Multichoice Minority Game: Dynamics and Global Cooperation

Abstract

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.

revtex4, 19 pages with 12 figures; extensively rewritten, more justification added