Theory of the Three-Group Evolutionary Minority Game

TL;DR

This paper analyzes a three-group evolutionary minority game using adiabatic theory, deriving a critical point formula for behavioral transition and highlighting intermittent strategy switching in extreme groups, with results matching simulations.

Contribution

It provides a detailed theoretical analysis of the three-group EMG, including a new formula for the critical transition point and insights into strategy switching behavior.

Findings

Derived a formula for the critical point of transition in three-group EMG

Identified intermittent strategy switching in the extreme group

Confirmed theoretical predictions with numerical simulations

Abstract

Based on the adiabatic theory for the evolutionary minority game (EMG) that we proposed earlier[1], we perform a detail analysis of the EMG limited to three groups of agents. We derive a formula for the critical point of the transition from segregation (into opposing groups) to clustering (towards cautious behaviors). Particular to the three-group EMG, the strategy switching in the "extreme" group does not occur at every losing step and is strongly intermittent. This leads to an correction to the critical value of the number of agents at the transition, $N_c$. Our expression for $N_c$ is in agreement with the results obtained from our numerical simulations.