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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 

References

[1] Arthur, W. B. (1994). Inductive reasoning and bounded rationality. Amer. Econom. Assoc. Papers Proc. 84, 406–411.Google Scholar
[2] Cavagna, A., Garrahan, J. P., Giardina, I. and Sherrington, D. (1999). A thermal model for adaptive competition in a market. Phys. Rev. Lett. 83, 4429.Google Scholar
[3] Challet, D. and Marsili, M. (2003). Criticality and market efficiency in a simple realistic model of the stock market. Phys. Rev. E 68, 036132.CrossRefGoogle Scholar
[4] Challet, D. and Zhang, Y. C. (1997). Emergence of cooperation and organization in an evolutionary game. Physica A 246, 407.Google Scholar
[5] Challet, D., Marsili, M. and Zhang, Y. C. (2000). Modeling market mechanism with minority game. Physica A 276, 284–315.Google Scholar
[6] Challet, D., Marsili, M. and Zhang, Y. C. (2004). Minority Games: Interacting Agents in Financial Markets. Oxford University Press.Google Scholar
[7] Garrahan, J. P., Moro, E. and Sherrington, D. (2000). Continuous time dynamics of the thermal minority game. Phys. Rev. E 62, R9–R12.Google Scholar
[8] Laureti, P., Ruch, P., Wakeling, J. and Zhang, Y. C. (2004). The interactive minority game: a web-based investigation of human market interactions. Physica A 331, 651–659.Google Scholar
[9] Marsili, M. and Challet, D. (2001). Continuum time limit and stationary states of the minority game. Phys. Rev. E 056138.CrossRefGoogle Scholar
[10] Skorokhod, A. V. (2004). Basic Principles and Applications of Probability Theory. Springer, Berlin.Google Scholar
[11] Veretennikov, A. Y. (1997). On polynomial mixing bounds for stochastic differential equations. Stoch. Process. Appl. 70, 115–127.CrossRefGoogle Scholar