Fig 1.
Long-run cooperation by Greed by Fear, with four levels of initial cooperation. (A) 10% Initial cooperators. (B) 30% Initial cooperators, (C) 50% Initial cooperators. (D) 70% Initial cooperators.
The effects of Greed and Fear on long-run cooperation are highly nonlinear, with cooperation exploding or collapsing at particular combinations of Greed and Fear. With initial cooperators randomly dispersed, higher initial levels of cooperation generally make cooperation more viable at the system level, because the viability of cooperation depends on local clusters of cooperators. However, the relationship between initial cooperation and long-run cooperation is not simple and may even be non-monotonic in some conditions, depending on the levels of Greed and Fear.
Fig 2.
Long-run cooperation by Greed by Fear, with 90% initial cooperators.
Results for high initial cooperation (90%) offer the most general and revealing view of the effect of Greed and Fear on cooperation. This highlights that the effects of Greed and Fear are nonlinear, as cooperation explodes (or collapses) at critical values of Greed and Fear. Although individual agents do not respond differently to Greed or Fear, the system-level effects of these two parameters of the dilemma are quite different, and these effects are interactive: The figure shows that there is a primary cliff that is a function of both Greed and Fear. When Fear is high, cooperation is a gradually decreasing function of Greed. When Fear is low, Greed has little effect on cooperation over the bottom half of the range, and then cooperation falls steeply. At both low and high levels of Greed cooperation is relatively insensitive to Fear, but at middle levels of Greed cooperation plummets as Fear exceeds a moderately low value.
Fig 3.
Replication of experiment on empirical inter-organizational network data, with 90% initial cooperators.
The model is applied to empirical data on relationships among 2,400 corporations, which are similar in several ways to the Moore neighborhood (high clustering, similar network size and density and thus similar average neighborhood size) but also include short path lengths and a skewed degree distribution. The figure shows that there is a primary cliff that is a function of both Greed and Fear. When Fear is high, cooperation is a gradually decreasing function of Greed. When Fear is low, Greed has little effect on cooperation over the bottom half of its range, and then cooperation falls steeply. At both low and high levels of Greed cooperation is relatively insensitive to Fear, but at middle levels of Greed cooperation plummets as Fear exceeds a moderately low value.