Synergy and discounting effects in spatial public goods games on hypergraphs: The role of third-order reputation-based dynamic assessment

Hypergraphs provide a precise framework for capturing higher-order interactions in complex social systems, as well as synergy and discounting effects describe the nonlinear accumulation of benefits in social dilemmas initially. Inspired by the accurate representation of environmental evaluation trends by higher-order reputation, we propose a novel model called third-order reputation-based dynamic assessment to adjust synergy and discounting effects dynamically. Specifically, behavioral shifts are evaluated using third-order reputation, considering both personal and opponent reputations, alongside the dynamic reputation threshold adapting based on global average reputation and local conditions. Synergy and discounting effects dynamically adjust based on the gap between group reputation and the established threshold. Numerical simulations reveal that the third-order reputation-based dynamic assessment effectively promotes the evolution of cooperation in spatial public goods games on uniform random hypergraphs. An increase in the environmental reputation-adjusted investment factor α, the reputation gap factor β, and the reputation change value w all contribute to enhancing cooperation. The local–global reputation weighting factor θ indicates that global reputation has a more significant impact on promoting cooperation than local reputation. All four reputation rules promote cooperation, with the Shunning rule resulting in the clearest distinction between full cooperation and defection. Image Scoring is particularly effective in reducing defection. Furthermore, Simple Standing and Stern Judging similarly reduce defection, but they achieve lower levels of cooperation than Shunning.