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

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      Author(s)
      Kazıklı, E.
      Gezici, Sinan
      Yüksel, S.
      Date
      2022-05-23
      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
      Item Usage Stats
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      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.
      Keywords
      Signaling games
      Nash equilibrium
      Stackelberg equilibrium
      Privacy
      Estimation
      Information bottleneck
      Permalink
      http://hdl.handle.net/11693/111315
      Published Version (Please cite this version)
      https://www.doi.org/10.1109/TIT.2022.3177258
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      • Department of Electrical and Electronics Engineering 4011
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