2003/03/28 by Tobias Galla, T. Galla, A C C Coolen +3 · 1 citation
Economics, Econometrics and Finance · Physics and Astronomy · #Complex Systems and Time Series Analysis #Opinion Dynamics and Social Influence #Theoretical and Computational Physics #cond-mat.dis-nn #cond-mat.stat-mech
paper · pdf · doi:10.1088/0305-4470/36/43/034
published as J. Phys. A: Math. Gen. 36 (2003) 11159-11172 · 16 pages, 3 figures; submitted to J. Phys. A
arxiv created 2003/03/28 · openalex publication_date 2003/10/15 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/04
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.