Vector field plots of differential equations (2), (3) and (4). (A) in the absence of punishment and blackmailing (y = 0, a = 0), (B) in the presence of punishment but no blackmailing (y > 0, a = 0) and (C) in the presence of punishment and blackmailing (y > 0, a > 0). Arrows indicate the direction of change in strategy. Grey circle indicates unstable equilibrium and black circle indicates stable equilibrium. (A) and (B) end up at the stable equilibrium (0,1,0) whereas (C) leads to cyclic oscillations in strategies with no ESS. Other parameter values are l = z = 0.2, α = β = 0.2, cP = 0.01, cG = 0.02, y = 0.1, s = 0.4 and a = 0.08.
Watve et al. BMC Evolutionary Biology 2011 11:345 doi:10.1186/1471-2148-11-345