Quickest Change Detection With Time Inconsistent Anticipatory Agents In Cyber-Physical Systems

In behavioral economics, anticipatory agents make decisions by taking into account the probability of future decisions (plans). We consider the interaction between anticipatory agents and statistical detection. A sensing device records the decisions of an anticipatory agent. Given these decisions, how can the sensing device achieve quickest detection of a change in the anticipatory system? 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 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. Our methodology yields a useful framework for anticipatory human decision makers interacting with sequential detectors in cyber-physical systems.