  In the original two-choice minority game (MG), selfish players cooperate with
each other even though direct communication is not allowed. Moreover, there is
a periodic dynamics in the MG whenever the strategy space size is much smaller
than the number of strategies at play. Do these phenomena persist if every
player has $N_c > 2$ choices where all player's strategies are picked from a
reduced strategy space? We answer this question by studying a multichoice
minority game model known as MG($N_c$,$|{\mathbb S}|$). Numerical simulation
shows that these two models have very similar global cooperative behaviors.
Nevertheless, unlike in the MG, periodic dynamics does not always appear in the
MG($N_c$,$|{\mathbb S}|$) even when the strategy space size is much smaller
than the number of strategies at play.
