Multi-games with voluntary participation on a dynamic network and the evolution of cooperation

Research indicates that introducing loner strategy into a population can spontaneously generate a cyclic dominance mechanism, with the loner strategy playing a pivotal role in the coevolution of cooperative behavior. However, existing multi-games on dynamic networks, which have been shown to promote cooperation, typically do not incorporate the loner strategy. This prompts the question: How would cooperation, defection, and the loner strategy evolve if the loner strategy were integrated into such models? To address this question, we develop three-strategy multi-games in a dynamic network context. We design coevolutionary rules for strategies and network structure and explore the evolutionary dynamics of group cooperation through numerical simulations. Our experimental results show that parameter variation in the magnitude of the sucker's payoff significantly suppresses loners and defectors, thereby promoting the proliferation of cooperators. Specifically, a larger magnitude of the sucker's payoff enhances this inhibitory effect, increasing the cooperation probability. Once the magnitude of the sucker's payoff reaches a certain threshold, the cooperation probability plateaus. We also examined the underlying mechanisms driving the substantial increase in group cooperation probability. Overall, this study enriches the theoretical framework of dynamic network games and provides new insights into fostering cooperative behavior in real-world contexts.