Privacy-Aware Stochastic Control with a "Snoopy" Adversary: A Game-Theoretic Approach

We consider a scenario in which a controller and an adversary dynamically act on a system over a finite or infinite horizon. The controller and the adversary do not want to reveal their actions to each other, and at the same time, the controller acts to minimize an expected cost, and the adversary acts to maximize it. We model this scenario as a dynamic zero-sum game, prove the existence of a unique saddle-point equilibrium, and devise an algorithm to compute the equilibrium for finite and infinite horizon settings.