Statistical mechanics of the mixed majority–minority game with random external information

We study the asymptotic macroscopic properties of the mixed majority–minority game, modelling a population in which two types of heterogeneous adaptive agents, namely 'fundamentalists' driven by differentiation and 'trend-followers' driven by imitation, interact. The presence of a fraction f of trend-followers is shown to induce (a) a significant loss of informational efficiency with respect to a pure minority game (in particular, an efficient, unpredictable phase exists only for f 1/2. We solve the model by means of an approximate static (replica) theory and by a direct dynamical (generating functional) technique. The two approaches coincide and match numerical results convincingly.

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