Figure 1: Evolutionary dynamics in the space of deterministic reactive strategies, .

(a) Illustration of the dynamical process. Each grey circle represents a homogeneous population using one of the four possible strategies. Blue lines indicate whether a mutant strategy is advantageous (solid line), neutral (dashed line), or disadvantageous (dotted line). For advantageous mutants, the blue numbers show the mutant’s fixation probability according to Eq. (9). The graph suggests there are two likely paths for evolution: a short cycle from AllD, to TFT to AllC and back to AllD, or the longer cycle through AllD, TFT, AllC, ATFT, and back to AllD (in particular, eliminating the second cycle by removing ATFT from the strategy set would only lead to a minor modification of the general dynamics). The numbers within the grey circles give the abundance of each strategy according to the invariant distribution of the dynamical process; for the chosen parameters, AllD is the most abundant strategy. (b,c) show the abundance of each strategy depending on the cost of cooperation and for two different selection strengths w = 0.1 and w = 10. Other parameters: population size N = 100, error rate ε = 0.01, and in (a) w = 0.1.