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Memory is relevant in the symmetric phase of the minority game

K. H. Ho·W. C. Man·F. K. Chow·H. F. Chau
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Abstract

Minority game is a simple-mined econophysical model capturing the cooperative behavior among selfish players. Previous investigations, which were based on numerical simulations up to about 100 players for a certain parameter $α$ in the range $0.1 \lesssim α\lesssim 1$, suggested that memory is irrelevant to the cooperative behavior of the minority game in the so-called symmetric phase. Here using a large scale numerical simulation up to about 3000 players in the parameter range $0.01 \lesssim α\lesssim 1$, we show that the mean variance of the attendance in the minority game actually depends on the memory in the symmetric phase. We explain such dependence in the framework of crowd-anticrowd theory. Our findings conclude that one should not overlook the feedback mechanism buried under the correlation in the history time series in the study of minority game.

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K. H. Ho, W. C. Man, F. K. Chow, H. F. Chau. 2005-04-26. Memory is relevant in the symmetric phase of the minority game. https://doi.org/10.1103/physreve.71.066120

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