Figure 2
From: Direct reciprocity and model-predictive rationality explain network reciprocity over social ties
Invasion, persistence, and fixation of cooperation under direct reciprocity and model-predictive rationality. Panels show the level of cooperation reached in 104 game rounds starting from 1% inital C’s on different network structures (left: average degree \(\langle k\rangle =4\); right: \(\langle k\rangle =8\)) as a function of the PD return r. Solid lines show the average fraction over 100 random initializations (random placement of the initial C’s in planar lattices; network generation and random placement of the initial C’s for random—single scale and scale free—networks; the average % of isolated initial C’s is reported). Dots show the outcome of single simulations (only for \({r}_{{\rm{inv}}} < r < {r}_{{\rm{fix}}}\), i.e., only if some of the outcomes lie in the open interval (0, 1)); transparency is used to show dots accumulation. Colors code the predictive horizon h, from 2 to 5, and the corresponding upper bound \({\bar{R}}_{{\rm{fix}}}\) to the threshold Rfix is reported. Model parameters: reference values in Table 1. See Sects S11 and S12 for further details on networks and numerical simulations.
