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In this paper, we explore the effects of inertia on the evolution of cooperation in voluntary prisoner’s dilemma on a square lattice. In real life, individual inertia is hard to change due to the inherent characteristics of players. Only when he meets lazy and rich people, he will try to change his inertia. Inspired by this, the evolution of inertia is constructed as follows: initially each individual sets a different inertia value due to the heterogeneities among them. Considering loner is a risk averse player, we assume that he has the largest inertia during the simulation. Subsequently, as long as an individual encounters a loner and decides to change his strategy, he will learn his neighbor’s inertia simultaneously. Otherwise, his inertia will remain unchanged. Through a large number of simulations we find that, counterintuitively, individual inertia will impede cooperation. Especially, the larger value of inertia, the less likely the individual to change his strategy, and it severely weakened the effect of rock-scissor-paper cyclic dominance in promoting cooperation by making it happen less and less frequently, further leading to a full loner phase. For a comprehensive understanding, we give an explanation from macroscopic and microscopic aspects. Besides, we use a small-world network to verify the robustness of this mechanism. The results also suggest that individuals can maintain the diversity of the population only if they maintain appropriate enthusiasm to participate in social activities. Our work may provide further insight in understanding the role of inertia on the evolution of cooperation. [ABSTRACT FROM AUTHOR]

Cooperation in human interactions often involves voluntary participation rather than obligatory requirements. This paper investigates the impact of voluntary exit strategies on cooperation within scale-free networks, employing spatial prisoner's dilemma games as the framework. We analyze three distinct exit strategies: leader priority exit, fringe priority exit, and random exit, across varying dilemma strengths. Our findings reveal that in scenarios of weak dilemma strength, leader priority exit significantly diminishes cooperation, particularly when only a small subset of players is granted exit rights. In contrast, under strong dilemma strength conditions, both leader priority and random exits serve to unexpectedly bolster cooperation. This enhancement is primarily facilitated by high-degree nodes opting out, thereby enabling low-degree nodes to establish stable cooperation. Furthermore, our study underscores the pivotal role of network structure. In assortative networks, random exit emerges as the most effective strategy in promoting cooperation. On the other hand, disassortative networks exhibit a substantial increase in cooperation levels when employing leader priority exit. These results highlight the intricate interplay between exit strategies, dilemma strength, and network topology, offering critical insights for promoting cooperation in varied social contexts. • Study on leaders' priority exit's impact on cooperation dynamics. • Cooperation affected by leader priority exit varies with dilemma strength and network type. • Leader priority exit boosts cooperation in disassortative networks. • Random exit boosts cooperation in assortative networks. [ABSTRACT FROM AUTHOR]