When users exercise data deletion rights under the General Data Protection Regulation (GDPR) and similar regulations, mobile network operators face a tradeoff: excessive machine unlearning degrades model accuracy and incurs retraining costs, yet existing pricing mechanisms for data retention require the server to know every user's private privacy and accuracy preferences, which is infeasible under the very regulations that motivate unlearning. We ask: what is the welfare cost of operating without this private information? We design an information-free ascending quotation mechanism where the server broadcasts progressively higher prices and users self-select their data supply, requiring no knowledge of users' parameters. Under complete information, the protocol admits a unique subgame-perfect Nash equilibrium characterized by single-period selling. We formalize the Price of Ignorance -- the welfare gap between optimal personalized pricing (which knows everything) and our information-free quotation (which knows nothing) -- and prove a three-regime efficiency ordering. Numerical evaluation across seven mechanisms and 5000 Monte Carlo runs shows that this price is near zero: the information-free mechanism achieves >=99% of the welfare of its information-intensive benchmarks, while providing noise-robust guarantees and comparable fairness.

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