Hierarchy is an efficient way for a group to organize, but often goes along with inequality that benefits leaders. To control despotic behaviour, followers can assess leaders’ decisions by aggregating their own and their neighbours’ experience, and in response challenge despotic leaders. But in hierarchical social networks, this interactional justice can be limited by (i) the high influence of a small clique who are treated better, and (ii) the low connectedness of followers. Here we study how the connectedness of a social network affects the co-evolution of despotism in leaders and tolerance to despotism in followers. We simulate the evolution of a population of agents, where the influence of an agent is its number of social links. Whether a leader remains in power is controlled by the overall satisfaction of group members, as determined by their joint assessment of the leaders behaviour. We demonstrate that centralization of a social network around a highly influential clique greatly increases the level of despotism. This is because the clique is more satisfied, and their higher influence spreads their positive opinion of the leader throughout the network. Finally, our results suggest that increasing the connectedness of followers limits despotism while maintaining hierarchy.

Direct reciprocity is one of the mechanisms for sustaining mutual cooperation in repeated social dilemma games. Zero-determinant (ZD) strategies allow a player to unilaterally set a linear relationship between the player’s own payoff and the co-player’s payoff regardless of the strategy of the co-player. The original ZD strategies were derived for infinitely repeated games. Here, we analytically search for ZD strategies in finitely repeated prisoner’s dilemma games. Our results can be summarized as follows. First, we present the forms of ZD in finitely repeated games, which are directly extended from the known results for infinitely repeated games. Second, for the three most notable ZD strategies, the equalizers, extortioners, and generous strategies, we derive the threshold discount factor value above which the ZD strategies exist. Finally, we show that the only strategy sets that enforce a linear payoff relationship are either the ZD strategies or unconditional strategies.