Minority Game — Grand Canonical Phase Transition

Adaptive agents competing to be in the minority — phase transition at α_c = (m/2)^0.5 separating predictable from chaotic regimes

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σ²/N (volatility)

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α = P/N

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Efficiency η

Round

Agents N 101

Memory m 3

Strategies S per agent 2

Speed (steps/frame) 5

The minority game (Challet-Zhang 1997) models markets: N agents each pick 0 or 1; winners are in the minority. With memory m and P=2^m strategies, the grand canonical version shows a phase transition at α_c: below α_c agents coordinate (herd), above α_c they decorrelate (efficient market). Volatility σ²/N peaks at α_c.