Information Concealing Games

Saswati Sarkar, Eitan Altman, Pramod Vaidyanathan
2010 IEEE Transactions on Information Theory  
We consider a system whose state is a vector of dimension n, whose value is chosen randomly by nature. The system consists of two entities. The first entity (controller) has complete information about the state of the system, and must reveal a certain "minimum" amount of information about the system state to the second entity. It can however choose the nature of the information it reveals subject to satisfying the above constraint. The second entity (actor) takes certain actions based on the
more » ... ons based on the information the controller reveals, and the actions are associated with certain utilities for both the controller and the actor which also depend on the state of the system. The controller needs to decide the information it would reveal, or equivalently conceal, so as to maximize its own utility, and the actor needs to determine its actions based on the information the controller reveals so as to again maximize its utility. We demonstrate that the above problem forms the basis of several technical and social systems. We show that the decision problems for the entities can be formulated as a signaling game. The Perfect Bayesian Equilibrium (PBE) for this game exhibits several counter intuitive properties, e.g., some intuitively appealing greedy policies for the controller and the actor turn out to be suboptimal. We prove that the PBE of this game can be obtained as a saddle point of a different two person zero sum game. The number of policies of the players in this two person zero sum game is however superexponential in n, which implies that standard linear programs for obtaining its saddle points will be computationally intractable even for moderate n. Next, using specific characteristics of the problem, we develop linear programs that compute the optimal policies using a computation time that increases exponentially with n, and can therefore be numerically solved for moderate n. We finally propose simple linear time computable policies that approximate the optimal policies within guaranteeable approximation ratios. S. Sarkar is with the
doi:10.1109/tit.2010.2053899 fatcat:eoantoqqivfd5gks66dymdmlze