Belief Shaping Through Signaling in Non-Cooperative Multi-Agent Environments

In this talk, we will analyze the interaction between intelligent and selfish agents in non-cooperative environments with a specific focus on the transmission of some private information among them. We will seek to quantify the ability of informed agents to shape the uninformed (rational) agents' beliefs about private information through signals crafted strategically. Due to the versatility of the Gaussian distribution, we will first derive the optimal signaling strategies for Gauss Markov information in dynamic communication settings by formulating an equivalent semi-definite program instead of addressing this problem over the original infinite-dimensional strategy spaces. We will show that the optimal signaling strategies are linear within the general class of measurable policies when the agents have different quadratic cost measures. This formulation brings in the possibility of adopting strategic information transmission in dynamic control systems based on the common theme of communication and control settings. In this context, we will introduce a robust sensor design framework and compute the associated sensor outputs to provide resiliency in linear-quadratic-Gaussian control systems against advanced attackers with malicious and unknown control objectives.

In order to extend these results to distributions other than Gaussian, we will address the problem of optimal hierarchical signaling for a general class of square-integrable multivariate distributions. Again instead of addressing the problem directly over the original strategy spaces, we will formulate an equivalent linear optimization problem over the cone of completely positive matrices when the underlying state space is finite. The ability to compute the optimal signaling strategies for large finite state spaces enables us to address the signaling problem approximately also for continuous distributions, e.g., via quantization of the state space, and we can provide analytical guarantees on the level of accuracy for such approximations.

Joint work with Tamer Başar.