Figure 1: The competition between pool exclusion and pool punishment in the optional PGG.
From: Competitions between prosocial exclusions and punishments in finite populations

Without second-order exclusion or punishment, shown in panel (a), the frequency of pool excluders is significantly higher than the portion of pool punishers, but all strategies can coexist in time average. In the presence of second-order exclusion and punishment, presented in panel (b), pool excluders prevail and dominate in the strong selection limit. Parameters: N = 5, r = 3, c = 1, μ = 10−6, σ = 1, M = 100, δ = 0.4, and G = B = 0.4.