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.

翻译：在多智能体系统中，有限资源应集中分配给少数高效智能体，还是分散给众多简单智能体？本文提出了 $n$ 个智能体共享资源问题，其中一组 $n$ 个智能体平均共享公共资源（例如，货币预算、计算资源、物理尺寸）。我们以多智能体覆盖问题为案例，其中智能体圆盘形覆盖范围的面积按 $1/n$ 缩放。正式分析表明，初始覆盖率随 $n$ 增加而增长。然而，若智能体速度与其半径成正比减小，则所有规模小组表现相同；若速度与其覆盖范围成正比减小，则单个智能体表现最优。我们还通过计算机仿真展示了资源分配会增加单个智能体的故障率。该模型和发现有助于确定最佳分散程度，并为资源约束下多智能体系统的设计提供参考。