Evolutionary Dynamics and the Phase Structure of the Minority Game

We show that a simple evolutionary scheme, when applied to the minority game (MG), changes the phase structure of the game. In this scheme each agent evolves individually whenever his wealth reaches the specified bankruptcy level, in contrast to the evolutionary schemes used in the previous works. We show that evolution greatly suppresses herding behavior, and it leads to better overall performance of the agents. Similar to the standard non-evolutionary MG, the dependence of the standard deviation $\sigma$ on the number of agents $N$ and the memory length $m$ can be characterized by a universal curve. We suggest a Crowd-Anticrowd theory for understanding the effect of evolution in the MG.