Order and disorder in the Local Evolutionary Minority Game

TL;DR

This paper introduces the Local Evolutionary Minority Game (LEMG), a variant where agents update decisions based on local neighborhoods, revealing how local information improves coordination and interpolates between order and disorder.

Contribution

The paper proposes the LEMG model with local decision updates and analyzes its behavior on various graph topologies, connecting it to spin systems and disorder.

Findings

Local information leads to better agent coordination.

LEMG interpolates between ordered and disordered states.

Surprising improvement in system performance with local updates.

Abstract

We study a modification of the Evolutionary Minority Game (EMG) in which agents are placed in the nodes of a regular or a random graph. A neighborhood for each agent can thus be defined and a modification of the usual relaxation dynamics can be made in which each agent updates her decision scheme depending upon the options made in her immediate neighborhood. We name this model the Local Evolutionary Minority Game (LEMG). We report numerical results for the topologies of a ring, a torus and a random graph changing the size of the neighborhood. We focus our discussion in a one dimensional system and perform a detailed comparison of the results obtained from the random relaxation dynamics of the LEMG and from a linear chain of interacting spin-like variables at a finite temperature. We provide a physical interpretation of the surprising result that in the LEMG a better coordination (a lower frustration) is achieved if agents base their actions on local information. We show how the LEMG can be regarded as a model that gradually interpolates between a fully ordered, antiferromagnetic system and a fully disordered system that can be assimilated to a spin glass.