Dynamics of a spherical minority game

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.

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

References in corpus (4)

• Generating Functional Analysis of the Dynamics of the Batch Minority Game with Random External Information
• Dynamics of the Batch Minority Game with Inhomogeneous Decision Noise
• Dynamical Solution of the On-Line Minority Game
• The minority game: effects of strategy correlations and timing of adaptation

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• Optimal coordination of resources: A solution from reinforcement learning
• Dynamics of adaptive agents with asymmetric information
• Complex dynamics in learning complicated games
• Statistical Mechanics of Dilute Batch Minority Games with Random External Information
• Market response to external events and interventions in spherical minority games