Figure 1
From: Fixation Probabilities for Any Configuration of Two Strategies on Regular Graphs
Calculation of the local frequencies of Eqs (3),(4),(5),(6), f1(x, ξ), f0(x, ξ), and f10(x, ξ), where ξ is the configuration consisting of a defector at vertex y and cooperators elsewhere.
Among the three neighbors of the player at vertex x, two are cooperators (u and v) and one is a defector (y); thus, f1(x, ξ) = 2/3 and f0(x, ξ) = 1/3. Furthermore, of the nine paths of length two that begin at vertex x, only two (x → u → y and x → v → y) consist of a cooperator followed by a defector, and it follows that f10(x, ξ) = 2/9.
