Extended Data Fig. 2: For M = 2, aggregating discriminators evolve versus unconditional strategies.

We estimated the volume of the basins of attraction towards aggregating discriminators, for a strategy space containing either strict (DISC_2/2,2) or tolerant (DISC_1/2,2) aggregating discriminators in the presence of ALLC and ALLD (left of dashed lines); and for the full strategy space with unconditional strategies and both aggregating discriminators (right of dashed lines). Each panel corresponds to a fixed, shared social norm. We estimated the basins by numerically integrating trajectories from evenly distributed initial frequencies in the interior of the simplex (171 for triplets and 975 for quartets; see Methods). The bars concatenate the steady states of all these trajectories. Regardless of the norm, tolerant discriminators are stable against unconditional strategies, while strict discriminators are not. When the full strategy space is considered, aggregating discriminators always have a basin of attraction. Under scoring or simple-standing, the stable equilibrium is a mix, with a large fraction of ‘look twice, forgive once’ coexisting with a small fraction of strict discriminators. Under stern-judging or shunning, we find a pure ‘look twice, forgive once’ stable equilibrium. The rate of cooperation at the discriminating equilibrium is 99.5% for scoring, 99.8% for stern-judging, 99.4% for simple-standing, and 99.8% for shunning. For all panels, the benefit-to-cost ratio is b/c = 5, with error rates of assessment and execution α = 0.02 and ε = 0.02, respectively.