Thermal treatment of the minority game

Details Thermal treatment of the minority game Thermal treatment of the minority game

2001-07-04

arxiv.org/abs/cond-mat/0107088v1

Physics

Condensed Matter

9 pages in PRE format, 6 figures

Scientific paper

10.1103/PhysRevE.65.036711

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 to define a deterministic, synchronous dynamics 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.

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