提出新框架，让本地模型更理性地匿名文本，避免隐私泄露与信息损失。

Current LLM-based frameworks for text anonymization usually rely on remote API services from powerful LLMs, which creates an inherent privacy paradox: users must disclose the raw data to untrusted third parties for guaranteed privacy preservation. Moreover, directly migrating current solutions to local small-scale models (LSMs) offers a suboptimal solution with severe utility collapse. Our work argues that this failure stems not merely from the capability deficits of LSMs, but significantly from the inherent irrationality of the greedy adversarial strategies employed by current state-of-the-art (SOTA) methods. To address this drawback, we propose Rational Localized Adversarial Anonymization (RLAA), a fully localized and training-free framework featuring an Attacker-Arbitrator-Anonymizer architecture. We model the anonymization process as a trade-off between Marginal Privacy Gain (MPG) and Marginal Utility Cost (MUC), demonstrating that greedy strategies tend to drift into an irrational state. Instead, RLAA introduces an arbitrator that acts as a rationality gatekeeper, validating the attacker's inference to filter out ghost leaks. This mechanism promotes a rational early-stopping criterion, and structurally prevents utility collapse. Extensive experiments on different benchmarks demonstrate that RLAA achieves a superior privacy-utility trade-off compared to strong baselines.