Memory is relevant in the symmetric phase of the minority game

TL;DR

This study reveals that memory influences the cooperative behavior in the symmetric phase of the minority game, challenging previous beliefs that memory was irrelevant, through large-scale simulations and theoretical analysis.

Contribution

The paper demonstrates, via extensive simulations and crowd-anticrowd theory, that memory affects the symmetric phase of the minority game, contrary to prior assumptions.

Findings

Memory impacts the variance of attendance in the symmetric phase.

Large-scale simulations show dependence on memory up to 3000 players.

Feedback mechanisms in history correlation are significant in minority game dynamics.

Abstract

Minority game is a simple-mined econophysical model capturing the cooperative behavior among selfish players. Previous investigations, which were based on numerical simulations up to about 100 players for a certain parameter $\alpha$ in the range $0.1 \lesssim \alpha \lesssim 1$, suggested that memory is irrelevant to the cooperative behavior of the minority game in the so-called symmetric phase. Here using a large scale numerical simulation up to about 3000 players in the parameter range $0.01 \lesssim \alpha \lesssim 1$, we show that the mean variance of the attendance in the minority game actually depends on the memory in the symmetric phase. We explain such dependence in the framework of crowd-anticrowd theory. Our findings conclude that one should not overlook the feedback mechanism buried under the correlation in the history time series in the study of minority game.