Fig. 3

Hawk-Dove, death-birth. Fraction of cooperators for the Hawk-Dove game as the graph structure change. The three communities here have degree k=3, k=4, k=7, and c/b=3/8. The black triangle is the level of cooperation in the mean-field case, at x^∗=5/8. When \(\sum _{i} \frac {k_{i}(k_{i}-1)}{(k_{i} +1)} > 8/3\) cooperation prevails, while for all other cases hawks and doves coexist in equilibrium, with a minimum level of cooperation when the graph is 5-regular