# Polynomial rate convergence to an invariant measure for the continuum time limit of the Minority Game - Mathematics > Probability

Abstract: In this paper we show that the continuum time version of the Minority Gamesatisfies the criteria for the application of a theorem on the existence of aninvariant measure. We consider the special case of a game with -sufficiently-asymmetric initial condition where the number of possible choices for eachindividual is S=2 and $\Gamma<+\infty$. An upper bound for the asymptoticbehavior, as the number of agents grows to infinity, of the waiting time forreaching the stationary state is then obtained.

Author: Matteo Ortisi

Source: https://arxiv.org/