Multiple learning mechanisms promote cooperation in public goods games with project selection

•Project selection mechanism is incorporated into threshold public goods game.•Multiple updating rules in project selection promote cooperation.•Higher cooperation corresponds to larger preferred project scale. How evolution favors cooperation is a fundamental issue in social and economic systems. In the business world, actively selecting a suitable project is usually helpful for a businessman to be in an advantageous position. By incorporating project selection mechanism into the threshold public goods game, we have investigated the coupling effect of mutation and imitation in updating one’s preferred project scale on the evolution of cooperation. Compared with the situation where there is no project selection mechanism, the existence of project selection may suppress or promote cooperation depending upon different updating rules. There exists a critical ratio of the imitators in the population, below which cooperation is suppressed while above which cooperation is promoted. With the coevolving of individual strategies and preferred project scales, a higher level of cooperation corresponds to a larger average value of the preferred project scales. A theoretical analysis indicates that, as most of the individuals are mutants, the coevolving process is governed by the mutation process, which leads to a smaller average value of the preferred project scales and a lower level of cooperation. As most of the individuals are imitators, the coevolving process is governed by the coupling of the mutation and imitation processes, which leads to a larger average value of the preferred project scales and a higher level of cooperation. As all the individuals are imitators, the coevolving process is governed by the imitation process, which leads to an intermediate average value of the preferred project scales and an intermediate level of cooperation.