Role of second-order reputation evaluation in the multi-player snowdrift game on scale-free simplicial complexes

Over the past few decades, the network topology is often characterized via pairwise interactions in the field of indirect reciprocity. However, from human society to ecosystem, interactions usually occur in a group with three or more agents and cannot be fully explained in term of dyadic interactions. In this paper, we improve the multi-player snowdrift game based on scale-free simplicial complexes, and introduce four representative second-order assessment norms to analyze the impact of higher-order topology and reputation evaluation on collective cooperation behaviors. In the model, a focal player i’s general payoff will be regulated by the weight (λ) of player i’s payoff gained in 1-simplices and 2-simplices. Through plenty of Monte Carlo simulations, the results of numerical simulation show that cooperation level can be elevated under certain parameters by introducing non-pairwise interactions. The frequency of cooperation increases (decreases) with the growth of percentage of 2-simplex (ρ) when the cost-to-benefit (r) is smaller (larger). Meanwhile, cooperation behavior can be greatly changed by different reputation evaluation norms (e.g., Shunning rule presents the worst case in terms of the stationary cooperation level, while Image scoring norm creates the highest one). Current results provide some insightful clues for us to comprehend the emergence of mutually beneficial symbiosis in the realistic networked population.