Competition and Investment Model of Wealth Distribution

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.