Statistical Mechanics of Dilute Batch Minority Games with Random External Information

TL;DR

This paper analyzes the dynamics of a dilute batch minority game with random external information, revealing a unique ergodicity breaking scenario characterized by the onset of long-term memory at finite response, differing from standard phase transitions.

Contribution

It introduces a detailed analysis of dilute batch minority games with infinite connections, highlighting a new ergodicity breaking mechanism linked to finite memory and comparing it with related market impact models.

Findings

Long-term memory appears at the AT-line from replica calculations.

Ergodicity breaking differs from standard phase transitions.

Dilute model behavior is similar to minority games with market impact correction.

Abstract

We study the dynamics and statics of a dilute batch minority game with random external information. We focus on the case in which the number of connections per agent is infinite in the thermodynamic limit. The dynamical scenario of ergodicity breaking in this model is different from the phase transition in the standard minority game and is characterised by the onset of long-term memory at finite integrated response. We demonstrate that finite memory appears at the AT-line obtained from the corresponding replica calculation, and compare the behaviour of the dilute model with the minority game with market impact correction, which is known to exhibit similar features.