تقسیم کار به عنوان نتیجه انتقال فاز

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.

The economic system is no doubt a many-particle system—it can be viewed as a collection of numerous interacting agents. So it is possible that the methods and concepts developed in the study of strongly fluctuating systems might yield new results in this area. In fact, in the past decades the approaches from statistical physics have been applied in economics and many interesting results, including empirical laws and theoretical models, have been achieved (see [1], [2], [3], [4] and [5] as a review of Econophysics). In all these studies, a great deal of research is on the agent-based modelling and related non-trivial self-organizing phenomena. In the economic system, the agents learn from each other, and their activities may be influenced by others’ actions. These interactions between agents may be simple and local, but they may have important consequences related to the emergence of the global structure. To understand the mechanism behind these innovation phenomena, the methods and concepts in phase transitions and critical phenomena are helpful; for instance, in the study of majority and minority game [6] and [7], opinion formation [8], and computational ecosystems [9].

A distinctive feature of the organization of a human society is the division of labor. From the classical economic theory [10], the division of labor comes from the development of endogenous comparative advantages. So there is the intrinsic relationship between technical progress and the evolution of the division of labor. But how and why does it emerge from the system consisting of identical individuals? We have studied the formation of labor division by the approach of statistical physics. The results reveal that there is a phase transition with this pattern formation. Although the progress of productivity dominated the phase transition occurs or not, the competitive cooperation among the agents has important effects on the critical point. So the market formation and labor division usually reinforce each other. All the above results give us deep understanding of the evolution of labor division.