Qunatifying Complexity in the Minority Game

TL;DR

This paper introduces a Lempel-Ziv complexity measure into the Minority Game to better understand collective behavior and volatility, providing new insights beyond traditional measures.

Contribution

It presents a novel application of complexity theory to analyze the Minority Game, linking complexity with volatility analytically.

Findings

Complexity captures features of collective behavior not seen in volatility.

An analytical expression relates volatility to complexity.

Complexity provides additional insights into the dynamics of the game.

Abstract

A Lempel-Ziv complexity measure is introduced into the theory of a Minority Game (MG) in order to capture some features that volatility, one of the central quantities in this model of interacting agents, is not able to. Extracted solely from the binary string of outcomes of the game complexity offers new and valuable information on collective behavior of players. Also, we show that an expression for volatility may be included in the analytical expression for complexity.