  We consider a class of games that are generalizations of the minority game,
in that the demand and supply of the resource are specified independently. This
allows us to study systems in which agents compete under different demand
loads. Among other features, we find the existence of a robust phase change
with a coexistence region as the demand load is varied, separating regions with
nearly balanced supply and demand from regions of scarce or abundant resources.
The coexistence region exists when the amount of information used by the agents
to make their choices is greater than a critical value, which is related to the
point at which there is a phase transition in the standardd minority game.
