Social influence preserves cooperative strategies in the conditional cooperator public goods game on a multiplex network

Numerous empirical studies show that when people play social dilemma games in the laboratory they often cooperate conditionally, and the frequency of conditional cooperators differs between communities. However, this has not yet been fully- explained by social dilemma models in structured populations. Here we model a population as a two-layer multiplex network, where the two layers represent economic and social interactions respectively. Players play a conditional public goods game on the economic layer, their donations to the public good dependent on the donations of their neighbours, and player strategies evolve through a combination of payoff comparison and social influence. We find that both conditional cooperation and social influence lead to increased cooperation in the public goods game, with social influence being the dominant factor. Cooperation is more prevalent both because conditional cooperators are less easily exploited by free-riders than unconditional cooperators, and also because social influence tends to preserve strategies over time. Interestingly the choice of social imitation rule does not appear to be important: it is rather the separation of strategy imitation from payoff comparison that matters. Our results highlight the importance of social influence in maintaining cooperative behaviour across populations, and suggest that social behaviour is more important than economic incentives for the maintenance of cooperation