A binary game is introduced and analysed. N players have to choose one of the two sides independently and those on the minority side win. Players use a finite set of ad hoc strategies to make their decision, based on the past record. The analysing power is limited and can adapt when necessary....

We investigate further several properties of the minority game we have recently introduced. We explain the origin of the phase transition and give an analytical expression of σ2/N in the N⪡2M region. The ability of the players to learn a given payoff is also analyzed, and we show that the...