Self-questioning dynamical evolutionary game with altruistic behavior and sharing mechanism in scale-free network

Abstract

The spatial evolutionary game is one of the efficient models to explain the emergence and maintenance of cooperation among selfish individuals. In the existing work, the relationship between self-questioning dynamical evolutionary game model and Ising model has been discussed. However, the study on the dividing lines which were used to distinguish entirely cooperative phase, entirely defective phase and cooperative and defective coexistence in the ground state is not enough. That is, the dividing lines were only considered to be suitable for regular networks before. To address this issue, a self-questioning evolutionary game model with altruistic or sharing preference is studied in scale-free Barabasi–Albert networks. Using the Ising model theory and Monte Carlo simulation, it is found that the players considering their opponents’ payoffs with probability p are equivalent to the players sharing their payoffs with probability $$p/(1+p)$$ . A further research on the relationship between the self-questioning dynamical evolutionary game model and Ising model shows that the dividing lines are in fact unrelated to network structure, which means that the dividing lines are suitable for arbitrary networks. In addition, the nodes with large degree have higher stability and robustness than those with small degree.