Figure 3
Myopic best response updating in structured populations stabilizes extortion and cooperation.
Depicted are the stationary frequencies of surviving strategies in dependence on the strength of the social dilemma b, as obtained for the strength of extortion χ = 1.5 on the square lattice (top), the random regular graph (middle) and the scale-free network (bottom). It can be observed that players adopting the WSLS strategy dominate for sufficiently small values of b on homogeneous interaction networks (top and middle), but as b increases or if the interaction network is heterogeneous (bottom), the pure WSLS phase gives way to a stable five-strategy WSLS + D + Eχ + TFT + C phase. Here defectors emerge and coarsen spontaneously because for sufficiently large values of b their payoff becomes larger than that of clustered WSLS players. The emergence of defectors immediately opens the door to the survival of extortioners and TFT players, which both emerge by chance and spread by means of neutral drift. Lastly, with the emergence of extortioners and TFT players cooperators become viable as well, thus forming the stable five-strategy phase. The latter is virtually unaffected by different values of χ, as demonstrated in Fig. 4. Importantly, the described coexistence of the competing strategies is a universal behavior that can be observed in structured populations regardless of the properties of the interaction network and even across the whole span of b values, as illustrated in the bottom panel. Characteristic snapshots depicting the described key stages of the evolutionary process are presented in Fig. 5.
