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

arXiv:2510.07157v5 Announce Type: replace Abstract: Efficient large-scale network allocation requires data-driven pricing mechanisms that internalize stochastic, nonlinear user behavior. We move beyond the classic fully strategic agents to study oblivious users (agents with bounded rationality and imperfect information). Rather than assuming an infinite horizon, our regime acknowledges that real-world flows are too transient to equilibrate among users. We introduce a novel Optimal Network Pricing (ONP) problem for such users, which induces Performativity: a Decision-Dependent environment where pricing decisions endogenously shift the flow distribution. Without a closed-form distribution, the platform must learn optimal prices from sampled responses. This setting introduces a new challenge: capacity boundaries and projection operators make the optimization landscape nonsmooth, invalidating gradient-based methods. We show that a widely adopted optimality concept Performative Stability (PS) fails in ONP, collapsing to a trivial solution. We then define a new optimality concept, the Projected Performative Optimum ({\Pi}PO) for the unique global optimum. Targeting {\Pi}PO is algorithmically hard given the performative nonsmooth Jacobian, so we propose a novel framework combining Sample Average Approximation with Trust-Region Sequential Quadratic Programming, explicitly handling the capacity boundaries, with theoretical guarantees on probabilistic convexity, sample complexity, and computational complexity. Experiments show that our {\Pi}PO solver significantly outperforms PS-seeking heuristics and a proposed baseline (improving social welfare by 81\% on GEANT), highlighting that properly handling capacity boundaries unlocks substantial gains in social welfare. More broadly, this work advances intelligent systems that learn under performative, capacity-constrained feedback, a core challenge in real-world AI applications.