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Co-evolutionary dynamics of threshold PGGs with collective-risk environment feedback

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  • Zhang, Zhipeng
  • Yang, Chen
  • Han, Weiwei
  • Xia, Chengyi

Abstract

At present, the collective-risk dilemma game has recognized the feedback loops between strategies and collective-risk. However, understanding how individual decision-making in complex real-world societies impacts collective-risk, and in turn influences individual strategies through such feedback mechanisms, remains an area that requires further exploration. We consider the co-evolutionary dynamics based on threshold Public Goods Games (PGGs) under collective-risk. First, this co-evolutionary game framework can be divided into two parts: threshold PGGs and the dynamics of collective-risk. The former represents the group dynamics of betrayal and cooperation strategies, while the latter can be seen as the evolutionary dynamics of collective-risk under strategic influences. Next, we examine the presence and stability of possible equilibrium points that could emerge from co-evolutionary dynamics. Subsequently, we introduce the method of manifold control to extend the framework and guide the co-evolutionary dynamics of threshold PGGs to a certain extent. Finally, a particular example is presented to validate the theoretical approaches. In summary, the method of manifold control offers a new perspective for exploring collective cooperation in the context of collective-risk dilemmas.

Suggested Citation

  • Zhang, Zhipeng & Yang, Chen & Han, Weiwei & Xia, Chengyi, 2025. "Co-evolutionary dynamics of threshold PGGs with collective-risk environment feedback," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 658(C).
    • Handle: RePEc:eee:phsmap:v:658:y:2025:i:c:s0378437124007854
    DOI: 10.1016/j.physa.2024.130275
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