Multichoice minority game: dynamics and global cooperation

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 Nc>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(Nc,|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(Nc,|S|) even when the strategy space size is much smaller than the number of strategies at play.