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Highlight • The result exists an obvious piecewise phenomenon for individual's aspiration level on promoting cooperation Abstract In real life, everyone is full of yearning and pursuit for future life. The difference between reality and ideals encourage people to constantly adjust the current state, so that they can better adapt to changes in the surrounding environment. Thus, we propose a spatial prisoner's dilemma game model where individuals have expectation towards the payoff obtained from nearest neighbors, and individuals can adaptively adjust their update willingness based on the satisfaction of income. Through numerical calculation, we find that different b values will have an appropriate aspiration level to promote cooperation. In addition, the results have an obvious phase transition phenomenon for individual's aspiration level on promoting cooperation. Moreover, only moderate aspiration level can promote the evolution of cooperative behavior, due to it can lead to the heterogeneous distribution of update willingness, which will be beneficial to the evolution of cooperation. [ABSTRACT FROM AUTHOR]

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]

The emergence and maintenance of cooperation remains to be one of the overreaching problems and a number of scholars have devoted endless efforts to resolve such problems. To further explore this issue, we focus on the impact of heterogeneity of updating rules on cooperative behavior in voluntary prisoner's dilemma; here, two types of strategy updating rules are considered to mimic social facts which are listed as strategy learning mechanism and strategy teaching mechanism. The stability of different mechanisms on promoting cooperation is thoroughly investigated in this manuscript. Numerical simulations are conducted while corresponding results are presented with sufficient clarifications. We find that the strategy learning mechanism can promote cooperation steadily. However, with the variance in the proportion of the two update rules in the investigated community, the strategy teaching mechanism seems to be more sensitive. Moreover, compared with strategy learning mechanism, strategy teaching mechanism plays a more important and apparent role in promoting cooperation. We also find that personal strategy is sensitive to the varying of Loner's payoff σ, especially when σ is close to 1. We hope our findings will shed some lights on resolving the social dilemmas. [ABSTRACT FROM AUTHOR]