Emergence of cooperation promoted by higher-order strategy updates
Fig 4
Increasing overlap strength can foster cooperation.
a- c, Three homogeneous hypergraphs with large size N = 1000, hyperdegree k = 2, and order g = 4, differing only in the overlap strength between hyperedges, as defined in Eq (3). The overlap strengths are 1/4 in a (weak), 1/2 in b (moderate), and 5/8 in c (strong). d, Comparison of critical synergy factors for different overlap strengths under GMC, HDB, and HIM mechanisms. e- g, Another set of homogeneous hypergraphs with large size N, hyperdegree k = 3, and order g = 3, also differing in overlap strength: 1/3 in e (weak), 13/27 in f (moderate), and 5/9 in g (strong). h, Comparison of critical synergy factors for increasing overlap strengths under the same mechanisms as in d. Both comparison results ( d, h) show that stronger overlap decreases critical synergy factors across all the three mechanisms thereby promoting the emergence of cooperation.