Interaction stochasticity may hinder cooperation in the spatial public goods game

• Published in: Physics letters. A 2020-02, Vol.384 (5), p.126121, Article 126121
• Main Authors: Gao, Shiping, Wu, Te, Wang, Long
• Format: Article
• Language: English
• Subjects: Cooperation; Interaction stochasticity; Percolation threshold; Spatial public goods game
• ISSN: 0375-9601; 1873-2429
• DOI: 10.1016/j.physleta.2019.126121

•Whether cooperation can dominate crucially depends on the probability of opting-out.•Stochastic opting-out enhances cooperation when the probability is less enough.•Otherwise the evolution of cooperation may be hindered by stochastic opting-out.•There is an optimal probability of opting-out that is most beneficial for cooperation.•The optimal probability is related to the percolation threshold of the graph. We propose an analytic model to explore the effect of interaction stochasticity on the evolution of cooperation in spatial public goods game. The results show that whether cooperation can dominate in populations crucially depends on the player's probability of opting-out. Stochastic opting-out enhances cooperation as long as the probability of opting-out is less than a threshold depending on the graph's degree. Otherwise the promoting effect of spatial structures on cooperation is hindered even neutralized by stochastic opting-out. Moreover, there exists an intermediate optimal probability with which the advantage of cooperation over defection is maximized in the evolutionary race. Interestingly, the optimal probability is related to the percolation threshold of the underlying graph. Our findings illustrate that spatial structures may not facilitate cooperation when stochastic opting-out is allowed, and provide a link between physics and social sciences.