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Polynomial rate convergence to an invariant measure for the continuum time limit of the Minority Game

Matteo Ortisi

posted on 17 April 2010

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In this paper we show that the continuum time version of the Minority Game satisfies the criteria for the application of a theorem on the existence of an invariant measure. We consider the special case of a game with "sufficiently" asymmetric initial condition where the number of possible choices for each individual is S=2 and $\Gamma<+\infty$. An upper bound for the asymptotic behavior, as the number of agents grows to infinity, of the waiting time for reaching the stationary state is then obtained.