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Information Concealing Games

机译：信息隐藏游戏

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摘要

A system with an $n$-dimensional state vector and a controller and an actor is considered. The controller has complete information about the system state, and reveals a certain “minimum” amount of information to the actor. The actor takes certain actions based on the information the controller reveals, and the actions fetch certain utilities for each entity. Both the controller and actor seek to maximize their individual utilities by respectively selecting the information to reveal and the actions to adopt. This decision problem forms the basis of several technical and social systems, and can be formulated as a signaling game. It is shown that the Perfect Bayesian Equilibrium of this game has several counterintuitive properties and can be obtained as a saddle point of a different two person zero sum game. The computation time for saddle points using standard linear programs however turns out to be superexponential in $n$, which leads to computational intractability even for moderate $n$. Algorithms for computing saddle point policies using a computation time that is exponential in $n$ are presented. Finally, simple linear time computable policies that approximate the saddle-point policies within guaranteeable approximation ratios are obtained.
机译：考虑一个具有$ n $维状态向量以及一个控制器和一个参与者的系统。控制器具有有关系统状态的完整信息，并向参与者显示一定量的“最少”信息。参与者根据控制器显示的信息采取某些措施，并且这些措施为每个实体获取某些实用程序。控制器和参与者都试图通过分别选择要显示的信息和要采取的动作来最大化其各自的效用。这个决策问题构成了一些技术和社会系统的基础，可以被表述为一个信号游戏。结果表明，该博弈的完美贝叶斯均衡具有若干违反直觉的特性，可以作为不同的两人零和博弈的鞍点获得。但是，使用标准线性程序对鞍点的计算时间竟然是$ n $的指数级，即使对于中等$ n $，这也导致了计算难点。提出了使用$ n $的指数计算时间来计算鞍点策略的算法。最后，获得了在可保证的近似比率内近似鞍点策略的简单线性时间可计算策略。

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