Strategy evolution on interdependent networks

Cooperation is essential to the prosperity of human and biological systems. Its emergence depends on not only on the structure of interactions within a single system but also the coupling between interdependent systems. While the analytical theory for strategy evolution in isolated systems is well established, the effect of coupling has been studied mainly through specific models and simulations. Here, we develop a general analytical framework for strategy evolution on interdependent networks with arbitrary within-system structures and cross-system coupling. We derive the explicit condition under which natural selection favors cooperation and show that coupling can promote cooperation even when no isolated system sustains it. Cooperation is maximized under weak but non-zero coupling, while excessively strong interdependence suppresses it. Cooperation is further enhanced when strategy updating is biased toward the larger or less cooperation-prone system. Our analysis explains when and why coupling promotes cooperation.