Memory is relevant in the symmetric phase of the minority game

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 < approximately alpha < approximately 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 < approximately alpha < approximately 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.