Structure-aware imitation dynamics on higher-order networks

Imitation is a basic updating mechanism for strategy evolution in structured populations, determining how individuals sample social information and translate it into behavioral changes. Higher-order networks, such as hypergraphs, generalize pairwise links to hyperedges and provide a natural representation of group interactions. Yet existing studies on higher-order networks largely emphasize structural effects, while the impact of imitation-based update rules and how they interact with group structures remains poorly understood. Here, we introduce a class of structure-aware imitation rules on hypergraphs that explicitly parameterize how many groups are sampled and how many peers are consulted within each sampled group. Under weak selection, we derive an analytical condition for the success of cooperation for any multiplayer social dilemmas on homogeneous hypergraphs. This analysis yields an interpretable metric, information diversity, which quantifies how an update rule diversifies the sources of social information across groups. Analytical predictions and numerical simulations show that cooperation is more effectively promoted by update rules that induce higher information diversity for three representative dilemmas. Further simulations demonstrate that this principle extends to non-homogeneous hypergraphs and a broad class of multiplayer social dilemmas. Our work thus provides a unifying metric that links microscopic updating to evolutionary outcomes in higher-order networked systems and establishes a general design principle for promoting cooperation beyond pairwise interactions.

💡 Research Summary

The paper addresses a gap in the literature on evolutionary game dynamics on higher‑order networks (hypergraphs) by focusing not on structural effects alone but on the interplay between network structure and the microscopic imitation update rules that individuals use to revise their strategies. The authors introduce a class of “structure‑aware imitation” rules parameterized by two integers, s and q. When a focal individual is selected to update, it first randomly samples s hyperedges from its k incident hyperedges, then from each sampled hyperedge it randomly chooses q neighbors as role models. The set of sq role models is denoted Ω(s,q). The focal individual then imitates one of these models with probability proportional to the model’s fitness f = exp(w·π), where π is the average payoff obtained from all multiplayer games the individual participates in, and w is the selection intensity.

Under weak selection (w ≪ 1), the authors analytically derive fixation probabilities for cooperators (ϕC) and defectors (ϕD) on homogeneous hypergraphs where every node has the same hyperdegree k and every hyperedge contains exactly m nodes. They obtain a condition for cooperation to be favored (ϕC > ϕD) that can be written as a sum over payoff differences weighted by a factor η(s,q). The factor

η(s,q) = k(m‑1)·