Optimal Network Pricing for Oblivious Users under Projected Decision-Dependent Distributions

Efficient large-scale network allocation requires pricing mechanisms that internalize the stochastic and non-linear dynamics of user behavior. Moving beyond classical models of strategic agents, we introduce an Optimal Network Pricing (ONP) problem for ``oblivious'' users. This shift introduces a Decision-Dependent (DD) environment where pricing decisions endogenously shift the flow demand distribution. A key novelty of our model is the incorporation of a projection operator, creating a nonsmooth optimization landscape. We demonstrate that Performative Stability (PS) fails in ONP, degenerating to a trivial solution. Instead, we prove that the expected objective admits a unique global optimum, termed the Projected Performative Optimum ({\Pi}PO). To overcome the algorithmic challenges, we propose a rigorous framework combining Sample Average Approximation (SAA) with a Trust-Region Sequential Quadratic Programming (TR-SQP) solver. Our method targets {\Pi}PO by explicitly modeling the nonsmooth Jacobian, effectively handling saturation constraints. We establish theoretical guarantees for probabilistic convexity and sample complexity, and exploit network sparsity to reduce per-iteration computational complexity to near-linear in the number of routes. Experimental validation on the classic Braess network and large-scale real-world topologies demonstrates that our {\Pi}PO-targeting solver significantly outperforms PS-seeking heuristics and our proposed baseline. The results highlight that properly accounting for the ``gating'' effects of capacity unlocks substantial gains in social welfare, providing a robust foundation for network pricing.