Avoiding the bullies: The resilience of cooperation among unequals
Fig 2
In games of conflict with power asymmetry and random interaction, individuals with different ranks effectively face different games.
A, Analytical analysis of our model reveals that, under random interaction, individuals play different games, depending on their rank and the degree of the power asymmetry f (see S1 Text). For f < dh, power asymmetry has no effect and individuals of all ranks engage in a mean game of conflict (the orange area). For f ≥ dh, the game is dominant-solvable for the top ranked individual(s). B, Numerical results from evolutionary simulations show that conventions prevail when f is below the critical value dh; individuals of all ranks play correlated conventions (either all ownership or host-guest; each appear with equal frequency in simulation seeds; ownership shown). At f ≥ dh a transition occurs as ranking individuals break from the convention and adopt pure hawk behavior both home and away. The correlated convention is resilient among most individuals until high values of f make it unsustainable. A hierarchy forms in which the top-half of individuals are pure hawks while the bottom-half are pure doves. Note how the analytic result on the left matches the numeric result on the right. (Both panels use n = 20; dh = 0.4; dd = 0.6).