Theory of Minority Games

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  • 27 April 1999
Abstract
We study analytically the Minority Game, a system of heterogeneous interacting agents in a simplified model market. We show that the stationary state of the system is described by the ground state of a disordered spin model which is exactly solvable within the simple replica symmetric ansatz. Such a stationary state differs from the Nash equilibrium where each agent maximizes his own utility. The latter turns out to be characterized by a replica symmetry broken structure. We show that, if agents know their impact on the ``market'', the same learning dynamics of minority game converges to the Nash equilibrium, thus showing the importance of knowledge and information in these systems. Numerical results fully agree with our analytic findings.

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