Study of the Wealth Inequality in the Minority Game

TL;DR

This paper investigates wealth inequality in the minority game using the Gini index, revealing that optimal cooperation correlates with severe wealth disparity, and supports findings with semi-analytical methods.

Contribution

It demonstrates the application of physical approaches to analyze wealth inequality in the minority game, linking cooperation with inequality and providing semi-analytical validation.

Findings

Wealth inequality peaks near maximum cooperation in the minority game.

Optimal cooperation coincides with severe wealth disparity.

Semi-analytical methods reproduce numerical results in the asymmetric phase.

Abstract

To demonstrate the usefulness of physical approaches for the study of realistic economic systems, we investigate the inequality of players' wealth in one of the most extensively studied econophysical models, namely, the minority game (MG). We gauge the wealth inequality of players in the MG by a well-known measure in economics known as the modified Gini index. From our numerical results, we conclude that the wealth inequality in the MG is very severe near the point of maximum cooperation among players, where the diversity of the strategy space is approximately equal to the number of strategies at play. In other words, the optimal cooperation between players comes hand in hand with severe wealth inequality. We also show that our numerical results in the asymmetric phase of the MG can be reproduced semi-analytically using a replica method.