Figure 2.

(a) For BD updating, only the payoff of the two individuals right at the boundary between two clusters matters. The cluster of A players expands if $a+b>c+d$. (b) For DB and IM updating, the payoff of the four individuals closest to the boundary between two clusters matters. The cluster of A players increases if $2a+(a+b)>(c+d)+2d$ for DB updating and if $2a+3(a+b)>3(c+d)+2d$ for IM updating. All these results hold for weak selection. This figure gives the intuitive explanation of why cooperation can be favoured over defection for DB and IM updating, but not for BD updating.