Among purely selfish agents, where defecting always pays more than cooperating, can cooperation survive at all — or is it doomed?
▶ Launch the interactive simulationThe spatial prisoner's dilemma (Nowak–May 1992). Cooperators and Defectors on a grid; each plays the PD with its 8 neighbours and itself (C–C=1, C–D=0, D–C=b, D–D=0, temptation 1<b<2), sums the payoff, then copies the best-scoring strategy nearby. Sweep the temptation b and measure the equilibrium cooperator fraction f_C; run one regime live, coloured by the four strategy transitions.
cooperation SURVIVES — rescued by space. In a well-mixed crowd defection is the only outcome (f_C→0): a defector always out-earns the cooperators it exploits. But on a lattice, cooperators huddle into CLUSTERS whose interiors prosper and resist invasion, so f_C stays well above zero across the whole 1<b<2 range — and in the chaotic regime near b≈1.9 it locks onto f_C≈0.31 (converging to the Nowak–May value ≈0.318 at larger lattice / longer averaging), the frontier churning forever in the famous 'evolutionary kaleidoscope'. Only at b=2 does cooperation finally collapse. (The survival is itself a finite-size effect: robust on a large grid L≥100, but on small lattices cooperation can stochastically collapse to zero in this chaotic window.) Spatial structure alone — no memory, kinship, or foresight, and the self-game is what lets a lone cooperator pair seed a cluster — lets cooperation persist where rational selfishness says it must die