Interactive Bayesian Deception under Strategic Timing

We introduce a novel framework of interactive Bayesian deception understrategictiming, whichintegratesideasfromBayesianpersuasion, sequentialdecision-making, andstochasticchangepointdetection. Hereareceiver(Agent)observesasequenceofsignalstodetect a latent change point in an underlying state of the world. However, unlike standard settings, the sequence is generated strategically by a selfish sender (Principal), who designs the signal distributions, both before and after the change, with the goal of maximizing their own utility, and thereby possibly inducing timing deception. Their utilities may differ and are defined over the true change point and the receiver’s random stopping rule, creating an interactive and coupled dynamic wherein the sender can either align with or mislead the receiver by shaping the observed sequence. We show that, under separable utilities and fixed sender strategy, the receiver’s optimal stopping policy reduces to a simple one-sided threshold test. From the sender’s perspective, the problem becomes a form of dynamic persuasion, albeit under a novel stopping-time-dependent objective, which we characterize in a spirit similar to the classic work of Kamenica and Gentzkow [AER, 2011]. Our work opens up a new class of dynamic information design problems where strategic timing and deception fundamentally interact.

Authors

• Amitalok J. Budkuley IIT Kharagpur
• Arya Choudhuri IIT Kharagpur

Keywords

• Interactivedeception
• Changepointdetection
• Sequentialinference
• Random stopping time
• Persuasion