Fig. 3: Dynamics on the edges of the simplex for alternative consensus making processes.
Left. Instead of a frequency-dependent process as in Eq. (SI.1), if the consensus belief is decided with the flip of a fair coin then the eventual outcome is as shown in the figure. We do not show the links in the interior as all of them consist of an unstable equilibrium and are hence impassable. A population starting at (H,H,1) will be stuck in the hare equilibrium (H,H,⋆). The appearance of the unstable fixed points along the edges lock the population in pure hare or pure stag states. The consensus function f(k, u⋆) = 0.5. Qualitatively similar dynamics are obtained for other fixed values of f(k, u⋆). Right. The consensus belief is chosen by a majority vote. The group belief is then the one which more than G/2 members prefer. In this case we see the appearance of a loop where (S,H,2)and (S,H,1)can lead back to the all hare hunters. However, in the long run, stag hunting in the ultimate sink for the dynamics. Now, the consensus function f(k, ustar) returns the chosen belief if the majority believes in it. For both the figures the other parameters are, G = 5, M = 4, PS = 4 and PH = 1.
