标题： 财富分配的竞争与投资模型 显示英文标题

标题： Competition and Investment Model of Wealth Distribution

摘要： 解释观察到的财富和收入分布——具有幂律尾部以及伽马分布或对数正态分布主体形状——挑战了专注于成对竞争或个体投资机制的模型。 本研究提出并分析了一个统一模型，通过可调参数$\alpha$整合了成对竞争和个体投资。 数值模拟被用来使用互补累积分布函数和拟合优度检验来分析模型的基尼系数和分布形状。 结果显示，该模型捕捉到了主体分布从伽马型（低$\alpha$）到对数正态型（高$\alpha$）的系统性转变。 此外，中间水平的机制混合可以减少与原始机制相比的不平等。 然而，很难区分与幂律一致的重尾和对数正态尾。 这些发现强调了考虑不同经济机制之间相互作用的重要性，但表明准确复制经验上的幂律尾部需要比所调查的简单组合更多的内容。 显示英文摘要

摘要： Explaining empirically observed wealth and income distributions, featuring power-law tails alongside gamma or log-normal bulk shapes, challenges models that focus on either pairwise competition or individual investment mechanisms. This study proposes and analyzes a unified model that integrates pairwise competition and individual investment via an adjustable parameter, $\alpha$. Numerical simulations are conducted to analyze the model's Gini coefficient and distributional shapes using the complementary cumulative distribution function and goodness-of-fit tests. Results show that the model captures a systematic transition in the bulk distribution from gamma like (low $\alpha$) to log-normal like (high $\alpha$). Additionally, intermediate levels of mechanism mixing can reduce inequality compared with the original mechanisms. However, it is difficult to distinguish heavy tails consistent with power-laws from log-normal tails. These findings highlight the importance of considering the interaction between different economic mechanisms but suggest that accurately replicating the empirical power-law tail requires more than the simple combination investigated.