Division of labor as the result of phase transition

The emergence of labor division in a multi-agent system is analyzed by the method of statistical physics. We consider a system consisting of N homogeneous agents. Their behaviors are determined by the returns from their production. Using the Metropolis method in statistical physics, which in this model can be regarded as a kind of uncertainty in decision making, we constructed a Master equation to describe the evolution of the agent's distribution. We introduce an earning function including learning by doing to describe the effect of technical progress and a formula for competitive cooperation. And we also introduce two order parameters to characterize the division behavior. The model gives us the following interesting results: (1) As a result of long-term evolution, the system can reach a steady state. (2) When the parameters exceed a critical point, the division of labor emerges as the result of phase transition. (3) Although the technical progress decides whether or not phase transition occurs, the critical point is strongly affected by the competitive cooperation. From the above physical model and the corresponding results, we can get a more deeply understanding about the labor division.