Partial behavioral switching. - Hiroyuki Ichijo (13891153) (2025)
At Nash equilibrium, we observed two forms of probabilistic speed change: partial behavioral switching, in which only one agent changed speed probabilistically (type 1), and behavioral switching, in which both predator and prey did so (type 2). A illustrates both types of switching across various behavioral cost coefficients (cb) and the reproduction coefficients of predators (r) under a detection distance for both agents (Dw = Ds = 2). The upper (a–d), middle (e–h), and lower rows (i–l) correspond to r = 4.0, 3.6, and 3.2, respectively. The left (a, e, and i), the middle-left (b, f, and j), the middle-right (c, g, and k), and the right columns (d, h, and l) correspond to cb = 0, 0.001, 0.02, and 0.04, respectively. Circle positions on the x- and y-axes indicate the Nash equilibrium speed changes of prey (s) and predators (w), respectively, aligned with the payoff landscape coordinates. Orange circles indicate the cases where the predator and prey probabilistically perform their behaviors with increasing and decreasing speeds. The diameters of the orange circles are proportional to the occurrence probabilities of the behaviors (i) (0 <i < 1). The prey increase or decrease their speeds (either escape or freeze), whereas the predators do not; i.e., partial behavioral switching is observed in e. Both agents probabilistically increase or decrease their speeds in a, b, c, f, g, and j. Blue circles indicate the cases where i is uniquely determined (i = 1) in d, h, i, k, and l. B shows percentages of behavioral switching in one of the agents (type 1, partial behavioral switching) and both agents (type 2, behavioral switching) across all combinations of cb and r. (TIF)