According to prior research on partner-switching games, altering partners could stabilize cooperation. Yet the role of per-edge (interactive diversity, ID) vs. per-node (interactive identity, II) strategies under a single co-evolutionary rule remains deficiently understood. In this letter, we propose an edge-based game as a natural extension of a well-studied node-based model in adaptive networks. By varying only the initial distribution of strategies, our framework can transition from interactive identity to interactive diversity without altering the update rules. Permitting edge-specific strategies enables a structural mechanism where defectors can transition to cooperation through rewiring dynamics, substantially expanding the cooperation-supporting parameter region compared to node-based games. We find that cooperation in the edge-based (ID) setup can emerge even from low initial cooperation, because defectors may incrementally increase their cooperative ratio by severing disadvantageous edges. This effect is absent in node-based (II) games, which constrain each node to a single global strategy. Moreover, numerical evidence suggests that higher initial cooperation does not guarantee higher final cooperation in ID games, underscoring the non-monotonic and homophily-driven nature of cooperative cluster formation. Our results thus clarify how partner-switching, when combined with interactive diversity, yields complex threshold behaviors unseen in the conventional node-based setting. Finally, we use pair approximation to illustrate why accurate theoretical predictions require richer local information in edge-based models, where each directed edge may evolve independently.
Dr. Hsuan-Wei "Wayne" Lee is an Assistant Professor in the Department of Biostatistics and Health Data Science at Lehigh University. His research applies statistical physics, network science, and evolutionary game theory to understand collective behavior and public health dynamics. Using mathematical modeling, differential equations, and agent-based simulations, he studies how behavioral responses co-evolve with epidemic spread and how social network structures influence cooperation, vaccination uptake, and health behaviors. His methodological toolkit spans statistical physics, stochastic processes, machine learning, and computational simulation, developed through collaborations across mathematics, physics, sociology, and public health.