Hierarchical Multi-stage Gaussian Signaling Games: Strategic Communication and Control

We analyze in this paper finite horizon hierarchical signaling games between informed senders and decision maker receivers in a dynamic environment. The underlying information evolves in time while sender and receiver interact repeatedly. Different from the classical communication models, however, the sender and the receiver have different objectives and there is a hierarchy between the players such that the sender leads the game by announcing his policies beforehand. He needs to anticipate the reaction of the receiver and the impact of the actions on the horizon while controlling the transparency of the disclosed information at each interaction. With quadratic objective functions and stationary multi-variate Gaussian processes, evolving according to first order auto-regressive models, we show that memoryless linear sender policies are optimal (in the sense of game-theoretic hierarchical equilibrium) within the general class of policies.