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Updated: Apr 25, 2026

The HoneyComb Paradigm for Research on Collective Human Behavior
Published on: January 19, 2019
Local Nash equilibrium in social networks.
Yichao Zhang1, M A Aziz-Alaoui2, Cyrille Bertelle3
11] Normandie Univ, France; ULH, LMAH, F-76600 Le Havre; FR-CNRS-3335, ISCN, 25 rue Ph. Lebon, 76600 Le Havre, France [2] Department of Computer Science and Technology, Tongji University, 4800 Cao'an Road, Shanghai 201804, China.
This study introduces local Nash equilibrium for structured populations, offering a new way to predict evolutionary stability in games like Prisoner's Dilemma. It helps determine if cooperators can survive in evolving social networks.
Area of Science:
- Game Theory
- Evolutionary Biology
- Network Science
Background:
- Nash equilibrium is prevalent in social disputes but underexplored in structured populations like social networks.
- Rational agents in static gaming networks must consider opponent strategies, leading to new equilibrium concepts.
Purpose of the Study:
- To define and investigate local Nash equilibrium in two-strategy games within structured populations.
- To analyze conditions for evolutionary stable states in Prisoner's Dilemma and snow-drift games using this new equilibrium concept.
Main Methods:
- Explicitly defining local Nash equilibrium for structured populations.
- Investigating evolutionary stability conditions based on the local Nash equilibrium definition.
Main Results:
- Local Nash equilibrium provides a criterion to assess if a structured population has reached an evolutionary stable state.
- It enables prediction of cooperator survival in Prisoner's Dilemma games before the system stabilizes.
Conclusions:
- Local Nash equilibrium offers a theoretical framework for understanding evolutionary stability in structured gaming populations.
- This concept enhances our ability to predict game dynamics and cooperator persistence in social networks.
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