Integrating the environmental factor into the strategy updating rule to promote cooperation in evolutionary games

Many previous studies have shown that the environment plays an important role for social individuals. In this paper, we integrate the environmental factor, which is defined as the average payoff of all a player's neighbours, with the standard Fermi updating rule by introducing a tunable parameter, ω. It is found that the level of cooperation increases remarkably, and that the cooperators can better resist the invasion of defection with an increase in ω. This interesting phenomenon is then explained from a microscopic view. In addition, the universality of this mechanism is also proved with the help of the small-world network and the random regular graph. This work may be helpful in understanding cooperation behaviour in species from unicellular organisms up to human beings.