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 measure the value of the prize for winning measured in units of the fine for losing. We also provide an annealing protocol by which the quenched configuration of the GMG can progressively be modified to reach an asymptotic equilibrium state that coincides with the one obtained with the BAM.