Higher-order interactions with payoff weighting promote cooperation in public goods on simplicial complexes

Cooperation is commonly observed in social and natural systems. Interaction topology is recognized as a catalyst for cooperation, and most work has focused on pairwise interactions. However, higher-order interactions among three or more participants are widespread in real-world, and pairwise models do not fully capture them. In this work, we improve the public goods game model on simplicial complexes that combines higher-order interactions, nonlinear synergy parameters, and payoff weighting. This model allows the payoff weights on 1-simplices and 2-simplices to be adjustable. The effects of the nonlinear synergy parameter ω, the 2-simplex fraction P, and the weighting coefficients λ and β on cooperation are investigated through Monte Carlo simulations. On the simplicial complexes, the results indicate that higher-order structures alone do not promote cooperation. When nonlinear synergy and higher-order interactions work together, a significant reduction in the cooperation threshold and a substantial expansion of the cooperation region are observed. Various allocations of the payoff weight parameter have a moderating effect on the cooperative evolutionary process. Furthermore, strategic coherence of multi-party interactions in a network can facilitate cooperative diffusion.