Moving cooperators toward public goods destroys the public goods.
In a spatial public goods game (arXiv:2603.21025), cooperators who actively migrate toward regions with high public goods provision — chemotaxis-like directed motion — decrease overall cooperation and environmental quality. The intuition that cooperators should congregate where cooperation pays off is exactly wrong.
The mechanism: when cooperators cluster around existing public goods, they create concentrated islands of cooperation surrounded by depleted territory. Defectors exploit the boundaries — benefiting from the concentrated public goods without contributing — and the territory between islands degrades. The cooperator clusters produce more per capita but cover less ground. Total cooperation drops even as local cooperation intensifies.
The contrast with passive diffusion is sharp. When cooperators spread randomly through the landscape — moving without regard to public goods concentration — cooperation increases. Diffusion distributes cooperators into underserved areas where their contribution has the highest marginal impact. Directed motion concentrates them where cooperation already exists, wasting marginal contributions where they're least needed.
This is a spatial instantiation of a general principle: optimizing locally can degrade globally. Each cooperator is individually rational to move toward better-provisioned regions. The collective effect of this individually rational movement is collectively destructive. The cooperators are not competing with each other. They're crowding each other, and the crowding makes the landscape worse for everyone including themselves.
The spatial pattern that emerges — cooperation islands in a sea of defection — is stable but suboptimal. The system self-organizes into the wrong configuration, and the wrong configuration persists because no individual cooperator benefits from leaving the island. The trap is not defection. The trap is congregation.