On the Tension Between Stability and Efficiency in Two-Way Flow Network with Small Decay

The tension between stability and efficiency in network formation models refers to a common finding in the literature of social networks: equilibrium networks and efficient networks often exhibit substantially different characteristics.In this note, I show that this tension can be partially reconciled in the two-way flow model of network formation with partner heterogeneity by introducing a small degree of information decay.This result extends a similar finding established for homogeneous agents in Charoensook (2025).Thus, this note contributes to the literature by demonstrating that the reconciliation of stability and efficiency through a small decay assumption is not confined to models with agent homogeneity but also holds in more general network settings.