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.

翻译：当用户依据《通用数据保护条例》（GDPR）及类似法规行使数据删除权时，移动网络运营商面临两难困境：过度执行机器遗忘会降低模型准确率并产生重新训练成本，然而现有的数据留存定价机制要求服务器知晓每位用户的隐私偏好和精度偏好——这恰恰违背了推动遗忘机制的法规精神。我们提出以下问题：在缺乏这类私有信息的情况下运行产生多少社会福利损失？为此，我们设计了一种无信息的递增报价机制：服务器逐步广播递增价格，用户自主选择其数据供给量，且该机制无需知晓用户任何参数。在完全信息条件下，该协议存在以单周期销售为特征的唯一子博弈完美纳什均衡。我们形式化定义了“无知的代价”——即最优个性化定价（知晓全部信息）与本无信息报价机制（不知晓任何信息）之间的福利差距——并证明了其包含三个区域效率排序。通过七种机制与5000次蒙特卡洛模拟的数值评估表明，该代价趋近于零：无信息机制可实现信息密集型基准模型社会福利的≥99%，同时具备噪声鲁棒性保障与可比的公平性。