Stylized facts in minority games with memory: a new challenge

TL;DR

This paper introduces finite memory into Minority Games, revealing that while it removes initial condition dependence, it unexpectedly increases fluctuations over time, challenging existing analytical methods.

Contribution

It presents a novel extension of Minority Games with finite memory, highlighting new complex behaviors not captured by current analytical approaches.

Findings

Finite memory removes initial condition dependence.

Unexpected increase in fluctuations over time.

Current analytical methods are insufficient.

Abstract

A finite memory is introduced in the score dynamics of Minority Games. As expected, this removes the dependence of the stationary state on the initial conditions. However, it also causes an unexpected increase of fluctuations in grand-canonical models for very large times. Current analytical methods are inadequate to solve this simple and natural extension.