资产交换模型中新资源的引入和现有资源的分散对限制财富分配的影响
Effects of introduction of new resources and fragmentation of existing resources on limiting wealth distribution in asset exchange models
摘要：
帕累托定律（Pareto law）指出社会财富分布具有幂律尾，一直是统计物理学界深入研究的主题。有几种模型被用来解释这种行为。然而，大多数基于代理的模型假设代理和财富的数量守恒。这两种假设都是不现实的。在本文中，我们研究了当这些假设中的一个或两个都无效时的限制财富分布。鉴于这一规律的普适性，我们试图从资产交换模型的角度来研究财富分配问题。我们考虑模型，其中a）新的代理商以恒定的速率进入市场b）更丰富的代理商碎片，在系统中引入新的代理商的概率更高c）新代理商的碎片和进入正在发生。虽然模型a）和c）不保存总财富或代理人的数量，但模型b）保存总财富。所有这些模型都导致了财富分布中的幂律尾部，这表明更广义的资产交换模型可以帮助我们解释财富分布中幂律尾部的出现。
英文摘要：
Pareto law, which states that wealth distribution in societies have a power-law tail, has been a subject of intensive investigations in statistical physics community. Several models have been employed to explain this behavior. However, most of the agent based models assume the conservation of number of agents and wealth. Both these assumptions are unrealistic. In this paper, we study the limiting wealth distribution when one or both of these assumptions are not valid. Given the universality of the law, we have tried to study the wealth distribution from the asset exchange models point of view. We consider models in which a) new agents enter the market at constant rate b) richer agents fragment with higher probability introducing newer agents in the system c) both fragmentation and entry of new agents is taking place. While models a) and c) do not conserve total wealth or number of agents, model b) conserves total wealth. All these models lead to a power-law tail in the wealth distribution pointing to the possibility that more generalized asset exchange models could help us to explain emergence of power-law tail in wealth distribution.
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