Deceptive Multi-dimensional Information Disclosure over a Gaussian Channel

We analyze deceptive multi-dimensional information disclosure over a channel between an information provider and a decision maker. The information provider has access to noisy versions of an underlying information. Different from the classical communication models, the provider has a different (hidden) objective while he/she must still honestly and transparently provide the information for his/her reputation. However, how well the provider has access to the information is private to him/her. We address how he/she can exploit this asymmetry according to his/her deceptive goal by modeling the interaction as a Stackelberg game, where the information provider is the leader. With quadratic objective functions, multi-variate Gaussian information and additive Gaussian noise channel, we analytically formulate the optimal linear deception strategy and the corresponding optimal decision strategy.