Abstract
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 σ 2/ N in the N ⪡ 2 M region. The ability of the players to learn a given payoff is also analyzed, and we show that the Darwinian evolution process tends to a self-organized state, in particular, the lifetime distribution is a power-law with exponent −2. Furthermore, we study the influence of identical players on their gain and on the systems performance. Finally, we show that large brains always take advantage of small brains.
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