标题： 关于在厄尔多斯-雷尼随机网络上扩展的后院销售模型财富分布的研究 显示英文标题

标题： Study of the Extended Yard Sale model of wealth distribution on Erdős-Rényi random networks

摘要： 过度的财富集中可能会削弱经济和社会的发展。 随机资产交换（RAE）模型提供了有价值的工具来研究这一现象。 假设经济系统可能在连续相变的临界点附近最优运行，Boghosian等人引入的扩展yard sale（EYS）模型提供了一个引人注目的框架。 该模型捕捉了财富再分配和积累之间的相互作用，在临界点表现出一个连续相变，以财富分布广泛为标志，区分了一个凝聚相——其中微小比例的代理人持有总财富的大份额——与一个轻尾财富分布的分散相。 虽然原始的EYS模型假设完全连接的交互，这项工作引入并研究了一种网络化变体，其中代理人在Erdős-Rényi随机网络上进行交互。 分析结合了蒙特卡洛模拟与淬火平均场和平均场近似，探索了各种交互和税收方案。 尺度分析表明，尽管网络化模型也经历了连续相变，但它导致的是局部财富凝聚而不是完全连接情况下的全局凝聚。 这些结果深化了我们对结构化群体中财富动态的理解，并可能有助于制定更有效的经济和社会政策。 显示英文摘要

摘要： Excessive wealth concentration can undermine economic and social development. Random Asset Exchange (RAE) models provide valuable tools to investigate this phenomenon. Assuming that economic systems may operate optimally near the critical point of a continuous phase transition, the Extended Yard Sale (EYS) model introduced by Boghosian et al.~[Physica A 476, 15 (2017)] offers a compelling framework. This model captures the interplay between wealth redistribution and accumulation, exhibiting a continuous phase transition marked by a broad wealth distribution at criticality, separating a condensed phase -- where a microscopic fraction of agents holds a macroscopic share of total wealth -- from a distributed phase with a light-tailed wealth distribution. While the original EYS model assumes fully connected interactions, this work introduces and studies a networked variant where agents interact over Erd\H{o}s-R\'enyi random networks. The analysis combines Monte Carlo simulations with Quenched Mean Field and Mean Field approximations, exploring a variety of interaction and taxation schemes. A scaling analysis shows that, although the networked model also undergoes a continuous phase transition, it leads to local wealth condensation rather than the global condensation found in the fully connected case. These results deepen our understanding of wealth dynamics in structured populations and may help inform the development of more effective economic and social policies.