二次隐私信号博弈与高斯信源的MMSE信息瓶颈问题
Quadratic Privacy-Signaling Games and the MMSE Information Bottleneck Problem for Gaussian Sources
摘要：
我们研究了一个隐私信号博弈问题，在这个博弈中，一个有隐私问题的发送者观察到一对被建模为联合高斯的相关随机向量。发送方的目标是隐藏这些随机向量中的一个并传送另一个，而接收方的目标是准确地估计这两个随机向量。我们分析这些相互冲突的目标，在一个博弈论的框架与二次成本取决于承诺条件（发送者），我们认为纳什或Stackelberg（贝叶斯说服）均衡。我们证明了在所有可允许的策略中，一个支付占优的纳什均衡是由一组明确刻画的线性策略得到的。我们还表明，一个收益占主导地位的纳什均衡与斯塔克尔伯格均衡。我们制定我们的Stackelberg框架下的均方误差失真准则的信息瓶颈问题，其中的信息瓶颈设置有一个进一步的限制，只有一个随机变量在发送端观察。我们表明，这个MMSE高斯信息瓶颈问题承认一个线性的解决方案，这是明确的特点，在文件中。我们提供了明确的条件时，最优解，或均衡解的纳什设置，是信息或非信息。
英文摘要：
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.
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