Title: Detecting and Deterring Manipulation in a Cognitive Hierarchy

Abstract: Social agents with finitely nested opponent models are vulnerable to manipulation by agents with deeper reasoning and more sophisticated opponent modelling. This imbalance, rooted in logic and the theory of recursive modelling frameworks, cannot be solved directly. We propose a computational framework, $\aleph$-IPOMDP, augmenting model-based RL agents' Bayesian inference with an anomaly detection algorithm and an out-of-belief policy. Our mechanism allows agents to realize they are being deceived, even if they cannot understand how, and to deter opponents via a credible threat. We test this framework in both a mixed-motive and zero-sum game. Our results show the $\aleph$ mechanism's effectiveness, leading to more equitable outcomes and less exploitation by more sophisticated agents. We discuss implications for AI safety, cybersecurity, cognitive science, and psychiatry.