Theory
El Farol (Arthur 1994):
Go if expected attendance < θN
Every agent uses different predictor
Minority Game (Challet 1997):
N odd agents, win if minority side
Score +1 if correct, -1 if wrong
Phase transition at α = M/N:
α < α_c: inefficient (herd)
α > α_c: efficient coordination
α_c ≈ 0.34 (memory M=2)
In the minority game, agents using the same limited history will correlate — herding increases volatility. At the phase transition point, the collective achieves near-optimal efficiency. Below it, strategies are anti-correlated and the system self-organizes. Above, strategies are uncorrelated (random). This is a model of financial markets, traffic, and resource allocation.