Dynamics of a spherical minority game

Details Dynamics of a spherical minority game Dynamics of a spherical minority game

2003-03-28

arxiv.org/abs/cond-mat/0303615v1

J. Phys. A: Math. Gen. 36 (2003) 11159-11172

Physics

Condensed Matter

Disordered Systems and Neural Networks

16 pages, 3 figures; submitted to J. Phys. A

Scientific paper

10.1088/0305-4470/36/43/034

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.

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