Reputation-regulated punishment promotes cooperation in spatial public goods games on hypergraphs

In evolutionary game theory, promoting the emergence and maintenance of cooperation among self-interested individuals remains a fundamental challenge. Although punishment mechanisms can effectively suppress defection and promote cooperation, their implementation cost may weaken the competitiveness of punishers and affect their long-term stability. Moreover, interactions in real social systems often involve higher-order relationships, while most previous studies rely on pairwise network structures, which cannot fully capture the effects of group interactions on cooperative evolution. To address these issues, we propose a reputation-regulated punishment mechanism in spatial public goods games on a uniform random hypergraph, which captures how individual reputation regulates punishment behavior. Simulation results show that the punishment mechanism plays a fundamental role in promoting cooperation, where lower punishment costs and higher fines imposed on defectors significantly enhance the cooperation level. Meanwhile, reputation regulation strengthens the stability of punishment and further suppresses defection. In addition, the structural parameters of the hypergraph strongly influence cooperation. Higher hyperlink order accelerates the spread of cooperation, while variations in the number of hyperlinks shift the critical conditions for cooperation transitions. Moreover, a simplified theoretical analysis provides theoretical support for the cooperation-promoting effect of the proposed mechanism. These findings provide new insights into the emergence of cooperation.