Modeling Coprolalia as a Bipartite Matching and Potential Game With Learning Dynamics

Coprolalia, a prominent symptom of Tourette’s syndrome, is characterized by the involuntary utterance of obscene or socially inappropriate words, often contextually associated with local or sexual references. This symptom frequently leads to social isolation, heightened anxiety, and behavioral withdrawal, severely impacting patients’ quality of life. In this work, we propose a novel computational framework to model and analyze the mechanisms underlying Coprolalia. First, we employ a bipartite graph matching formulation to represent the cognitive rerouting of thoughts, whereby benign thoughts are misassociated with intrusive, obscene counterparts. This abstraction provides a structural perspective for decoding the underlying neural operations responsible for the manifestation of Coprolalia. Building upon this foundation, we introduce a game-theoretic model inspired by the Battle of the Sexes paradigm, capturing the strategic interplay between suppressing and expressing intrusive thoughts. The model considers two pure-strategy equilibria: (i) actively jamming intrusive coprolalic thoughts, and (ii) allowing the thoughts to pass through, aligning with therapeutic approaches such as Cognitive Behavioral Therapy (CBT). To enhance clinical interpretability, we extend the model into a multi-stage repeated game framework with adaptive learning dynamics. Players iteratively update their strategies via fictitious play and Q-learning algorithms, adjusting their responses based on reinforcement signals and past outcomes. Furthermore, we incorporate a strategy entropy analysis to quantify the uncertainty and instability in the neural decision-making process, highlighting the balance between exploration and convergence in symptom regulation. This integrative framework not only advances the theoretical understanding of Coprolalia but also offers actionable insights for therapeutic interventions, particularly by identifying conditions under which adaptive neural strategies can promote social reintegration and improved quality of life.