Emergence of cooperation promoted by higher-order strategy updates
Fig 6
Higher-order updates tend to be more beneficial to cooperation than pairwise updates.
a, Higher-order updates involve two-stage selection: group selection followed by individual selection. b, Pairwise updates involve only individual selection. c, An empirical higher-order network of congress bills with N = 57 nodes and E = 108 edges (or hyperedges), where each node represents a congressperson and each hyperedge represents a bill composed of sponsors and co-sponsors. d, Comparisons of synergy factors between higher-order updates (HDB and HPC) and pairwise updates (DB and PC). e, Comparisons between the critical synergy factor for higher-order updates and
for pairwise updates. All seven-node subgraphs of the empirical network in c are extracted and sorted by
, with hyperedges formed by cliques. The results show that
in most of the seven-node hypergraphs, indicating that higher-order updates generally promote cooperation more effectively than pairwise updates.