Dynamics of a spherical minority game

TL;DR

This paper provides an exact dynamical analysis of a spherical minority game model, revealing a phase diagram with three distinct phases and exact calculations of volatility, highlighting both similarities and differences with standard MG models.

Contribution

The paper introduces an exact dynamical solution for a spherical version of the minority game, including a detailed phase diagram and volatility calculations.

Findings

Identified three phases: oscillating, frozen, and divergent response.

Calculated volatility exactly for the spherical MG.

Confirmed analytical results with numerical simulations.

Abstract

We present an exact dynamical solution of a spherical version of the batch minority game (MG) with random external information. The control parameters in this model are the ratio of the number of possible values for the public information over the number of agents, and the radius of the spherical constraint on the microscopic degrees of freedom. We find a phase diagram with three phases: two without anomalous response (an oscillating versus a frozen state), and a further frozen phase with divergent integrated response. In contrast to standard MG versions, we can also calculate the volatility exactly. Our study reveals similarities between the spherical and the conventional MG, but also intriguing differences. Numerical simulations confirm our analytical results.