Figure 3
From: Strategic tradeoffs in competitor dynamics on adaptive networks
Dynamical trajectories for competitor using strategies p 1 = 0.5, p 2 = 0.4, and p 3 = 0.3. (left) This triangle contains all possible dynamics: we show trajectories through a space where every point is defined by a unique (x 1, x 2, x 3) state. Therefore, any point within the triangle correspond to a mixed state where all competitors have non-zero frequencies, whereas the edges correspond to two-competitor dynamics. All stable fixed points are shown as black dots, and semi-stable and unstable fixed points appear as open circles (their stability can also be deduced by the linear flows shown in black arrows around them). We delineate the three regions corresponding to states where one of the three competitors are respectively winning by a relative majority. While competitor 1 uses p 1 = 0.5, which is optimal on a one-on-one basis as shown by the two fixed points close to the (1, 0, 0) apex, it systematically loses when all three strategies are involved. (middle) Example of a time series starting at (0.099, 0.002, 0.899), which corresponds to the one highlighted in the left figure. (right) The network structure when two strategies are aggressive and one is defensive corresponds to a core-periphery structure with the core corresponding to the highest p value. The network display style is the same as used in Fig. 2. The core is denser with nodes having a higher average total degree, but it does not target the periphery whereas nodes on the periphery preferentially targets the core and eventually win.
