Freedom of choice disrupts cyclic dominance but maintains cooperation in voluntary prisoner's dilemma game

Cyclic dominance has become a pivotal factor in sustaining cooperation within structured populations. However, this comprehension has predominantly revolved around node dynamics, where agents are constrained to adopt a uniform strategy with all neighbors. This constraint restricts agents’ capabilities to respond differently to various neighbors. In this study, we explore the under-emphasized role of freedom of choice in spatial games, applying a voluntary prisoner's dilemma model across diverse network structures. We differentiate between ‘node agents,’ who adhere to a consistent strategy with all neighbors, and ‘link agents,’ who adjust their strategies based on specific interactions, influenced by direct and indirect emotional factors. Direct emotion governs the strategy between two interacting agents, while indirect emotion encompasses the impact of third-party influences on strategic decisions. Our Monte Carlo simulations reveal that freedom of choices disrupts cyclic dominance establishment – particularly as the proportion of link agents grows – and influences the evolution of cooperation in nuanced ways. Specifically, a minor preference for upstream strategy delivery markedly promotes cooperation, while a strong preference diminishes it. Our findings suggest that the importance of cyclic dominance in promoting cooperation may have been overestimated, revealing that cooperation can flourish with varied strategies even in the absence of strong cyclic dominance.