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Updated: Apr 23, 2026

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Indirect reciprocity with environmental feedback
Yishen Jiang1,2,3, Xin Wang2,3,4,5,6, Ming Wei1,2,3
1School of Mathematical Sciences, Beihang University, Beijing 100191, China.
Chaos (Woodbury, N.Y.)
|April 21, 2026
Summary
Environmental feedback lowers the threshold for cooperation. Strict norms are crucial for maintaining cooperation in dynamic environments, unlike lenient norms in static settings.
Area of Science:
- Evolutionary game theory
- Social dynamics
- Environmental science
Background:
- Cooperation in human societies is often maintained by indirect reciprocity and social norms.
- Traditional models assume static environments, neglecting the impact of collective actions on resource dynamics.
- Real-world systems exhibit dynamic interactions where behavior influences reputation and environmental conditions.
Purpose of the Study:
- To develop a co-evolutionary framework integrating moral assessment, strategy updating, and environmental dynamics.
- To investigate how environmental feedback influences the emergence and maintenance of cooperation.
- To compare the effectiveness of different social norms (lenient vs. strict) in dynamic environments.
Main Methods:
- Established a co-evolutionary model coupling individual behavior, reputation, and environmental changes.
- Simulated the dynamics of cooperation under varying environmental feedback mechanisms.
- Analyzed the impact of norm strictness on cooperation stability and evolutionary resilience.
Main Results:
- Environmental feedback significantly lowers the threshold for cooperation emergence.
- The system can spontaneously transition from low to high cooperation states, reducing initial condition dependence.
- Strict norms are essential for curbing opportunism and ensuring evolutionary resilience in dynamic settings, while lenient norms are more suited for static environments.
Conclusions:
- Dynamic environmental feedback is a critical factor in promoting and sustaining cooperation.
- Strict social norms are vital for robust cooperation in complex, changing environments.
- This study provides a novel perspective on the interplay between social institutions and environmental constraints in governing collective behavior.
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