The evolution of cooperation in public goods games on signed networks

Evolutionary game theory describes a system in which individuals interact with each other. In recent years, the combination of complex network and evolutionary game theory, which is supposedly the best way to interpret how cooperate strategies are maintained in rational population pursuing maximum benefit, has gained considerable attention. There are numerous studies on public goods game (PGG), which is the classic laboratory paradigm for studying collective action problem. Now, we consider a PGG on the random signed network. Individuals interact and play games along the social ties defined by a signed network, where the positive links indicate the friendship and the negative links indicate the hostile relationship among the players. Here, we design an evolutionary mechanism: the rule is that a friendly relationship leads to a higher probability for a subject to imitate the neighbor with the highest payoff, whereas a hostile relationship leads to a less probability. Then, we conduct the game on four types of community structure signed networks, a random signed network, and two real-world signed networks. The simulation result indicates that there is a slight difference in the level of cooperation among the four clustering networks. In addition, the most interesting thing is that the negative edges hinder cooperation when the enhancement factor is low and promote the cooperation when the enhancement factor is high on the random signed network.