Re-identification methods serve as a concrete instantiation of the Motivated Intruder Test in privacy-preserving problems, and current state-of-the-art attack techniques are predominantly built upon Large Language Models (LLMs) which are also core components of robust pseudonymized methods. Therefore, it requires the rich training dataset. However, as research demands continue to grow while publicly available data for each domain remains limited and the cost of direct human supervision is high, a central question arises: how can a human-in-the-loop approach be integrated to generate high-quality data and improve the performance of LLMs in psedonymization. To address this limitation, we propose MOTIGAN1 - a gamified framework that transforms the motivated intruder test into a competitive three population tournament. In this game, human characters and AI characters compete to re-identify individuals from each essay. At every stage, players both commit their guesses and contribute to enriching the synthesized dataset. In our experiments, the synthesized dataset contributes to improving the performance of multiple models in several experiments (achieving up to 37.6% improvement on a well-established benchmark).