Enhancing cooperation through payoff-related inertia in networked prisoner's dilemma game

In human societies and animal groups, individual behavior is often driven by self-interest, with actions typically avoided if they do not yield benefits. This paper focuses on payoff-related inertia, which describes the tendency of individuals to resist updating their strategies when faced with significant decreases in total payoffs compared to the last round. Through extensive simulations in both regular lattice and small-world networks, we find that individual inertia and its impact on cooperation evolves over time in Prisoner's Dilemma game. At early stages, increased inertia due to decreased payoffs reduces transition probabilities between cooperators and defectors, preventing rapid collective shifts to defection and allowing the formation of cooperative clusters. As these clusters form, payoff-related inertia facilitates the transition of defectors to cooperators, promoting the expansion and stability of cooperative groups. Furthermore, we find that the introduction of payoff-related inertia enhances cooperation levels more significantly in small-world networks compared to regular lattice. Our study sheds light on the mechanisms that foster cooperation among self-interested individuals, contributing to a deeper understanding of cooperative behavior. By examining the dynamic interplay between strategy-updating inertia and evolutionary cooperation, we provide insights into the conditions that promote the emergence and stability of cooperation in social dilemmas.