  Multi-agent systems are designed to concurrently accomplish a diverse set of
tasks at unprecedented scale. Here, the central problems faced by a system
operator are to decide (i) how to divide available resources amongst the agents
assigned to tasks and (ii) how to coordinate the behavior of the agents to
optimize the efficiency of the resulting collective behavior. The focus of this
paper is on problem (i), where we seek to characterize the impact of the
division of resources on the best-case efficiency of the resulting collective
behavior. Specifically, we focus on a team Colonel Blotto game where there are
two sub-colonels competing against a common adversary in a two battlefield
environment. Here, each sub-colonel is assigned a given resource budget and is
required to allocate these resources independent of the other sub-colonel.
However, their success is dependent on the allocation strategy of both
sub-colonels. The central focus of this manuscript is on how to divide a common
pool of resources among the two sub-colonels to optimize the resulting
best-case efficiency guarantees. Intuitively, one would imagine that the more
balanced the division of resources, the worse the performance, as such
divisions restrict the sub-colonels' ability to employ joint randomized
strategies that tend to be necessary for optimizing performance guarantees.
However, the main result of this paper demonstrates that this intuition is
actually incorrect. A more balanced division of resources can offer better
performance guarantees than a more centralized division. Hence, this paper
demonstrates that the resource division problem is highly non-trivial in such
enmeshed environments and worthy of significant future research efforts.
