PMID: 11909311Mar 23, 2002Paper

Thermal treatment of the minority game

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
E BurgosR P J Perazzo

Abstract

We study a cost function for the aggregate behavior of all the agents involved in the minority game (MG) or the bar attendance model (BAM). The cost function allows us to define a deterministic, synchronous dynamic that yields results that have the main relevant features than those of the probabilistic, sequential dynamics used for the MG or the BAM. We define a temperature through a Langevin approach in terms of the fluctuations of the average attendance. We prove that the cost function is an extensive quantity that can play the role of an internal energy of the many-agent system while the temperature so defined is an intensive parameter. We compare the results of the thermal perturbation to the deterministic dynamics and prove that they agree with those obtained with the MG or BAM in the limit of very low temperature.

References

Oct 4, 2000·Physical Review Letters·D ChalletR Zecchina
Nov 23, 2000·Physical Review. E, Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics·T S LoN F Johnson
Jul 20, 2001·Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics·E BurgosR P Perazzo
Apr 24, 2002·Physical Review. E, Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics·D Challet, M Marsili
May 13, 1983·Science·S KirkpatrickM P Vecchi

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Citations

Nov 13, 2003·Physical Review Letters·E BurgosR P J Perazzo
Dec 17, 2004·Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics·Roland Kay, Neil F Johnson
Jul 13, 2004·Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics·Shahar Hod, Ehud Nakar
Oct 4, 2003·Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics·Shahar Hod, Ehud Nakar

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