Grand canonical minority game as a sign predictor

TL;DR

This paper introduces an extended Minority Game model, called Grand Canonical, which effectively predicts signals by using a single agent with all strategies, demonstrating high adaptability and success in various scenarios.

Contribution

It presents a novel Grand Canonical Minority Game model for prediction, highlighting the effectiveness of a degenerated single-agent system with full strategy sets.

Findings

Single-agent system with full strategies yields optimal prediction.

The method adapts quickly with the λ-GCMG modification.

Prediction success depends on proper memory length setting.

Abstract

In this paper the extended model of Minority game (MG), incorporating variable number of agents and therefore called Grand Canonical, is used for prediction. We proved that the best MG-based predictor is constituted by a tremendously degenerated system, when only one agent is involved. The prediction is the most efficient if the agent is equipped with all strategies from the Full Strategy Space. Each of these filters is evaluated and, in each step, the best one is chosen. Despite the casual simplicity of the method its usefulness is invaluable in many cases including real problems. The significant power of the method lies in its ability to fast adaptation if \lambda-GCMG modification is used. The success rate of prediction is sensitive to the properly set memory length. We considered the feasibility of prediction for the Minority and Majority games. These two games are driven by different dynamics when self-generated time series are considered. Both dynamics tend to be the same when a feedback effect is removed and an exogenous signal is applied.