  We study the dynamics of a generalized Minority Game (GMG) and of the Bar
Attendance Model (BAM) in which a number of agents self-organize to match an
attendance that is fixed externally as a control parameter. We compare the
usual dynamics used for the Minority Game with one for the BAM that makes a
better use of the available information. We study the asymptotic states reached
in both frameworks. We show that states that can be assimilated to either
thermodynamic equilibrium or quenched configurations can appear in both models,
but with different settings. We discuss the relevance of the parameter $G$ that
measures the value of the prize for winning in units of the fine for losing. We
also provide an annealing protocol by which the quenched configurations of the
GMG can progressively be modified to reach an asymptotic equlibrium state that
coincides with the one obtained with the BAM.
