A Game Theoretical Analysis on the Gray-Wyner System and Generalised Common Information

TL;DR

This paper explores the common information problem in a generalized Gray-Wyner network, analyzing risks of information leakage in a control system and proposing a game-theoretic approach with simulations validating the scheme.

Contribution

It introduces a novel game-theoretic framework for the Gray-Wyner problem, addressing information security risks in networked control systems.

Findings

Existence of Nash equilibrium proven.

Information-theoretic relaxations characterized.

Simulation results validate the proposed scheme.

Abstract

We analyse the common information problem for the generalised Gray-Wyner problem. We aim to explore the problem and solution in relation to the non-orthogonality among the source decoders' components. We consider a simple networked control system consisting of 2 groups of users: (i) one sender or Observer named Alice; and (ii) a group of multiple receivers or Controllers, named Bobs. In order to tackle the possible risk arisen from the common information among Bobs, Alice provides a redundancy creating some virtual messages which are in the null of each specific Bob, but not for others. The aforementioned possible risk is inevitable since, non-impossibly speaking, some/all of them may instantaneously act as potential Eavesdropper(s) with the abuse of the aforementioned common information. This novel discipline, which has not been investigated yet to the best of our knowledge, is theoretically interpreted from a mirror-game-theoretical point-of-view. Novel mathematical problems are derived specifically including some proofs for the information-theoretic relaxations and non-stationarity as well as the existence of the Nash equiblirium. Finally speaking, simulations approve our scheme.