Optimal Network Pricing for Oblivious Users under Projected Decision-Dependent Distributions
For network operators designing pricing mechanisms, this work provides a theoretically grounded and computationally efficient approach to handle user behavior dynamics, outperforming existing heuristics.
The paper introduces an Optimal Network Pricing (ONP) problem for oblivious users under decision-dependent distributions, showing that performative stability fails and proposing a Projected Performative Optimum (ΠPO) with a trust-region SQP solver. Experiments on Braess and real-world networks demonstrate significant social welfare gains over baselines.
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 (ΠPO). 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 ΠPO 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 ΠPO-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.