Spillover modes in multiplex games: double-edged effects on cooperation and their coevolution

In recent years, there has been growing interest in studying games on multiplex networks that account for interactions across linked social contexts. However, little is known about how potential cross-context interference, or spillover, of individual behavioural strategy impact overall cooperation. We consider three plausible spillover modes, quantifying and comparing their effects on the evolution of cooperation. In our model, social interactions take place on two network layers: repeated interactions with close neighbours in a lattice, and one-shot interactions with random individuals. Spillover can occur during the learning process with accidental cross-layer strategy transfer, or during social interactions with errors in implementation. Our analytical results, using extended pair approximation, are in good agreement with extensive simulations. We find double-edged effects of spillover: increasing the intensity of spillover can promote cooperation provided cooperation is favoured in one layer, but too much spillover is detrimental. We also discover a bistability phenomenon: spillover hinders or promotes cooperation depending on initial frequencies of cooperation in each layer. Furthermore, comparing strategy combinations emerging in each spillover mode provides good indication of their co-evolutionary dynamics with cooperation. Our results make testable predictions that inspire future research, and sheds light on human cooperation across social domains.