We study the dynamics of a generalized minority game (GMG) and of the bar a
ttendance 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 r
eached in both frameworks. We show that states that can be assimilated to e
ither thermodynamic equilibrium or quenched configurations can appear in bo
th models, but with different settings. We discuss the relevance of the par
ameter G that measures the value of the prize for winning in units of the f
ine for losing. We also provide an annealing protocol by which the quenched
configurations of the GMG can progressively be modified to reach an asympt
otic equilibrium state that coincides with the one obtained with the BAM.