Interactive diversity disrupts cyclic dominance but maintains cooperation in spatial social dilemma games

Cyclic dominance has become a pivotal factor in sustaining cooperation within structured populations. However, this comprehension has predominantly revolved around node dynamics, where players are confined to employing the same strategy with all their neighbors. What has been largely overlooked is the profound influence of interactive diversity, where players can adapt distinct responses to different neighbors, on the dynamics of cyclic dominance and the broader patterns of cooperation. This investigation delves into the often-neglected role of interactive diversity in cyclic dominance and cooperation, utilizing a volunteer prisoner's dilemma model deployed on various network structures. Within this framework, we differentiate between `node players,' who adhere to a consistent strategy with all their neighbors, and `link players,' who adjust their strategies based on specific interactions, influenced by both direct and indirect emotional factors. Direct emotion governs the strategy between two interacting players, while indirect emotion encompasses the impact of third-party influences on strategic decisions. Through Monte Carlo simulations, we unveil a multifaceted relationship: interactive diversity generally disrupts cyclic dominance, yet its impact on cooperation varies, contingent on the prevalence of indirect strategy formulation. These findings suggest that the significance of cyclic dominance in fostering cooperation may have been overemphasized, as cooperation can persist even in the absence of strong cyclic dominance, owing to the presence of interactive diversity.