Endogenous Stabilization in Directed Production Networks: An Optimal Control Model with Stochastic Capacity Constraints

This paper develops a stochastic network-control framework for analyzing structural growth transitions in directed production economies subject to congestion constraints. The economy is modeled as a dynamically evolving weighted production network in which inter-firm linkages generate amplification effects, while infrastructure capacity imposes nonlinear attenuation through congestion. The interaction between network propagation and capacity geometry determines an effective amplification index that governs transitional stability. We show that sustained structural upgrading requires keeping amplification below a critical stability threshold. When propagation dominates attenuation, stochastic shocks spread through the network and throughput stagnates. When capacity expansion anticipates network deepening, attenuation dominates propagation, producing a smooth phase transition toward a high-productivity regime. This shift can be summarized by a macroeconomic order parameter capturing the move from amplification-dominated to attenuation-dominated dynamics. Formulated as a finite-horizon stochastic control problem with endogenous network evolution, Monte Carlo simulations confirm the existence of a stabilization threshold and quantify the volatility-reducing role of anticipatory infrastructure expansion.