Direct reciprocity between individuals that use different strategy spaces
Fig 4
A bifurcation analysis of the evolutionary dynamics of memory spaces.
We explore the replicator dynamics of the three different memory spaces for four different selection strengths β. In each case, we first classify the dynamics as we vary the cooperation cost from c = 0 to c = 1 (left graphs). Here, triangles show representative depictions of the dynamics. Colors indicate basins of attractions of each possible fixed point. If a given memory space Si is globally stable in a given cost interval, the respective line segment is appropriately colored. Colored shades around these line segments indicate a memory dilemma. Second, we also illustrate the average cooperation rate in monomorphic populations for each of the possible memory spaces (right graphs). If the respective monomorphic population is stable according to replicator dynamics, we use a solid line; otherwise we use a dashed line. a-d, For weak selection, unconditional strategies are globally stable for all cost values. As we increase selection strength, memory-1 strategies become stable when cooperation costs are sufficiently small. For large cooperation costs, reactive strategies are globally stable.