Effects of inertia on the evolution of cooperation in the voluntary prisoner’s dilemma game

Abstract

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.