Effect of heterogeneous investments on the evolution of cooperation in spatial public goods game.

Understanding the emergence of cooperation in spatial public goods game remains a grand challenge across disciplines. In most previous studies, it is assumed that the investments of all the cooperators are identical, and often equal to 1. However, it is worth mentioning that players are diverse and heterogeneous when choosing actions in the rapidly developing modern society and researchers have shown more interest to the heterogeneity of players recently. For modeling the heterogeneous players without loss of generality, it is assumed in this work that the investment of a cooperator is a random variable with uniform distribution, the mean value of which is equal to 1. The results of extensive numerical simulations convincingly indicate that heterogeneous investments can promote cooperation. Specifically, a large value of the variance of the random variable can decrease the two critical values for the result of behavioral evolution effectively. Moreover, the larger the variance is, the better the promotion effect will be. In addition, this article has discussed the impact of heterogeneous investments when the coevolution of both strategy and investment is taken into account. Comparing the promotion effect of coevolution of strategy and investment with that of strategy imitation only, we can conclude that the coevolution of strategy and investment decreases the asymptotic fraction of cooperators by weakening the heterogeneity of investments, which further demonstrates that heterogeneous investments can promote cooperation in spatial public goods game.