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Diffusion and Localization of Relative Strategy Scores in The Minority Game

Journal article
Authors Mats Granath
Alvaro Perez-Diaz
Published in Journal of statistical physics
Volume 165
Issue 1
Pages 94-114
ISSN 0022-4715
Publication year 2016
Published at Department of Physics (GU)
Pages 94-114
Language en
Links dx.doi.org/10.1007/s10955-016-1607-...
Keywords Minority game Market dynamics Agent based models
Subject categories Statistical physics

Abstract

We study the equilibrium distribution of relative strategy scores of agents in the asymmetric phase (α≡P/N≳1) of the basic Minority Game using sign-payoff, with N agents holding two strategies over P histories. We formulate a statistical model that makes use of the gauge freedom with respect to the ordering of an agent’s strategies to quantify the correlation between the attendance and the distribution of strategies. The relative score x∈Z of the two strategies of an agent is described in terms of a one dimensional random walk with asymmetric jump probabilities, leading either to a static and asymmetric exponential distribution centered at x=0 for fickle agents or to diffusion with a positive or negative drift for frozen agents. In terms of scaled coordinates x/N−−√ and t / N the distributions are uniquely given by α and in quantitative agreement with direct simulations of the game. As the model avoids the reformulation in terms of a constrained minimization problem it can be used for arbitrary payoff functions with little calculational effort and provides a transparent and simple formulation of the dynamics of the basic Minority Game in the asymmetric phase.

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