Strategy configuration determines interaction patterns in partner-switching evolutionary games

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.