Figure 4.

Basin of a cooperative regime in the private monitoring system. (a) staying and (b) simple-standing. The triangles describe a simplex of the state space, S = {(x, y, z): x + y + z = N}, where x, y, and z are non-negative integers denoting the frequencies of unconditional cooperators, unconditional defectors, and discriminators, respectively. The colored dots correspond to the probability of finally reaching a cooperative regime. Here, ten trials were performed on each point, (x, y, z) ∈ S. The borders of the basin of attraction are approximately (a) z = 0.15 and (b) z = 0.4. The averages of the probabilities for all of the points to finally reach a cooperative regime are (a) 76.04% and (b) 33.37%. The parameter values are N = 100, b = 3, c = 1, e ₁ = 0.03, e ₂ = 0.03, T = 100,000, T _s = 90,000, μ = 0, and β = 3.