TOWARDS A MATHEMATICAL PSYCHIATRY – GAME THEORY MODELING OF OCD

  Purpose: Obsessive Compulsive Disorder (OCD), with a lifetime prevalence of 1.9% - 2.5% worldwide, causes considerable suffering. Compulsive repetition is a debilitating symptom in OCD. Neither Psychoanalysis nor Biological Psychiatry developed a satisfactory explanatory model for OCD, making it difficult to treat. We are the first to explore these 'irrational' behaviors by combining an information processing approach with Rational Choice Theory.  

  Method: We fit a set of rational choice models to the phenomenology described in the OCD literature. Each model assumes the OCD agent has already checked N times that, for example, the door is locked, in an attempt to avoid some catastrophic expected loss, i.e. U(open) << 0. We then focus on the marginal utility, to the agent, of deciding to check again, i.e. the N+1 time.

  Results: 1) In the Expected Utility Model with Bayesian Updating each checking event has a specificity and sensitivity (ROC analysis). The checking event thus updates the Bayesian prior probability, P(open | N checks) to the Bayesian posterior, P(open | N+1 checks), and thus also incrementally reduces the expected loss. The indifference point predicts that the agent will rationally continue to check until the next reduction in expected loss is equal to the (low) cost of another checking event, i.e. it predicts many repetitions without recourse to “irrationality”. 2) In the Markov Chain Stochastic Updating model there is no dynamically changing  probability estimates. Rather each check is memory-less and acts as a rational lottery with a small probability of getting all the information i.e. of being “sure” that risk has been reduced entirely. This model squares with phenomenological accounts of OCD, and predicts checking sequence lengths consistent with clinical observation. 3) The Regulatory Self-Signaling Game relies on Regret Theory to postulate that the factor most dreaded in OCD is not the catastrophic loss, but the sense of having been personally responsible. Repeated checking can then be formally modeled as a game having a Nash equilibrium in which one sends a costly, inter-temporal signal to a later self, to convey that due diligence was taken, and no regret punishment is warranted.

  Conclusion: These models may throw further light on the functioning of the mind in its normal and pathological dealings with perceived risk, and may inform future OCD treatments.