On the strategy frequency problem in batch Minority Games

Details On the strategy frequency problem in batch Minority Games On the strategy frequency problem in batch Minority Games

2006-11-20

arxiv.org/abs/physics/0611188v1

Physics

Physics and Society

17 pages

Scientific paper

10.1088/1742-5468/2007/01/P01006

Ergodic stationary states of Minority Games with S strategies per agent can be characterised in terms of the asymptotic probabilities $\phi_a$ with which an agent uses $a$ of his strategies. We propose here a simple and general method to calculate these quantities in batch canonical and grand-canonical models. Known analytic theories are easily recovered as limiting cases and, as a further application, the strategy frequency problem for the batch grand-canonical Minority Game with S=2 is solved. The generalization of these ideas to multi-asset models is also presented. Though similarly based on response function techniques, our approach is alternative to the one recently employed by Shayeghi and Coolen for canonical batch Minority Games with arbitrary number of strategies.

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