  We aim to study the effects of controlling the resource level in agent-based
models. We study, both numerical and analytically, a Binary-Agent-Resource
(B-A-R) model in which $N$ agents are competing for resources described by a
resource level $1/2 \leq {\cal L} < 1$, where ${\cal L} = L/N$ with $L$ being
the maximum amount of resource per turn available to the agents. Each agent
picks the momentarily best-performing strategy for decision with the
performance of the strategy being a result of the cumulative collective
decisions of the agents. The agents may or may not be networked for information
sharing. Detailed numerical simulations reveal that the system exhibits
well-defined plateaux regions in the success rate which are separated from each
other by abrupt transitions. As $L$ increases, the maximum success rate forms a
well defined sequence of simple fractions. We analyze the features by studying
the outcome time series, the dynamics of the strategies' performance ranking
pattern and the dynamics in the history space. While the system tends to
explore the whole history space due to its competitive nature, an increasing
$L$ has the effect of driving the system to a restricted portion of the history
space. Thus the underlying cause of the observed features is an interesting
self-organized phenomena in which the system, in response to the global
resource level, effectively avoids particular patterns of history outcomes. We
also compare results in networked population with those in non-networked
population.
