  Can egalitarian norms or conventions survive the presence of dominant
individuals who are ensured of victory in conflicts? We investigate the
interaction of power asymmetry and partner choice in games of conflict over a
contested resource. We introduce three models to study the emergence and
resilience of cooperation among unequals when interaction is random, when
individuals can choose their partners, and where power asymmetries dynamically
depend on accumulated payoffs. We find that the ability to avoid bullies with
higher competitive ability afforded by partner choice mostly restores
cooperative conventions and that the competitive hierarchy never forms. Partner
choice counteracts the hyper dominance of bullies who are isolated in the
network and eliminates the need for others to coordinate in a coalition. When
competitive ability dynamically depends on cumulative payoffs, complex cycles
of coupled network-strategy-rank changes emerge. Effective collaborators gain
popularity (and thus power), adopt aggressive behavior, get isolated, and
ultimately lose power. Neither the network nor behavior converge to a stable
equilibrium. Despite the instability of power dynamics, the cooperative
convention in the population remains stable overall and long-term inequality is
completely eliminated. The interaction between partner choice and dynamic power
asymmetry is crucial for these results: without partner choice, bullies cannot
be isolated, and without dynamic power asymmetry, bullies do not lose their
power even when isolated. We analytically identify a single critical point that
marks a phase transition in all three iterations of our models. This critical
point is where the first individual breaks from the convention and cycles start
to emerge.
