  We analyze in this paper finite horizon hierarchical signaling games between
(information provider) 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
(control) models, however, the sender (sensor) and the receiver (controller)
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 cost functions and multivariate Gaussian processes,
evolving according to first order auto-regressive models, we show that
memoryless "linear" sender signaling rules are optimal (in the sense of
game-theoretic hierarchical equilibrium) within the general class of measurable
policies in the noncooperative communication context. In the noncooperative
control context, we also analyze the hierarchical equilibrium for linear
signaling rules and provide an algorithm to compute the optimal linear
signaling rules numerically with global optimality guarantees.
