  We study a memory-based Boolean game (MBBG) taking place on the regular ring,
wherein each agent acts according to its local optimal states of the last M
time steps recorded in memory, and the agents in the minority are rewarded. One
free parameter p among 0 and 1 is introduced to denote the strength of the
agents' willing to make a decision according to its memory. We find that, given
proper willing strength p, the MBBG system can spontaneously evolve to a state
of better performance than the random game; while for larger p, the herd
behavior emerges which reduces the system profit. By analyzing the dependence
of the system's dynamics on the memory capacity M, we find that a higher memory
capacity favors the emergence of the better performance state, and effectively
restrains the herd behavior, therefore increases the system profit. Considering
the high cost of long-time memory, the enhancement of memory capacity for
restraining the herd behavior is also discussed, and the M=5 is suggested to be
one good choice.
