Effects of strategy-relationship coevolution on the emergence of cooperation in multilayer networks

Abstract

Since social interactions are inherently embedded in multiple relational contexts, single-network models often fall short in explaining the evolution of cooperation. This study develop a two-layer coevolutionary model where behavioral strategies in the upper interaction layer are coupled with the lower signed emotional layer, representing friendly or hostile ties. The framework of this study allows behavioral strategies, emotional attitudes, and the network structure to coevolve dynamically. It found that the dynamics of the emotional layer influence the evolutionary outcomes. Counterintuitively, a relatively low cross-layer coupling strength proves more favorable for sustaining cooperation. It also showed that stochasticity is crucial for breaking the monostability of the defection-dominated state. It provides the necessary conditions for the system to enter another stable cooperative state or mixed strategy, effectively leading to the existence of system bistability. In the end, although the evolution of emotions changes the distribution of the final probability of cooperation, it is more like a regulator of cooperation frequency and cannot significantly improve the overall level of cooperation. This highlights how the constantly evolving relationship environment affects the trajectory of social cooperation.