Personalized Belief-Action Game Data Augmentation: Three-Dimensional Evaluation and RAGDA

Given a limited participant-specific history, effective belief-action augmentation should preserve history-conditioned responses and belief–action relationships beyond marginal behavior. We therefore evaluate this task along three dimensions: history–response compatibility, model-relative belief–action consistency, and synthetic substitution utility. To preserve these structures, we propose RAGDA, a retrieval-based framework that uses an LLM to author and verify retrieval programs offline and learns their combination from training data. During generation, RAGDA retrieves an admissible historical case from the same participant and reuses its paired belief–action record. Across two datasets from game-theoretic experiments, RAGDA outperforms seven generators on all history-response compatibility and model-relative belief-action consistency metrics. Under fixed-budget substitution with replacement probability, it reduces held-out prediction errors on both ooExp26c tasks and incurs the smallest degradation on BiRG-finite. These results demonstrate RAGDA's ability to preserve personalized behavioral structure during synthetic substitution.