- freely available
Games 2017, 8(1), 7; doi:10.3390/g8010007
3.1. Influence of the Update Rule
3.1.1. Unconditional Imitation
3.1.2. Mixed Update Rule
3.2. Other Topologies
3.3. Different Initial Conditions
3.4. Case of Vigilant Defectors
4. Discussion and Conclusions
- Vigilance needs the small-world effect (the presence of short-cuts connecting individuals physically far away from each other) to be efficient in fostering cooperation: indeed, in regular lattices, Figure 7, it does not help, and the small-world property is ubiquitous in most real social systems (only the smallest communities can be modeled by complete graphs, and Euclidean topologies are even more uncommon in human societies).
- Vigilance works not only when the individuals update their strategy by means of an essentially evolutionary rule (REP), but also when they evolve through more typically “social” mechanisms as pure imitation (at least on ER networks); moreover, considering the mixed rule, which takes into account the intrinsic non-strategic component of humans’ decision making processes, we found that the cooperation can tolerate the influence of irrationality only when this is low (), coherently with the results of Ref. .
- Concerning again the update rule, it is worth stressing that, in heterogeneous networks (scale-free), vigilance is beneficial for cooperation only with replicator update, whilst with strategic imitation (UI) the presence of hubs appears to be detrimental for the emergence of pro-social behaviors.
- The results do not depend sensitively on the initial conditions (at least in heterogeneous topologies): this is a fundamental feature of the model since it is usually hard to determine the initial conditions for real social systems; on the other hand, in complete graphs (i.e., in mean-field approximation), this is not true, but only small human communities can be described in this way, and, in such cases, different dynamical mechanisms are at work .
Conflicts of Interest
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