Evolutionary game theory in the realm of network science appeals to a lot of research communities, as it constitutes a popular theoretical framework for studying the evolution of cooperation in social dilemmas. Recent research has shown that cooperation is markedly more resistant in interdependent networks, where traditional network reciprocity can be further enhanced due to various forms of interdependence between different network layers. However, the role of mobility in interdependent networks is yet to gain its well-deserved attention. Here we consider an interdependent network model, where individuals in each layer follow different evolutionary games, and where each player is considered as a mobile agent that can move locally inside its own layer to improve its fitness. Probabilistically, we also consider an imitation possibility from a neighbor on the other layer. We show that, by considering migration and stochastic imitation, further fascinating gateways to cooperation on interdependent networks can be observed. Notably, cooperation can be promoted on both layers, even if cooperation without interdependence would be improbable on one of the layers due to adverse conditions. Our results provide a rationale for engineering better social systems at the interface of networks and human decision making under testing dilemmas.

The emergence and persistence of cooperation among selfish individuals remain one of the most significant challenges that continues to intrigue scientists across various research fields. Evolutionary game theory has become a key tool in these studies, providing a robust theoretical framework to describe the evolutionary dynamics of strategies in social dilemmas. Simultaneously, advances in network science have significantly enhanced our understanding of numerous complex systems in the real world, including the development of cooperation in group decision-making and collective actions. A critical factor in this context is how individuals are embedded within society. Research over the past decades has showed that social network structure critically impacts cooperation. Moreover, as individuals are often mobile in most real-world scenarios, mobility and population mixing also play a crucial role in the evolution of cooperation. The primary aim of our study was to examine how different interaction networks and player mixing influence the evolution of cooperation in the public goods game.