平均场近似在财富分布模型中的失效
Breakdown of the mean-field approximation in a wealth distribution model
摘要：
要解释的一个关键的社会经济现象是财富的分配。Bouchaud和Mézard提出了一个有趣的经济模型[Bouchaud and Mézard（2000）]，该模型基于代理人的贸易和投资。在平均场近似下，该模型产生了一个具有幂律尾部的平稳财富分布。在本文中，我们研究的特征时间尺度的模型，并表明，对于任何有限数量的代理人，平均场结果的有效性是有时间限制的，该模型实际上没有固定的财富分布。进一步的分析表明，对于异质代理，限制甚至更强。最后，我们提出的结果的一般影响。
英文摘要：
One of the key socioeconomic phenomena to explain is the distribution of wealth. Bouchaud and Mézard have proposed an interesting model of economy [Bouchaud and Mézard (2000)] based on trade and investments of agents. In the mean-field approximation, the model produces a stationary wealth distribution with a power-law tail. In this paper we examine characteristic time scales of the model and show that for any finite number of agents, the validity of the mean-field result is time-limited and the model in fact has no stationary wealth distribution. Further analysis suggests that for heterogeneous agents, the limitations are even stronger. We conclude with general implications of the presented results.
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