Phase transition and evolutionary mechanisms in a grand canonical minority game

Abstract

We consider the grand canonical minority game as a model for financial markets. We first characterise the phase transition of the standard minority game and the grand canonical variant between a symmetric, unpredictable phase and an asymmetric, predictable phase and identify the critical point. Then we look at two evolutionary mechanisms: competitive selection and cooperation through imitation. Through overcrowding, competition destroys the asymmetric phase. Limited imitation recovers the asymmetric phase and reduces volatility relative to competitive selection. These results suggest that, in this model, coordination is not maximised by selecting the most successful agents but by preserving sufficient strategic heterogeneity