the increasing returns [to agent cooperation at the local level], but, since agents are constantly adjusting their effort levels, large firms are not stable. This is because once a firm becomes large each agent's share is only weakly related to its effort level, and so free-riding sets in. Agents eventually move out of firms "infected" with free riders. Exit decisions are, therefore, also endogenous. It is demonstrated analytically that there do not exist stable equilibria in this environment. Furthermore, it is argued that the nonequilibrium regime provides greater welfare for the agents than would equilibrium even if it were stable. An agent-based computational model is used to study the non-equilibrium dynamics, in which firms are perpetually born, growing and perishing. After an initial transient period there results stationary distributions of firm size (by both number of employees and output) and growth rate. Firm size follows a scaling (power law) distribution, in accord with empirical data.  In fact, for certain parameterizations the power law exponent estimated from the model data is similar to that for U.S. firms. In contrast to increasing returns at the firm level constant returns obtain at the macro-level. The computational model generates empirically testable patterns and regularities, about which there seem to be very little data, such as the distribution of firm lifetimes. Finally, there is a sense in which the model supports the idea that intra-firm cooperation between agents is a by-product of inter-firm competition for agents."

Excellent and insightful paper that outlines a different approach to the theory of the firm.  Those who are interested in leanring more about applying techniques to analyze disequilibrium economic behavior (or those who are just interested in disequilibrium economics generally) will want to read this paper...