Avoiding the bullies: The resilience of cooperation among unequals

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. Previous models of cooperation do not include both power inequality and partner choice. Furthermore, models that do include power inequalities assume a static game where a bully’s advantage does not change. They have therefore not attempted to model complex and realistic properties of social interaction. Here, 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.
Author summary Individuals often differ in their ability to resolve conflicts in their favor, and this can lead to the emergence of hierarchies and dominant alphas. Such social structures present a serious risk of destabilizing cooperative social interactions or norms. Why work together to find food when a more aggressive or stronger individual can take all of it? In this paper we use game theory and agent-based modeling to investigate how cooperative behavior evolves in the presence of powerful bullies who have no incentive to cooperate. We show that when individuals can choose their interaction partners, bullies do not always destabilize cooperation. Instead, cooperative norms survive as individuals learn to avoid dominant individuals who become isolated in the population. When competitive ability itself depends dynamically on past success, complex cycles of coupled network-strategy-rank changes emerge: effective collaborators gain popularity and thus power, adopt aggressive behavior, get isolated, then lose power. Our results have important implications: in our modeled scenario the rich do not always get richer, the dominance of bullies can be broken, and inequality in accrued resources can be eliminated. Thus, our work provides new insight into potential sources of, and strategies for avoiding, resource inequality.