Split over $n$ resource sharing problem: Are fewer capable agents better than many simpler ones?

In multi-agent systems, should limited resources be concentrated into a few capable agents or distributed among many simpler ones? This work formulates the split over $n$ resource sharing problem where a group of $n$ agents equally shares a common resource (e.g., monetary budget, computational resources, physical size). We present a case study in multi-agent coverage where the area of the disk-shaped footprint of agents scales as $1/n$. A formal analysis reveals that the initial coverage rate grows with $n$. However, if the speed of agents decreases proportionally with their radii, groups of all sizes perform equally well, whereas if it decreases proportionally with their footprints, a single agent performs best. We also present computer simulations in which resource splitting increases the failure rates of individual agents. The models and findings help identify optimal distributiveness levels and inform the design of multi-agent systems under resource constraints.