  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.
