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This paper introduces the "split over $n$" resource sharing problem, analyzing the trade-offs between concentrating resources in fewer, more capable agents versus distributing them among many simpler ones in multi-agent systems. Through formal analysis and simulations in a multi-agent coverage task, they show that while initial coverage rate increases with the number of agents, performance can degrade if agent speed is significantly affected by resource splitting, and individual agent failure rates increase. The study highlights the importance of considering the scaling relationship between agent capabilities and resource allocation when designing multi-agent systems.
More agents aren't always better: splitting resources too thinly can actually hurt multi-agent system performance, especially when individual agent failure rates increase.
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.
