Quickest Change Detection Using Time Inconsistent Anticipatory and Quantum Decision Modeling

This paper considers quickest detection scheme where the change in an underlying parameter influencing human decisions is to be detected by only observing the human decisions. Stemming from behavioral economics and mathematical psychology, we propose two generative models for the human decision maker. Namely, we consider an anticipatory decision making model and a quantum decision model. From a decision theoretic point of view, anticipatory models are time inconsistent, meaning that Bellman's principle of optimality does not hold. The appropriate formalism is thus the subgame Nash equilibrium. We show that the interaction between anticipatory agents and sequential quickest detection results in unusual (nonconvex) structure of the quickest change detection policy. In contrast the quantum decision model, despite its mathematical complexity, results in the typical convex quickest detection policy. The optimal quickest detection policy is shown to perform strictly worse than classical quickest detection for both models, via a Blackwell dominance argument. The model and structural results provided contribute to an understanding of the dynamics of human-sensor interfacing.