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Polynomial-Rate Convergence to the Stationary State for the Continuum-Time Limit of the Minority Game

Part of: Stochastic processes Time-dependent statistical mechanics (dynamic and nonequilibrium)

Published online by Cambridge University Press:  14 July 2016

Matteo Ortisi
Matteo Ortisi*
Affiliation:
UniCredit Markets & Investment Banking
*
∗Postal address: UniCredit Markets & Investment Banking, via Broletto 16, 20121 Milano, Italy. Email address: matteo.ortisi@gmail.com
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Abstract

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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 a ‘sufficiently’ asymmetric initial condition, where the number of possible choices for each individual is S = 2 and Γ < +∞. 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.

Keywords

Continuum-time minority gamestationary statepolynomial mixing bounds

MSC classification

Secondary: 60G10: Stationary processes 82C44: Dynamics of disordered systems (random Ising systems, etc.)
Type
Research Article
Information
Journal of Applied Probability , Volume 45 , Issue 2 , June 2008 , pp. 376 - 387
Copyright
Copyright © Applied Probability Trust 2008 

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