Figure 5
From: The shift between the Red Queen and the Red King effects in mutualisms
Complex cooperative behaviours in the snowdrift game with a reward or a general threshold.
(a) If the thresholds for the two species are M1 = 1 and M2 = 1, a bistability is observed between all cooperative individuals and all defectors. (b) When M1 = 1, M2 = 3, we observe the “white regions” with closed orbits in the interior. The initial conditions falling within the “grey region” will converge to the equilibrium (C1, D2) and those falling within the “green region” will converge to the equilibrium (D1, C2). (c) When M1 = 1, M2 = 6, all initial conditions lead to (D1, C2). At this point, only one side chooses to cooperate while the other side chooses to defect. (d) In the special case of Mi = di+1 and wi = 0 with i = 1,2, the equilibrium point (C1, C2) (the ‘pink region’) is an ESS. In this case, full cooperation among players becomes possible. The other parameters are fixed at di = 4, bi = 2, ci = 1,wi = 0 with i = 1,2 and rx = ry = 1.
