Integrating neighborhoods in the evaluation of fitness promotes cooperation in the spatial prisoner’s dilemma game

A fundamental question of human society is the evolution of cooperation. Many previous studies explored this question via setting spatial background, where players obtain their payoffs by playing game with their nearest neighbors. Another undoubted fact is that the environment plays an important role in the individual development. Inspired by these phenomena, we reconsider the definition of individual fitness which integrates the environment, denoted by the average payoff of all individual neighbors, with the traditional individual payoffs by introducing a selection parameter uu. Tuning uu equal to zero returns the traditional version, while increasing uu bears the influence of environment. We find that considering the environment, i.e.  , integrating neighborhoods in the evaluation of fitness, promotes cooperation. If we enhance the value of uu, the invasion of defection could be resisted better. We also provide quantitative explanations and complete phase diagrams presenting the influence of the environment on the evolution of cooperation. Finally, the universality of this mechanism is testified for different neighborhood sizes, different topology structures and different game models. Our work may shed light on the emergence and persistence of cooperation in our life.

Research highlights
► We take neighbors’ payoffs in the evaluation of individual fitness in spatial games.
► This mechanism is robust to promote cooperation.
► We also provide quantitative explanations presenting the evolution of cooperation.