标题： 指数财富分布：来自函数迭代理论的新方法 显示英文标题

标题： Exponential wealth distribution: a new approach from functional iteration theory

摘要： 指数分布在多智能体系统的框架中无处不在。 通常，它作为统计系统在渐近时间演化中的平衡状态出现。 它已经从非常不同的角度得到了解释。 在统计物理中，它是从最大熵原理得到的。 在同一背景下，也可以不考虑信息论，仅从相空间等概率假设下的几何论证中推导出来。 此外，基于映射的多种多智能体经济模型，具有随机、确定性或混沌相互作用，可以导致指数财富分布的渐近出现。 在分布空间中的迭代框架中，对这个问题的一种替代方法最近被提出。 具体来说，新的迭代由$ f_{n+1}(x) = \int\int_{u+v>x}{f_n(u)f_n(v)\over u+v} dudv.$给出。 发现指数分布是前一个函数迭代方程的稳定不动点。 从这个观点来看，很容易理解为什么指数财富分布（或通过扩展，其他类型的分布）在不同的多智能体经济模型中被渐近地获得。 显示英文摘要

摘要： Exponential distribution is ubiquitous in the framework of multi-agent systems. Usually, it appears as an equilibrium state in the asymptotic time evolution of statistical systems. It has been explained from very different perspectives. In statistical physics, it is obtained from the principle of maximum entropy. In the same context, it can also be derived without any consideration about information theory, only from geometrical arguments under the hypothesis of equiprobability in phase space. Also, several multi-agent economic models based on mappings, with random, deterministic or chaotic interactions, can give rise to the asymptotic appearance of the exponential wealth distribution. An alternative approach to this problem in the framework of iterations in the space of distributions has been recently presented. Concretely, the new iteration given by $ f_{n+1}(x) = \int\int_{u+v>x}{f_n(u)f_n(v)\over u+v} dudv.$. It is found that the exponential distribution is a stable fixed point of the former functional iteration equation. From this point of view, it is easily understood why the exponential wealth distribution (or by extension, other kind of distributions) is asymptotically obtained in different multi-agent economic models.