Multi-player snowdrift game on scale-free simplicial complexes

Abstract

Nowadays, a large number of complex systems have been characterized by networks connecting the pairwise interacting agents. However, from human decision-making behaviors to chemical reactions and biological activities, interactions can also occur within groups with three or more nodes, which cannot be simply expressed by pairwise links. In this work, we consider the interactions beyond pairwise connections, and then propose a completely new and general method to explore the evolutionary dynamics of multi-player snowdrift game on networks with higher-order interactions. Among them, simplicial complexes combining 1-simplex and 2-simplex interactions are adopted to establish the underlying network, and the impact of non-pairwise interactions on the dynamics of multi-player snowdrift game is studied by adjusting the proportion (ρ) of 2-simplex. Numerical simulations show that the global frequency of cooperation depends on both the cost-to-benefit ratio (r) and ρ: when r is too small or too large, the variation of ρ has no influence on the cooperation frequency; while r is medium-sized, the cooperation frequency reduces with the increase of ρ. Surprisingly, by introducing the non-pairwise interactions based on 2-simplex, cooperation can be facilitated under some special parameter settings. Moreover, when r is moderate, the decrease in the cooperation frequency of low-degree individuals is the main reason for causing the decline of the global cooperation frequency. Current results provide a new perspective for us to comprehend the evolution of cooperation within the realistic networked population.