Memory is relevant in the symmetric phase of the minority game

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 $\alpha$ in the range $0.1\lesssim \alpha \lesssim 1$, 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 $0.01\lesssim \alpha \lesssim 1$, 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.

5 pages, 4 figures, to appear in PRE

References in corpus (1)

• Generating functional analysis of Minority Games with real market histories

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• The Full Strategy Minority Game
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