<p>The mutual influence between two communities constitutes a subtle dynamical process. Coupling serves as a fundamental mechanism for investigating such interactions, in which synchronization emerges as a critical phenomenon in coupled systems. However, synchronization has rarely been employed to explain cooperation in evolutionary games. Our work establishes a framework for synchronization of cooperation in evolutionary games between two coupled communities to study the emergence and persistence of cooperation. Models for unidirectionally and bidirectionally coupled replicator dynamics involving two communities are proposed. Through stability theory analysis, sufficient conditions for synchronization with more cooperation are derived. Notably, while cooperation in a community playing the Stag-hunt Game may vanish under certain initial conditions, the synchronization mechanism facilitates the emergence of cooperation in a community playing the Prisoner s Dilemma Game. Numerical experiments are presented to validate the theoretical findings. Specifically, if the coupling strength from the paragon-community (where individuals play a cooperative game) to the learner-community (where individuals play a non-cooperative game) is sufficiently large and the coupling strength from the learner-community to the paragon-community is sufficiently small, the coupled systems synchronize with more cooperation in the learner-community and the permanence of cooperation in the paragon-community.</p>

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The Synchronization of Cooperation in Evolutionary Dynamics with Two Communities

  • Yafei Zhang,
  • Haiyan Tian,
  • Gang Zhang

摘要

The mutual influence between two communities constitutes a subtle dynamical process. Coupling serves as a fundamental mechanism for investigating such interactions, in which synchronization emerges as a critical phenomenon in coupled systems. However, synchronization has rarely been employed to explain cooperation in evolutionary games. Our work establishes a framework for synchronization of cooperation in evolutionary games between two coupled communities to study the emergence and persistence of cooperation. Models for unidirectionally and bidirectionally coupled replicator dynamics involving two communities are proposed. Through stability theory analysis, sufficient conditions for synchronization with more cooperation are derived. Notably, while cooperation in a community playing the Stag-hunt Game may vanish under certain initial conditions, the synchronization mechanism facilitates the emergence of cooperation in a community playing the Prisoner s Dilemma Game. Numerical experiments are presented to validate the theoretical findings. Specifically, if the coupling strength from the paragon-community (where individuals play a cooperative game) to the learner-community (where individuals play a non-cooperative game) is sufficiently large and the coupling strength from the learner-community to the paragon-community is sufficiently small, the coupled systems synchronize with more cooperation in the learner-community and the permanence of cooperation in the paragon-community.