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Minority game with SK interactions

A batch minority game with fake random history and additional SK-like quenched interaction is introduced and analysed. A mixing parameter λ quantifies the admixture and dictates the relative dominance of the two contributions: if λ → 0, agent decisions are based on their strategies and point-scores alone, as in the pure minority game, whereas for λ > 0 the agents also communicate with each other directly and update their points accordingly. Keeping the minority game dynamics in which the agents’ points are updated in parallel at each time step, the aim is to understand what happens if instead of simply using the normal strategy-based decisions, the agents also take account of an ‘effective field’ generated by the other agents. It is shown that the SK interaction introduces a ‘noise’ term which is broader than that in the normal minority game and which furthermore kills the normal phase transition. It is also shown that the same effect would occur if, instead of an SK interaction, Gaussian-distributed quenched random fields are added. By calculating order parameters in the time-translational invariant phase we show that the system is persistent in a ergodic phase. Both simulational and analytical results are presented.