Avoiding the bullies: The resilience of cooperation among unequals
Fig 3
Partner choice restores the correlated convention and increases cooperation in the presence of bullies.
A, With partner choice and low f-value, individuals of all ranks play correlated conventions (predominantly host-guest as first shown in [12]). A transition occurs at f ≥ dh, identical to the random interaction case, where top ranked individual(s) break from the convention and become pure hawks. The correlated convention is preserved among outranked individuals. However, contrary to the random interaction case, partner choice allows the convention to remain sustainable among a majority of individuals even for high f values. This is infeasible under random interaction. B, The pattern in which some top ranked individual(s) break from the convention is consistent across population sizes. Notice how the shape of the curve in B matches the boundary where strategies change in A. Pure hawks are defined conservatively as agents with a likelihood of at least 0.8 for playing hawk both at home and away. C, The network structure that emerges resembles a hierarchy. Ranking individuals play pure hawk strategies but receive few or no visitors at all. Outranked individuals adopt the correlated convention and attract many visitors. The individual who is outranked by all others is visited by everyone. The graph shows average in-weights across seeds grouped by rank. Node size is scaled by incoming edge weight (dh = 0.4;dd = 0.6; f = 0.6). D, The highest degree of network centralization (most hub-like) is reached at f = 0.2. Nodes with disproportionate (too many) connections stop emerging entirely at f = 0.8 (color by mean network centralization). E, Network centralization over time, averaged across seeds. Networks with heterogeneous node weights emerge for a period of time. Network centralization of random Erdős–Rényi networks of the same size and density are shown as reference (the dashed line shows the median, the grey area is 95% CI).