The evolution of cooperation in games with multiple strategies under different update rules

Cooperative is essential for the maintenance of public resource, however, individual's selfish behavior will reduce cooperation level and public resource. Here, we investigate the two-person public goods game in finite populations with multiple strategies. Under weak selection, theoretical results are found to be in excellent agreement with simulation results. Two representative update rules are used in our model and their results are compared: under weak selection, the cooperative level is higher in the Moran process than that in the Wright Fisher process, which is up to the payoff function and the strategy's update frequency. Besides, we also investigate how mutation rate or enhancement factor influences the amount of public resource. Under strong selection, public resource is more insensitive to mutation rate, and raising enhancement factor alone is in vain until its value gets large enough. However, under weak selection, even at a very low mutation rate, there is a better linear relation existing between public resource and enhancement factor. These findings not only have practical significance, but also provide a guidance to improve the cooperation level.