The behavior of the models under continuous variation of the structure of game <i>B</i>.

The color plot of the density of cooperators, ρC, in the direct interaction model A, and the reputation-based model B, in the SB − TB plane. The top panels show the result of the replicator-mutator dynamics and the bottom panels show the results of simulations in a population of 1000 individuals. In both cases, an unbiased initial condition (random assignment of strategies) is used. I have set R = 3, S = 0, P = 1, T = 5, RB = 3, and PB = 1. The boundaries of bistability are plotted as well. Below this boundary the dynamic is monostable, settling into a fixed point with a low level of cooperation. Above the boundary, a cooperative fixed point becomes stable and the dynamics become bistable. The two branches of the boundary meet at a critical point, where the transition becomes continuous. A comparison shows finite size effects strongly favor cooperation. Here, η = 0.1, and ν = 0.005.