Indirect punishment can outperform direct punishment in promoting cooperation in structured populations

• Yujia Wen,

  Roles Conceptualization, Formal analysis, Investigation, Methodology, Software, Writing – original draft

  Affiliation Interdisciplinary Graduate School of Engineering Sciences, Kyushu University, Fukuoka, Japan

  ⨯
• Zhixue He,

  Roles Formal analysis, Methodology, Software, Validation, Writing – original draft

  Affiliation School of Statistics and Mathematics, Yunnan University of Finance and Economics, Kunming, China

  ⨯
• Chen Shen ,

  Roles Conceptualization, Formal analysis, Funding acquisition, Investigation, Methodology, Project administration, Writing – original draft, Writing – review & editing

  * E-mail: steven_shen91@hotmail.com

  Affiliation Faculty of Engineering Sciences, Kyushu University, Fukuoka, Japan

  https://orcid.org/0000-0002-2725-9763

  ⨯
• Jun Tanimoto

  Roles Funding acquisition, Project administration, Supervision, Writing – original draft, Writing – review & editing

  Affiliations Interdisciplinary Graduate School of Engineering Sciences, Kyushu University, Fukuoka, Japan, Faculty of Engineering Sciences, Kyushu University, Fukuoka, Japan

  ⨯