Spatial Cooperation Simulator

What you just saw

In well-mixed populations, defection always wins the prisoner's dilemma. But on a 2D grid, cooperators can survive by clustering — the edge of a cooperator cluster loses to defectors, but the interior is safe, and the cluster as a whole outgrows defector patches. There's a sharp phase transition near T = 1.50: below it, cooperation dominates; above it, defection sweeps the grid.

The science behind it

Martin Nowak and Robert May introduced this model in Nature in 1992. It was one of the first convincing demonstrations that spatial structure — not kin selection, reciprocity, or reputation — is enough to sustain cooperation in a prisoner's dilemma. It became the foundation of an entire field studying the evolution of cooperation on networks, including modern results on heterogeneous scale-free networks (Santos & Pacheco, 2005).

Try these experiments

1. 1. Cooperator-dominated

   Settings: temptation=1.4

   What to look for: Cooperators survive in stable clusters. Fraction stabilizes around 0.6–0.8.

2. 2. Edge of chaos

   Settings: temptation=1.50

   What to look for: Noisy, turbulent boundaries. The cooperator fraction oscillates and the pattern looks alive.

3. 3. Defection wins

   Settings: temptation=1.7

   What to look for: Defection sweeps the grid in ~20 steps. No cooperator clusters survive.

from scirouter import SciRouter
client = SciRouter(api_key="sk-sci-...")
result = client.simulation.run(
    model="cooperation",
    params={"grid_size": 1000, "temptation": 1.45,
            "initial_cooperator_fraction": 0.5},
    steps=500, seed=42,
)