Detection in Human-sensor Systems under Quantum Prospect Theory using Bayesian Persuasion Frameworks

Human-sensor systems have a variety of applications in robotics, healthcare and finance. Sensors observe the true state of nature and produce strategically designed signals to help human arrive at more accurate decisions of the state of nature. We formulate the human-sensor system into Bayesian persuasion framework consolidated into prospect theories and construct a detection scheme where human wants to find out the true state by observing the realization of quantum states from the sensor. We obtain the optimal signaling rule for the sensor and optimal decision rule for the human receiver and verify that the total law of probability is violated in this scenario. We also illustrate how the concept of rationality influences human's detection performance and also the sender's signaling rules.