Hierarchical Multistage Gaussian Signaling Games in Noncooperative Communication and Control Systems

TL;DR

This paper studies hierarchical Gaussian signaling games over finite horizons where senders and receivers with different goals interact repeatedly, revealing that linear signaling rules are optimal under certain conditions and providing algorithms for their computation.

Contribution

It introduces a hierarchical game model with Gaussian processes, demonstrating the optimality of linear signaling rules and offering a numerical method with guarantees for computing these rules.

Findings

Memoryless linear signaling rules are optimal in the hierarchical equilibrium.

The model applies to both communication and control contexts with Gaussian processes.

An algorithm with global optimality guarantees for computing linear signaling rules is provided.

Abstract

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.