Quadratic Privacy-Signaling Games and the MMSE Information Bottleneck Problem for Gaussian Sources

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