Quadratic privacy-signaling games and the MMSE ınformation bottleneck problem for gaussian sources

Date
2022-05-23
Advisor
Supervisor
Co-Advisor
Co-Supervisor
Instructor
Source Title
IEEE Transactions on Information Theory
Print ISSN
00189448
Electronic ISSN
1557-9654
Publisher
Institute of Electrical and Electronics Engineers Inc.
Volume
68
Issue
9
Pages
6098 - 6113
Language
English
Type
Article
Journal Title
Journal ISSN
Volume Title
Series
Abstract

We investigate a privacy-signaling game problem in which a sender with privacy concerns observes a pair of correlated random vectors which are modeled as jointly Gaussian. The sender aims to hide one of these random vectors and convey the other one whereas the objective of the receiver is to accurately estimate both of the random vectors. We analyze these conflicting objectives in a game theoretic framework with quadratic costs where depending on the commitment conditions (of the sender), we consider Nash or Stackelberg (Bayesian persuasion) equilibria. We show that a payoff dominant Nash equilibrium among all admissible policies is attained by a set of explicitly characterized linear policies. We also show that a payoff dominant Nash equilibrium coincides with a Stackelberg equilibrium. We formulate the information bottleneck problem within our Stackelberg framework under the mean squared error distortion criterion where the information bottleneck setup has a further restriction that only one of the random variables is observed at the sender. We show that this MMSE Gaussian Information Bottleneck Problem admits a linear solution which is explicitly characterized in the paper. We provide explicit conditions on when the optimal solutions, or equilibrium solutions in the Nash setup, are informative or noninformative.

Course
Other identifiers
Book Title
Keywords
Signaling games, Nash equilibrium, Stackelberg equilibrium, Privacy, Estimation, Information bottleneck
Citation
Published Version (Please cite this version)