Repeated games for privacy-aware distributed state estimation in interconnected networks

The conflict between cooperation in distributed state estimation and the resulting leakage of private state information (competitive privacy) is studied for a system composed of two interconnected agents. The distributed state estimation problem is studied using an information theoretic rate-distortion-leakage tradeoff model and a repeated non-cooperative game framework. The objective is to investigate the conditions under which the repetition of the agents' interaction enables data sharing among the agents beyond the minimum requirement. In the finite horizon case, similarly to the one-shot interaction, data sharing beyond the minimum requirement is not a credible commitment for either of the agents. However, non-trivial mutual data sharing is sustainable in the long term, i.e., in the infinite horizon case.

I. Introduction

Classical state estimation requires a central coordinator that estimates the state using measurements from all the nodes in the network. Several distributed approaches to this problem have been considered [1] [2]. However, these approaches are essentially based on two-tier hierarchical models in which each local node estimates independently, and then, at a higher level, a central coordinator receives the estimation results from the individual areas and coordinates them to obtain a system-wide solution. However, this model does not scale with increasing measurement rates due to communication and reliability challenges inherent in systems with one coordination center. This requirement of estimating the state precisely and often is driving the need for a fully distributed approach wherein the local control centers interactively estimate the system state as a whole.