Quenching and annealing in the minority game

We study the bar attendance model (BAM) and a generalized version of the minority game (MG) in which a number of agents self organize to match an attendance that is fixed externally as a control parameter. We compare the probabilistic dynamics used in the MG with one that we introduce for the BAM that makes better use of the same available information. The relaxation dynamics of the MG leads the system to long lived, metastable (quenched) configurations in which adaptive evolution stops in spite of being far from equilibrium. On the contrary, the BAM relaxation dynamics avoids the MG glassy state, leading to an equilibrium configuration. Finally, we introduce in the MG model the concept of annealing by defining a new procedure with which one can gradually overcome the metastable MG states, bringing the system to an equilibrium that coincides with the one obtained with the BAM.