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Continuum time limit and stationary states of the minority game

By Matteo Marsili and Damien Challet


We reconsider the derivation of the continuum time limit for the Minority Game and confirm that the stationary state properties are given by the ground state configurations of a disordered (soft) spin system. We extend previous results and i) derive the stationary state distribution ii) characterize the dependence on initial conditions in the symmetric phase and iii) clarify the transition to a turbulent dynamics which occurs for fast learning rates. Strikingly we find that the temperature like parameter which is introduced in the choice behavior of individual agents turns out to play the role, at the collective level, of the inverse of a thermodynamic temperature.

Year: 2001
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