Fig 3. Coordination games with Proportional Imitation.

Stationary cooperation levels ρ _∞ vs α. The vertical solid lines identify the values of α _c. (a) ER graphs with m = 9 and various n. (b) SF networks with γ = 2.5 and various n; here α _c values were estimated from Equation (10) as ${\alpha }_c=c/{\Theta }_2\simeq c\overline{k}/\langle k^2\rangle$. (c) ER graphs with n = 10³ and various m. Note that for small values of m such that p = m/(n−1) < ln(n)/n the graph is disconnected: isolated nodes are bound to their initial action, so that full defection and full cooperation are not accessible states; additionally, defective behavior spreads easily inside isolated components which are poorly connected (also for high α), so that ρ _∞ remains far from 1.